# Can we observe changes in the CMB (surface of last scattering) over time?

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It is hard to determine the age of the Sun, because it won't change much over 100 million years or so. But what about the cosmic microwave background radiation, that is being mapped with ever better precision. It dates to only about 380 000 years after Big Bang. Is it possible to observe changes in it over a period of 10 years or 100 years, as it ages and cools, as the Hubble Bubble expands?

And how is the landscape of the CMB-map expected to change? Are relatively cool and hot areas permanent over time scale much larger than 380 000 years, or would our CMB-map be unrecognizable if we had lived, say, a billion years earlier or later?

It isn't all that hard to determine the age of the sun, provided you are content with an accuracy of 100 million years or so either way. The radiometric dating of zircon crystals, which are only a little younger than the sun, gives a date of about 4.6 billion years, and it is generally agreed that the sun is about 5 billion years old. This is compatible with its position in the main sequence of a Hertzsprung-Russell diagram. You certainly wouldn't notice any change on the CMB map in a mere ten years, but a billion years hence it will have a noticeably greater red shift, except for the fact that there will be nobody here to notice or record it. Our descendants, every last one of them, will all have gone to meet their maker in far less than a billion years.

## CMB Polarization

The Cosmic Microwave Background (CMB) is a relic radiation field that we observe in all directions at a uniform temperature of 3 Kelvin. This light last scattered during a hot and dense stage of the early universe, just as it was transitioning from ionized plasma to neutral gas. The discovery of the Cosmic Microwave Background by Penzias and Wilson in 1964 was a striking confirmation of the Big Bang theory, providing direct evidence of an early hot epoch.

Since its discovery, the CMB has been a crucial source of information about our universe. Numerous experiments have made increasingly detailed maps of the CMB temperature field, with accelerating progress over the last two decades since COBE reported the first detection of temperature anisotropies. Recently, the Planck satellite has produced extremely high signal-to-noise maps of the CMB temperature across the entire sky, while the South Pole Telescope and Atacama Cosmology Telescope have mapped smaller fields at arcminute resolution.

3K and the first stars appear significantly hotter (but they are not bright enough to see them in such a large distance with current telescopes).

30000 years) had no way to interact with the light any more (apart from the transition in its hyperfine structure, but that gives an extremely large wavelength) . Atomic hydrogen at 2000K does not glow like a metal would, for example. It is just transparent.

Yes, I mean 'bubble' as the sphere forming the surface of last scattering.

Thanks for the reply, so if I understand well it just happens that hydrogen at 3000 K (at that time) radiates enough so we can still see the glow (today looking like at 3 K due to redshift) but as soon as it cooled down below the 3000 K, say when it was at 2500 K it did not radiate anymore at any level which can be detectable today. So the CMB was like some 'instant flash of light' sandwiched by 'darkness' (= opacity) before and darkness (no emission of any detectable radiation) immediately after (lasting for millions of years until the first stars started to burn). Right?

Yes, I mean 'bubble' as the sphere forming the surface of last scattering.

Thanks for the reply, so if I understand well it just happens that hydrogen at 3000 K (at that time) radiates enough so we can still see the glow (today looking like at 3 K due to redshift) but as soon as it cooled down below the 3000 K, say when it was at 2500 K it did not radiate anymore at any level which can be detectable today. So the CMB was like some 'instant flash of light' sandwiched by 'darkness' (= opacity) before and darkness (no emission of any detectable radiation) immediately after (lasting for millions of years until the first stars started to burn). Right?

if it's hot enough to glow, it's hot enough to scatter
if it's not hot enough to scatter, it's not hot enough to glow.
absorbing and (re-) radiating are the same process just reverses of each other

so the surface of a star appears like a crisp transition because above it the gas is transparent and you can't see what's below because the surface is glowing, how else could it be?

the surface of a star is like a miniature "surface of last scattering"

I'm oversimplifying but I'm saying that it's not dreadfully surprising that CMB is a one-time flash.It's a tautology--kind of has to be that way.

That's more or less right. The transition of the plasma in the early universe to a gas wasn't instantaneous. This has the effect of blurring our image of the CMB, meaning that shorter wavelengths are suppressed by this effect. This can be seen directly in the CMB power spectrum:
http://lambda.gsfc.nasa.gov/product. s/nineyear/cosmology/images/med/gh9_f01_M.png

The shorter wavelengths are to the right. If the cooling of the CMB was instantaneous, then the even and odd peaks would have different heights, but the third, fifth, seventh, etc. peaks would all be as high as the first, and the fourth, sixth, etc. peaks would all be as high as the second.

Instead, the power tapers off pretty strongly as you get to shorter and shorter wavelengths.

So the transition happened fast enough that it isn't blurred out entirely, but slow enough that we can see the effect very strongly in the data. One thing to bear in mind is that the transition from a plasma to a gas is a phase transition: by the time the gas was at 1500K, it was not a plasma at all, and quite transparent.

There's a huge difference between an ideal black body and an ideal transparent body. An ideal black body radiates electromagnetically as a function of its temperature, per Planck's law. An ideal transparent body doesn't radiate according to Planck's law. It don't radiate, period.

While there is no such thing in nature as an ideal black body or an ideal transparent body, the early and current universe are pretty close to those two opposing ideals. The transition from opaque to transparent, while not instantaneous, was quite short in duration.

This gives an answer to the question posed in the title of this thread, "What is 'in front' of the CMB?". By looking "in front" of the CMB we are looking at some point in time after recombination. What we would see is a transparent warm gas if we could see it. We cannot see that transparent warm gas precisely because it's transparent.

That's more or less right. The transition of the plasma in the early universe to a gas wasn't instantaneous. This has the effect of blurring our image of the CMB, meaning that shorter wavelengths are suppressed by this effect. This can be seen directly in the CMB power spectrum:
http://lambda.gsfc.nasa.gov/product. s/nineyear/cosmology/images/med/gh9_f01_M.png

The shorter wavelengths are to the right. If the cooling of the CMB was instantaneous, then the even and odd peaks would have different heights, but the third, fifth, seventh, etc. peaks would all be as high as the first, and the fourth, sixth, etc. peaks would all be as high as the second.

Instead, the power tapers off pretty strongly as you get to shorter and shorter wavelengths.

So the transition happened fast enough that it isn't blurred out entirely, but slow enough that we can see the effect very strongly in the data. One thing to bear in mind is that the transition from a plasma to a gas is a phase transition: by the time the gas was at 1500K, it was not a plasma at all, and quite transparent.

Chalnoth posted a CMB power spectrum:

How does one interpret that plot relative to the usual 'ideal black body spectrum' of the CMBR??

The usual plot I see is like this: [Intensity versus frequency]

This plot is a plot that is purely showing the temperature differences at different places on the sky. It isn't about the wavelengths of the photons, but about the wavelengths of the sound waves in the early universe.

The CMB power spectrum is a visualization of these sound waves (specifically, the average amplitude of sound waves of various wavelengths), and has nothing to do with the black body spectrum.

The way to reconcile the two spectra is that at each point in the sky, the CMB photons at that point have a black body spectrum. At different places in the sky, that black body spectrum is at a slightly higher or slightly lower temperature (the variations are up to around 300 micro-Kelvin, so quite tiny). It is these small differences in temperature that stem from the sound waves in the early universe, and are represented by the CMB power spectrum.

This thread is very appropriate with what I intend to ask (at least for the first two questions), so please allow me to do it even it is an old thread.

From this forum I learned that the CMB radiation we receive today was emitted by primordial plasma when it was at 41 million ly away from our position at that moment. It is this accurate?
If yes, I asked myself what about all radiation emitted by the plasma between this two positions? I suppose all just simple passed us, I mean it hit us in the past and we will never see it again. Right?

The second question is: considering the above answers, how long (from now) we will be able to detect and measure the CMB radiation?

The third question I have about CMB refers to relation between measured temperature of CMB from different location in the sky and the change of our current position relative to the position we had when the measured radiation start to go toward us (let's name this position "Ground zero"). I expected this movement affect the measured values of CMB from different locations on the sky.
I know that the "natural" change of our position was done with too little "speed" compared with expansion "speed", but any motion must been largely affected by the expansion itself because we had 13.7 billion years for that. As we can read here, our motion relative to CMB is 360 +/- 20 kilometers/sec in the direction of constellation Leo. I don't know if we can consider that this was always our motion in respect to CMB, but let suppose it was. So, the Google calculator give for " (360 km / s)*(13.7 billion years) in light years " calculation the 16 451 381.2 light years result. This is almost 16.5 Mly. How much this distance was increased by 13.7 billion years of expansion? I don't know and maybe we will never know for sure. But I think that, consider all this, the distance from our current position and the "Ground Zero" it is large enough to alter the measured values of CMB in such way to see an anisotropy across the sky. And as I know, we actually see that.
So, the third question is: can our "proper" motion (because the complex action of gravity) increased by expansion during a large period be the cause of this anisotropy?

I do understand the question perfectly. The last scattering surface is not just a name given on a whim. Then it depends if you consider 300000 years "early". Do you understand that a mean free path orders of magnitude larger than the size of the observable universe means that scattering are not "constantly happening"? It did happen, but only until the Universe was 300000 years old.

The issue is what Gerinski meant by "primordial" versus emitted "at a later time." It is probably true that Gerinski was confused that expansion of the universe, and recombination of hydrogen, makes the photons able to go farther and farther with time, until they simply don't get absorbed any more at all. That's what Orodruin was answering. I was thinking that perhaps Gerinski had been told that the CMB is the "light from the Big Bang," or some such thing, and he is wondering why any of it is left, given all that absorption and re-emission going on. I'm saying the CMB is what you get after all absorption and re-emission is over, not the original "light from the Big Bang." However, it is certainly true that all this absorption and re-emission had to happen prior to encountering the surface of last scattering, that's what those words mean. So it amounts to guessing what parts of that story is creating the confusion, but we can agree there are two crucial aspects: the CMB is the result of absorption and re-emission, and there was a surface of last interaction long ago and far away. On re-reading the original question, I think perhaps the problem is in the term "scattering", which Gerinski is thinking is different from "absorption and re-emission", whereas no crucial distinction between those terms is relevant here.

What's more, CMB photons have been absorbed in the last 10 billion years, just not most of them. So yes, I agree with you that Gerinski was confused about that, but I still think he is also confused about the fact that the CMB is the result of an absorption and re-emission process, it is not really "primordial" if primordial takes its literal meaning (before history, or "existing at the beginning of time".) The bottom line to my answer was that the CMB is not the primordial light that was present at the beginning of time, it is the result of interactions with matter. That's perfectly correct. I also said that those interactions just happened a long time ago (because the universe has become very rarified), though that part had already been answered. Combining those two elements is crucial to answering the question, because the CMB is not "primordial," though its existence can be traced back to a primordial source.

## Can we observe changes in the CMB (surface of last scattering) over time? - Astronomy

The temperature anisotropy at a point on the sky (, ) can be expressed in the basis of spherical harmonics as

A cosmological model predicts the variance of the am coefficients over an ensemble of universes (or an ensemble of observational points within one universe, if the universe is ergodic). The assumptions of rotational symmetry and Gaussianity allow us to express this ensemble average in terms of the multipoles C as

The predictions of a cosmological model can be expressed in terms of C alone if that model predicts a Gaussian distribution of density perturbations, in which case the am will have mean zero and variance C .

The temperature anisotropies of the CMB detected by COBE are believed to result from inhomogeneities in the distribution of matter at the epoch of recombination. Because Compton scattering is an isotropic process in the electron rest frame, any primordial anisotropies (as opposed to inhomogeneities) should have been smoothed out before decoupling. This lends credence to the interpretation of the observed anisotropies as the result of density perturbations which seeded the formation of galaxies and clusters. The discovery of temperature anisotropies by COBE provides evidence that such density inhomogeneities existed in the early universe, perhaps caused by quantum fluctuations in the scalar field of inflation or by topological defects resulting from a phase transition (see Kamionkowski & Kosowsky, 1999 for a detailed review of inflationary and defect model predictions for CMB anisotropies). Gravitational collapse of these primordial density inhomogeneities appears to have formed the large-scale structures of galaxies, clusters, and superclusters that we observe today.

On large (super-horizon) scales, the anisotropies seen in the CMB are produced by the Sachs-Wolfe effect (Sachs & Wolfe, 1967).

where the first term is the net Doppler shift of the photon due to the relative motion of emitter and observer, which is referred to as the kinematic dipole. This dipole, first observed by Smoot et al. (1977), is much larger than other CMB anisotropies and is believed to reflect the motion of the Earth relative to the average reference frame of the CMB. Most of this motion is due to the peculiar velocity of the Local Group of galaxies. The second term represents the gravitational redshift due to a difference in gravitational potential between the site of photon emission and the observer. The third term is called the Integrated Sachs-Wolfe (ISW) effect and is caused by a non-zero time derivative of the metric along the photon's path of travel due to potential decay, gravitational waves, or non-linear structure evolution (the Rees-Sciama effect). In a matter-dominated universe with scalar density perturbations the integral vanishes on linear scales. This equation gives the redshift from emission to observation, but there is also an intrinsic T / T on the last-scattering surface due to the local density of photons. For adiabatic perturbations, we have (White & Hu, 1997) an intrinsic

Putting the observer at = 0 (the observer's gravitational potential merely adds a constant energy to all CMB photons) this leads to a net Sachs-Wolfe effect of T / T = - / 3 which means that overdensities lead to cold spots in the CMB.

Anisotropy measurements on small angular scales (0.ۡ to 1°) are expected to reveal the so-called first acoustic peak of the CMB power spectrum. This peak in the anisotropy power spectrum corresponds to the scale where acoustic oscillations of the photon-baryon fluid caused by primordial density inhomogeneities are just reaching their maximum amplitude at the surface of last scattering i.e. the sound horizon at recombination. Further acoustic peaks occur at scales that are reaching their second, third, fourth, etc. antinodes of oscillation.

Figure 2 (from Hu et al., 1997) shows the dependence of the CMB anisotropy power spectrum on a number of cosmological parameters. The acoustic oscillations in density (light solid line) are sharp here because they are really being plotted against spatial scales, which are then smoothed as they are projected through the last-scattering surface onto angular scales. The troughs in the density oscillations are filled in by the 90-degree-out-of-phase velocity oscillations (this is a Doppler effect but does not correspond to the net peaks, which are best referred to as acoustic peaks rather than Doppler peaks). The origin of this plot is at a different place for different values of the matter density and the cosmological constant the negative spatial curvature of an open universe makes a given spatial scale correspond to a smaller angular scale. The Integrated Sachs-Wolfe (ISW) effect occurs whenever gravitational potentials decay due to a lack of matter dominance. Hence the early ISW effect occurs just after recombination when the density of radiation is still considerable and serves to broaden the first acoustic peak at scales just larger than the horizon size at recombination. And for a present-day matter density less than critical, there is a late ISW effect that matters on very large angular scales - it is greater in amplitude for open universes than for lambda-dominated because matter domination ends earlier in an open universe for the same value of the matter density today. The late ISW effect should correlate with large-scale structures that are otherwise detectable at z

1, and this allows the CMB to be cross-correlated with observations of the X-ray background to determine (Boughn et al., 1998 Kamionkowski & Kinkhabwala, 1999 Crittenden & Turok, 1996 Kamionkowski, 1996) or with observations of large-scale structure to determine the bias of galaxies (Suginohara et al., 1998).

For a given model, the location of the first acoustic peak can yield information about , the ratio of the density of the universe to the critical density needed to stop its expansion. For adiabatic density perturbations, the first acoustic peak will occur at = 220 -1/2 (Kamionkowski et al., 1994). The ratio of values of the peaks is a robust test of the nature of the density perturbations for adiabatic perturbations these will have ratio 1:2:3:4 whereas for isocurvature perturbations the ratio should be 1:3:5:7 (Hu & White, 1996). A mixture of adiabatic and isocurvature perturbations is possible, and this test should reveal it.

As illustrated in Figure 2, the amplitude of the acoustic peaks depends on the baryon fraction b, the matter density 0, and Hubble's constant H0 = 100h km/s/Mpc. A precise measurement of all three acoustic peaks can reveal the fraction of hot dark matter and even potentially the number of neutrino species (Dodelson et al., 1996). Figure 2 shows the envelope of the CMB anisotropy damping tail on arcminute scales, where the fluctuations are decreased due to photon diffusion (Silk, 1967) as well as the finite thickness of the last-scattering surface. This damping tail is a sensitive probe of cosmological parameters and has the potential to break degeneracies between models which explain the larger-scale anisotropies (Hu & White, 1997b Metcalf & Silk, 1998). The characteristic angular scale for this damping is given by 1.8' B -1/2 0 3/4 h -1/2 (White et al., 1994).

There is now a plethora of theoretical models which predict the development of primordial density perturbations into microwave background anisotropies. These models differ in their explanation of the origin of density inhomogeneities (inflation or topological defects), the nature of the dark matter (hot, cold, baryonic, or a mixture of the three), the curvature of the universe (), the value of the cosmological constant (), the value of Hubble's constant, and the possibility of reionization which wholly or partially erased temperature anisotropies in the CMB on scales smaller than the horizon size. Available data does not allow us to constrain all (or even most) of these parameters, so analyzing current CMB anisotropy data requires a model-independent approach. It seems reasonable to view the mapping of the acoustic peaks as a means of determining the nature of parameter space before going on to fitting cosmological parameters directly.

The possibility that post-decoupling interactions between ionized matter and the CBR have affected the anisotropies on scales smaller than those measured by COBE is of great significance for current experiments. Reionization is inevitable but its effect on anisotropies depends significantly on when it occurs (see Haimann & Knox, 1999 for a review). Early reionization leads to a larger optical depth and therefore a greater damping of the anisotropy power spectrum due to the secondary scattering of CMB photons off of the newly free electrons. For a universe with critical matter density and constant ionization fraction xe, the optical depth as a function of redshift is given by (White et al., 1994)

which allows us to determine the redshift of reionization z* at which = 1,

where the scaling with applies to an open universe only. At scales smaller than the horizon size at reionization, T / T is reduced by the factor e - .

Attempts to measure the temperature anisotropy on angular scales of less than a degree which correspond to the size of galaxies could have led to a surprise if the universe was reionized after recombination to the extent that the CBR was significantly scattered at redshifts less than 1100, the small-scale primordial anisotropies would have been washed out. To have an appreciable optical depth for photon-matter interaction, reionization cannot have occurred much later than a redshift of 20 (Padmanabhan, 1993). Large-scale anisotropies such as those seen by COBE are not expected to be affeced by reionization because they encompass regions of the universe which were not yet in causal contact even at the proposed time of reionization. However, the apparently high amplitiude of degree-scale anisotropies is a strong argument against the possibility of early (z 50) reionization. On arc-minute scales, the interaction of photons with reionized matter is expected to have eliminated the primordial anisotropies and replaced them with smaller secondary anisotropies from this new surface of last scattering (the Ostriker-Vishniac effect and patchy reionization, see next section).

Secondary CMB anisotropies occur when the photons of the Cosmic Microwave Background radiation are scattered after the original last-scattering surface (see Refregier, 1999 for a review). The shape of the blackbody spectrum can be altered through inverse Compton scattering by the thermal Sunyaev-Zel'dovich (SZ) effect (Sunyaev & Zeldovich, 1972). The effective temperature of the blackbody can be shifted locally by a doppler shift from the peculiar velocity of the scattering medium (the kinetic SZ and Ostriker-Vishniac effects, Ostriker & Vishniac, 1986) as well as by passage through the changing gravitational potential caused by the collapse of nonlinear structure (the Rees-Sciama effect, Rees & Sciama, 1968) or the onset of curvature or cosmological constant domination (the Integrated Sachs-Wolfe effect). Several simulations of the impact of patchy reionization have been performed (Gruzinov & Hu, 1998 Peebles & Juszkiewicz, 1998 Aghanim et al., 1996 Knox et al., 1998). The SZ effect itself is independent of redshift, so it can yield information on clusters at much higher redshift than does X-ray emission. However, nearly all clusters are unresolved for 10' resolution so higher-redshift clusters occupy less of the beam and therefore their SZ effect is in fact dimmer. In the 4.5' channels of Planck this will no longer be true, and the SZ effect can probe cluster abundance at high redshift. An additional secondary anisotropy is that caused by gravitational lensing (see e.g. Cayon et al., 1994 Metcalf & Silk, 1997 Martinez-Gonzalez et al., 1997 Cayon et al., 1993). Gravitational lensing imprints slight non-Gaussianity in the CMB from which it might be possible to determine the matter power spectrum (Zaldarriaga & Seljak, 1998 Seljak & Zaldarriaga, 1998).

Polarization of the Cosmic Microwave Background radiation (Zaldarriaga & Seljak, 1997 Kamionkowski et al., 1997 Kosowsky, 1994) arises due to local quadrupole anisotropies at each point on the surface of last scattering (see Hu & White, 1997a for a review). Scalar (density) perturbations generate curl-free (electric mode) polarization only, but tensor (gravitational wave) perturbations can generate divergence-free (magnetic mode) polarization. Hence the polarization of the CMB is a potentially useful probe of the level of gravitational waves in the early universe (Kamionkowski & Kosowsky, 1998 Seljak & Zaldarriaga, 1997), especially since current indications are that the large-scale primary anisotropies seen by COBE do not contain a measurable fraction of tensor contributions (Gawiser & Silk, 1998). A thorough review of gravity waves and CMB polarization is given by Kamionkowski & Kosowsky (1999).

The processes turning density inhomogeneities into CMB anisotropies are linear, so cosmological models that predict gaussian primordial density inhomogeneities also predict a gaussian distribution of CMB temperature fluctuations. Several techniques have been developed to test COBE and future datasets for deviations from gaussianity (e.g. Ferreira et al., 1997 Kogut et al., 1996b Ferreira & Magueijo, 1997). Most tests have proven negative, but a few claims of non-gaussianity have been made. Gaztañaga et al. (1998) found a very marginal indication of non-gaussianity in the spread of results for degree-scale CMB anisotropy observations being greater than the expected sample variances. Ferreira et al. (1998) have claimed a detection of non-gaussianity at multipole = 16 using a bispectrum statistic, and Pando et al. (1998) find a non-gaussian wavelet coefficient correlation on roughly 15° scales in the North Galactic hemisphere. Both of these methods produce results consistent with gaussianity, however, if a particular area of several pixels is eliminated from the dataset (Bromley & Tegmark, 1999). A true sky signal should be larger than several pixels so instrument noise is the most likely source of the non-gaussianity. A different area appears to cause each detection, giving evidence that the COBE dataset had non-gaussian instrument noise in at least two areas of the sky.

Of particular concern in measuring CMB anisotropies is the issue of foreground contamination. Foregrounds which can affect CMB observations include galactic radio emission (synchrotron and free-free), galactic infrared emission (dust), extragalactic radio sources (primarily elliptical galaxies, active galactic nuclei, and quasars), extragalactic infrared sources (mostly dusty spirals and high-redshift starburst galaxies), and the Sunyaev-Zel'dovich effect from hot gas in galaxy clusters. The COBE team has gone to great lengths to analyze their data for possible foreground contamination and routinely eliminates everything within about 30° of the galactic plane.

An instrument with large resolution such as COBE is most sensitive to the diffuse foreground emission of our Galaxy, but small-scale anisotropy experiments need to worry about extragalactic sources as well. Because foreground and CMB anisotropies are assumed to be uncorrelated, they should add in quadrature, leading to an increase in the measurement of CMB anisotropy power. Most CMB instruments, however, can identify foregrounds by their spectral signature across multiple frequencies or their display of the beam response characteristic of a point source. This leads to an attempt at foreground subtraction, which can cause an underestimate of CMB anisotropy if some true signal is subtracted along with the foreground. Because they are now becoming critical, extragalactic foregrounds have been studied in detail (Gawiser et al., 1998 Gawiser & Smoot, 1997 Toffolatti et al., 1998 Refregier et al., 1998 Sokasian et al., 1998). The Wavelength-Oriented Microwave Background Analysis Team (WOMBAT, see Gawiser et al., 1998 Jaffe et al., 1999) has made Galactic and extragalactic foreground predictions and full-sky simulations of realistic CMB skymaps containing foreground contamination available to the public (see http://astro.berkeley.edu/wombat). One of these CMB simulations is shown in Figure 3. Tegmark et al. (1999) used a Fisher matrix analysis to show that simultaneously estimating foreground model parameters and cosmological parameters can lead to a factor of a few degradation in the precision with which the cosmological parameters can be determined by CMB anisotropy observations, so foreground prediction and subtraction is likely to be an important aspect of future CMB data analysis.

Foreground contamination may turn out to be a serious problem for measurements of CMB polarization anisotropy. While free-free emission is unpolarized, synchrotron radiation displays a linear polarization determined by the coherence of the magnetic field along the line of sight this is typically on the order of 10% for Galactic synchrotron and between 5 and 10% for flat-spectrum radio sources. The CMB is expected to show a large-angular scale linear polarization of about 10%, so the prospects for detecting polarization anisotropy are no worse than for temperature anisotropy although higher sensitivity is required. However, the small-angular scale electric mode of linear polarization which is a probe of several cosmological parameters and the magnetic mode that serves as a probe of tensor perturbations are expected to have much lower amplitude and may be swamped by foreground polarization. Thermal and spinning dust grain emission can also be polarized. It may turn out that dust emission is the only significant source of circularly polarized microwave photons since the CMB cannot have circular polarization. *****

## Title: Probing the last scattering surface through recent and future CMB observations

We have constrained the extended (delayed and accelerated) models of hydrogen recombination, by investigating associated changes of the position and the width of the last scattering surface. Using the recently obtained CMB and SDSS data, we find that the recently derived data constraints favor the accelerated recombination model, although the other models (standard, delayed recombination) are not ruled out at 1 confidence level. If the accelerated recombination had actually occurred in our early Universe, it is likely that baryonic clustering on small scales would have been the cause of it. By comparing the ionization history of baryonic cloud models with that of the best-fit accelerated recombination model, we find that some portion of our early Universe has baryonic underdensity. We have made a forecast for the PLANCK data constraint, which shows that we will be able to rule out the standard or delayed recombination models if the recombination in our early Universe had proceeded with >-0.01 or lower, and residual foregrounds and systematic effects are negligible.

I found this answer at Professor Douglas Scott's FAQ page. He researches CMB and cosmology at the University of British Columbia.

### How come we can tell what motion we have with respect to the CMB? Doesn't this mean there's an absolute frame of reference?

The theory of special relativity is based on the principle that there are no preferred reference frames. In other words, the whole of Einstein's theory rests on the assumption that physics works the same irrespective of what speed and direction you have. So the fact that there is a frame of reference in which there is no motion through the CMB would appear to violate special relativity!

However, the crucial assumption of Einstein's theory is not that there are no special frames, but that there are no special frames where the laws of physics are different. There clearly is a frame where the CMB is at rest, and so this is, in some sense, the rest frame of the Universe. But for doing any physics experiment, any other frame is as good as this one. So the only difference is that in the CMB rest frame you measure no velocity with respect to the CMB photons, but that does not imply any fundamental difference in the laws of physics.

“Where does it come from?” is also answered:

### Where did the photons actually come from?

A very good question. We believe that the very early Universe was very hot and dense. At an early enough time it was so hot, ie there was so much energy around, that pairs of particles and anti-particles were continually being created and annihilated again. This annihilation makes pure energy, which means particles of light - photons. As the Universe expanded and the temperature fell the particles and anti-particles (quarks and the like) annihilated each other for the last time, and the energies were low enough that they couldn't be recreated again. For some reason (that still isn't well understood) the early Universe had about one part in a billion more particles than anti-particles. So when all the anti-particles had annihilated all the particles, that left about a billion photons for every particle of matter. And that's the way the Universe is today!

So the photons that we observe in the cosmic microwave background were created in the first minute or so of the history of the Universe. Subsequently they cooled along with the expansion of the Universe, and eventually they can be observed today with a temperature of about 2.73 Kelvin.

@starwed points out in the comments that there may be some confusion as to whether someone in the rest frame is stationary with respect to the photons in the rest frame. I found a couple more questions on Professor Scott's excellent email FAQ page to clarify the concept.

## Cosmic microwave background

This is not correct (even if you put in the "billion"). Due to the expansion of the Universe, the distance to where the CMB that we see today originated is about three times as far away. It was also much closer than 13.9 billion light years when it was emitted.

This is not correct, or at least it's not a good way of looking at it. If you mean the "malleability of space" thread, you evidently didn't see my responses there. Try this post for a start:

OK. That makes sense. Thanks so much for this explanation. It really clarifies it for me. No Doppler effect. Just accrued expansion. Sorry I took so long to reply. I had to think about it a lot.

Not sure though about the last bit. CMC is curently receding at 3c, previously 60c. Is that a typo? It seems inconsistent with the acceleration of the expansion of the universe.

If you are worried about 60c Figure 1 in

might be helpful. In the very early universe comoving objects have been receding superluminal. The worldline of photons emitted then is designated as "particle horizon" which is 46 Glyr away today. In my opinion this article is really worthwhile to read.

If you are worried about 60c Figure 1 in

First, let me emphasize that I am really just trying to understand the accepted theory about the expansion of the universe, not speculating or proposing anything new. And I hope someone can explain the fallacy in my reasoning.

That being said, let me quote a textbook explanation of why fainter than expected supernovae mean accelerating expansion. This quotation is from a textbook by Rupert W Anderson. "The Cosmic Compendium: The Ultimate Fate of the Universe." p. 74, which can be accessed in google books using the search line: "decelerating universe dimmer OR fainter supernovae"

A simple derivation of the expansion rate of the universe can be given as follows:

The redshift z directly gives the cosmic scale factor at the time the supernova exploded.

/Added Note: Where a(t) is the scale factor expressed as a fraction of the universe's present size = 1./

So a supernova with a measured redshift z = 0.5 implies that the universe was 1/(1+0.5) = 2/3 of its present size when the the supernova exploded. In an accelerating universe, the universe was expanding more slowly in the past that it is today, which means it took a longer time to expand from 2/3 to 1.0 times its present size compared to a non-accelerating universe. This results in a larger light-travel time, larger distance, and fainter supernovae, which corresponds to the actual observation.

To illustrate my quandary, consider the following:

Hubble's law states that Hs = cz, from which z = Hs/c and dz/ds = H/c

So in an accelerating universe, at later times, H is greater than at earlier times and dz/ds is similarly greater (c being constant) i.e., given the same initial H,

dz/ds in an accelerating universe is greater than dz/ds in a non-acclerating universe . 1)

But the Quotation seems to be saying that it takes a larger change in s in an accelerating universe to achieve the same change in z i.e., given the same initial H,

ds/dz in an accelerating universe is greater than ds/dz in a non-accelerating universe . 2)

It is evident that equation 1) and 2) are contradictory hence, my quandary.

## Ask Ethan: Will The Cosmic Microwave Background Ever Disappear?

An illustration of the cosmic radiation background at various redshifts in the Universe. Note that . [+] the CMB isn't just a surface that comes from one point, but rather is a bath of radiation that exists everywhere at once.

Earth: NASA/BlueEarth Milky Way: ESO/S. Brunier CMB: NASA/WMAP

The earliest signal we’ve ever directly detected from the Universe comes to us from shortly after the Big Bang: when the Universe was merely 380,000 years old. Known today as the Cosmic Microwave Background, it’s alternatively been called the “primeval fireball” or the Big Bang’s leftover glow. It was an astonishing prediction dating back to George Gamow all the way in the 1940s, and it shocked the astronomical world when it was directly detected back in the 1960s. Over the past 55 years, we’ve measured its properties exquisitely, learning a tremendous amount about our Universe in the process. But will it always be around? That’s what Jürgen Sörgel wants to know, asking:

“The cosmic microwave background (CMB) was generated 380.000 years after the big bang, when the universe became transparent. The photons we will measure next week were generated a little bit further away from the position we had at that time compared to the photons we measure today. Our future is infinite, but the universe at year 380.000 was finite. Does that mean that the day will come when [the] CMB will disappear?”

It’s a simple question with a complex answer. Let’s dive in to what we know.

First noted by Vesto Slipher back in 1917, some of the objects we observe show the spectral . [+] signatures of absorption or emission of particular atoms, ions, or molecules, but with a systematic shift towards either the red or blue end of the light spectrum. When combined with the distance measurements of Hubble, this data gave rise to the initial idea of the expanding Universe: the farther away a galaxy is, the greater its light is redshifted.

Vesto Slipher, (1917): Proc. Amer. Phil. Soc., 56, 403

If we turn to the theoretical side, we can understand where the Cosmic Microwave Background comes from. The farther away a galaxy is from us today, the faster it appears to be speeding away from us. The way we observe this is the same way that scientists like Vesto Slipher observed it more than 100 years ago:

• we measure the light coming from a distant object,
• we break it up into its individual wavelengths,
• we identify sets of emission or absorption lines that correspond to specific atoms, ions, or molecules,
• and measure that they’re all systematically shifted, by the same percentage, towards either shorter (bluer) or longer (redder) wavelengths.

### Super Solstice Strawberry Moon: See And Stream Summer’s Biggest, Brightest And Best Moonrise This Week

Although there’s a bit of randomness to each individual galaxy’s motion — up to a few thousand kilometers-per-second, corresponding to the gravitational tugs on each galaxy by the surrounding matter — there’s a general, unambiguous trend that emerges. The farther away a galaxy is, the greater the amount its light is shifted towards longer wavelengths. This was first observed way back in the 1910s, and was some of the first evidence in support of the expanding Universe.

As the fabric of the Universe expands, the wavelengths of any radiation present will get stretched . [+] as well. This applies just as well to gravitational waves as it does to electromagnetic waves any form of radiation has its wavelength stretched (and loses energy) as the Universe expands. As we go farther back in time, radiation should appear with shorter wavelengths, greater energies, and higher temperatures.

E. Siegel / Beyond The Galaxy

Although many scientists took advantage of this observation, the first one to put this piece together into the framework we recognize as the modern Big Bang was George Gamow. In the 1940s, Gamow realized that a Universe that was expanding today — where the distance between any two points is increasing — must have been not only smaller in the past, but also hotter and denser. The reason is simple, but no one else had put the pieces together until Gamow.

A photon, or quantum of light, is defined by its wavelength. The energy of an individual photon is inversely proportional to its wavelength: a long-wavelength photon has less energy than a short-wavelength photon. If you have a photon traveling through your Universe and the Universe is expanding, then the space that the photon is passing through is stretching, meaning the photon itself gets stretched to longer wavelengths and lower energies. In the past, therefore, these photons must have had shorter wavelengths and higher energies, and higher energies mean hotter temperatures and a more energetic Universe.

The size, wavelength and temperature/energy scales that correspond to various parts of the . [+] electromagnetic spectrum. You have to go to higher energies, and shorter wavelengths, to probe the smallest scales. Ultraviolet light is sufficient to ionize atoms, but as the Universe expands, light gets systematically shifted to lower temperatures and longer wavelengths.

NASA / Wikimedia Commons user Inductiveload

Gamow, in a leap of faith, extrapolated this as far back as he could fathom. At some point in his extrapolation, he realized that the photons that exist in the Universe would have been heated up to such a high temperature that one of them, on occasion, would have enough energy to ionize hydrogen atoms: the most common type of atom in the Universe. When a photon strikes an atom, it interacts with the electron, either knocking it up to a higher energy level or — if it has sufficient energy — kicking the electron free of the atom entirely, ionizing it.

In other words, there must have been a time in the Universe’s past where there were enough high-energy photons compared to both:

so that every atom was ionized. As the Universe expanded and cooled, however, electrons and ions continue to find each other and re-form atoms, and eventually there weren’t enough photons of sufficient energy to keep ionizing them. At that point, the atoms become electrically neutral, the photons no longer bounce off of the free electrons, and the light that makes up the Cosmic Microwave Background simply travels freely through the Universe, which continues to expand.

In the hot, early Universe, prior to the formation of neutral atoms, photons scatter off of . [+] electrons (and to a lesser extent, protons) at a very high rate, transferring momentum when they do. After neutral atoms form, owing to the Universe cooling to below a certain, critical threshold, the photons simply travel in a straight line, affected only in wavelength by the expansion of space.

When we fast-forward to today, 13.8 billion years later, we can actually detect these leftover photons. When these neutral atoms formed, the Universe was less than one-billionth its present volume, and the temperature of this background radiation was right around 3,000 K: typical for the surface temperature of a red giant star. After billions of years of cosmic expansion, the temperature of this radiation is now a mere 2.725 K: less than three degrees above absolute zero.

And still, we’re able to detect it. There are 411 photons left over from the Big Bang permeating every cubic centimeter of space today. The photons we’re detecting today were emitted just 380,000 years after the Big Bang, journeyed through the Universe for 13.8 billion years, and are finally arriving at our telescopes right now. Tomorrow’s CMB might appear mostly identical to today’s, but it’s photons are one light-day behind.

This conceptual drawing shows a logarithmic conception of the Universe. The farthest red "wall" . [+] corresponds to light emitted from the moment that the atoms in the Universe became neutral and the leftover radiation from the Big Bang began traveling in a straight line. Yesterday's CMB took one fewer day to arrive at our eyes and originated from a point slightly closer than today's, while tomorrow's CMB will take one extra day and originate from a point farther away. We will never run out of CMB.

Wikipedia user Pablo Carlos Budassi

This doesn’t mean that the CMB we’re seeing today is going to wash over us and then disappear! What it means, instead, is that the CMB we see today was emitted 13.8 billion years ago when that portion of the Universe reached 380,000 years of age. The CMB we’ll see tomorrow will have been emitted 13.8 billion years plus one day ago, when that portion of the Universe reached 380,000 years of age. The light that we see is the light that is arriving after journeying through the Universe since it was first emitted, but there’s a key realization that needs to go along with that.

The Big Bang — if we could somehow step outside our Universe and watch it occur — is an event that occurred everywhere throughout our Universe at once. It occurred here, where we are, at the same instant it occurred 46 billion light-years away in all directions, as well as everywhere in between. When we look out at the great cosmic expanse, we’re looking farther and farther back in time. No matter how far away we look or how much the Universe expands, there will always be a “surface” we can see, in all directions, where the Universe is only just now reaching 380,000 years of age.

The leftover glow from the Big Bang, the CMB, isn't uniform, but has tiny imperfections and . [+] temperature fluctuations on the scale of a few hundred microkelvin. While this plays a big role at late times, after gravitational growth, it's important to remember that the early Universe, and the large-scale Universe today, is only non-uniform at a level that's less than 0.01%. Planck has detected and measured these fluctuations to better precision than ever before, and can use the fluctuation patterns that arise to place constraints on the Universe's expansion rate and composition.

ESA and the Planck collaboration

In other words, the Universe will never run out of photons for us to see. There will always be a faraway place, from our perspective, where the Universe is first forming stable, neutral atoms. At that location, the Universe becomes transparent to the

3000 K photons that were previously scattering off of the ions (mostly in the form of free electrons) that were omnipresent, enabling them to simply stream freely in all directions. What we observe as the Cosmic Microwave Background are the photons emitted from that location that happened to be traveling in our direction at that moment.

After journeying through the Universe for 13.8 billion years, they’re at last arriving at our eyes. If we fast forward far into the future, those components of the story will still be the same, but a few important aspects will change in vital ways. As more time passes, the Universe will continue to expand, meaning that:

• the photons get stretched to longer wavelengths,
• meaning that the CMB will be cooler,
• there will be a lower density of photons,
• and the specific pattern of fluctuations that we see will slowly begin to change over time.

The overdense, average density, and underdense regions that existed when the Universe was just . [+] 380,000 years old now correspond to cold, average, and hot spots in the CMB, which in turn were generated by inflation. These regions are three-dimensional in nature, and when the Universe expands sufficiently, this two-dimensional surface will appear to change in temperature over time.

E. Siegel / Beyond The Galaxy

What we see as the CMB, today, consists of hot spots and cold spots that correspond to regions of space that are slightly less dense or more dense than the cosmic average, albeit by a tiny, minuscule amount: about 1 part in 30,000. Those overdense and underdense regions have a finite, specific size to them, and eventually those regions will be in front of the CMB, rather than the point-of-origin of the CMB we see. If we wait for long enough — and long enough is at least hundreds of millions of years from where we presently sit — we’ll see an entirely foreign CMB.

But it won’t go away entirely. At some point, a hypothetical observer that’s still around will need to use radio waves to detect the Big Bang’s leftover glow, as the radiation will stretch so severely it will redshift out of the microwave portion of the spectrum and into the radio. We’ll have to build even more sensitive radio dishes, as the number density of photons will drop from hundreds per cubic centimeter to less than 1 per cubic meter. We’ll need larger dishes to detect these long-wavelength photons and gather enough light to identify this ancient signal.

Penzias and Wilson at the 15 m Holmdel Horn Antenna, which first detected the CMB. Although many . [+] sources can produce low-energy radiation backgrounds, the properties of the CMB confirm its cosmic origin. As time goes on and the leftover glow from the Big Bang continues to redshift, larger telescopes sensitive to longer wavelengths and smaller number densities of photons will be required to detect it.

However, the Big Bang’s leftover glow will never disappear entirely. No matter how far we extrapolate into the future, even as the density of photons and the energy-per-photon both continue to drop, a large enough, sensitive enough detector tuned to the right wavelength could always identify it.

At some point, of course, this becomes wildly impractical. When the wavelength of a leftover photon from the Big Bang becomes larger than a planet, or the spatial density of photons becomes lower than 1-per-solar system, it seems implausible that we’d ever build a detector capable of measuring it. On long enough cosmic timescales, the number density of particles — both matter particles and photons — as well as the energy per photon we’d observe, both asymptote towards zero.

But the rate at which it goes to zero is slow enough that, so long as we’re talking about a finite amount of time after the Big Bang, even if it’s an arbitrarily long time, we’ll always be able to design, at least in theory, a sufficiently large detector to reveal our cosmic origins.

The loneliest galaxy in the Universe, which has no other galaxies in its vicinity for 100 million . [+] light-years in any direction. In the far future, whatever our Local Group merges into will be the only galaxy around for billions upon billions of light-years. We will lack the clues that taught us to even search for the CMB.

ESA/Hubble & NASA and N. Gorin (STScI) Acknowledgement: Judy Schmidt

The biggest existential puzzle about all of it, however, is this: if creatures like us came into existence hundreds of billions of years (or more) from now, how would they ever know to look for this leftover glow from a Big Bang? The only reason we even thought to look for it is because we had evidence, everywhere we looked, for an expanding Universe. But in the very distant future, this won’t be the case at all! Dark energy is presently driving the Universe apart, and while the Milky Way, Andromeda, and the rest of the Local Group will remain bound together, every galaxy, galaxy group, and galaxy cluster beyond

3 million light-years away will be pushed away by the Universe’s expansion.

100 billion years from now, the nearest galaxy will be unobservably distant no optical or even infrared telescope in existence today would be able to see a single galaxy beyond our own. Without that clue to guide a civilization, how would they ever know to search for an ultra-faint, leftover glow? How would they ever surmise that our Universe arose from a hot, dense, uniform, rapidly expanding past? It may be the case that the only reason we determined our cosmic origins is because we came into existence so early in the Universe’s history. The signals will change and become harder to detect, sure, but even though they won’t quite disappear, future civilizations won’t have the same clues that we do. In a way, we really are the cosmically fortunate ones.

I have a somewhat related question(s) someone may be able to help me understand.

When I first learned about the CMB and how 'far away' it was, I wondered about the 'resolution' of distant cosmological objects.

To explain a bit, I knew that photons were 'particles' - and it struck me that there must be an awful lot of them being radiated from the 'surface of last scattering' for us to be able to resolve (from such a great distance) an image like the well known CMB images in the popular literature. I was vaguely aware that the resolution of the instumentation would be a factor too (even if I imagined the 'instrument' was a human eye) but still, it seemed to me that if photons were like tiny little 'bullets' radiating out in all directions, there would come a point where the photons from distant objects would be more likely to 'miss' our instruments here on earth (or in orbit nearby) rather than 'hit'.

Then I learned a little more about wave-particle duality, and it occurred to me that photons were more like an analog 'wave' radiating out from a distant source and so could be expected to 'hit' our instruments, even over great distances.

Since then, I've come to appreciate that photons aren't really either waves or particles (little bullets) they're 'just' photons, and wave-particle duality is more about how we describe some of their properties in relation to everyday objects that we understand more intuitively. I've also learned (a little) about quantisation(?) and planck scales, so now, when I think about a 'wave' radiating out from the surface of last scattering, I wonder if there comes a point at which we can (or would) 'observe' quantum properties in the CMBR photons? Do we see something like a planck scale 'resolution' in the CMBR (like I see in my computer monitor)? Is this a factor in observing other distant objects?

Do my questions even make sense?

A couple more questions that occurred while I was proof reading my last post:

When we think of the surface of last scattering, we can imagine that the region we observe today is like a distant sphere with us (and our instruments) at it's centre. Does this serve as a kind of lens to 'focus' the CMBR (at least the part we observe) at earth in some way?

We tend to think of a lens or mirror as a contiguous surface in everyday life. But even my shaving mirror is made of individual atoms. The surface of last scattering is a plasma of ionised hydrogen atoms, so the CMBR is actually radiated from individual atoms and not a contiguous surface, right? Is the surface of last scattering so distant that we can resolve those individual atoms in some way, like a cosmological microscope. or are atoms so small that even at this great distance they're too small to 'see'. Or is something else altogether going on here?

Firstly the CMBR has nothing to do with the resolution of distant cosmological objects.

The CMBR is here around us. There is no lens needed to focus it. There is some "focusing" in the sense that there are fluctuations in the CMBR caused by supervoids and superclusters.

The surface of last scattering was when the universe was filled with a plasma of ionised hydrogen atoms which happillion years ago and

70 billion lightyears away.. We cannot resolve these atoms.

The resolution of distant cosmological objects like galaxies is basically only limited by the given instrument, e.g. Hubble.

Maybe the actual 'nature' of a photon is where I struggle with it? If I'm getting your point correctly, you're saying that what our instruments (say WMAP) actually measure is a photon right here and now. it just happens (amongst other things) to have originated a long time ago and far away.

I can imagine that photon as a little 'bullet like' particle, in which case I'm kind of amazed it has hit the instrument at all, given the distance it has travelled and how that would amplify any 'angularity' it had at source. If I drew a picture for you of how I imagine it, the photons would be little arrows, and as they radiate out thru space their angular separation would get larger and larger, and I can imagine WMAP happily sitting 'between' the arrows such that the arrows 'miss'.

I can also imagine the photon as a wave of energy washing over the instrument. But it's still amazing to me when I imagine a 'wave' starting out all that time ago, expanding, expanding. until it passes our instrument. Does the 'wave' not have some sort of 'granularity' to it, having expanded so much? (If it was a water wave for example, by now it would be just widely separated moleclues of hydrogen and oxygen rushing by! ). If I drew a picture of this, it would be a circle getting ever larger as it radiates out thru space, such that eventually it has become so large that we notice some kind of quantisation so that the circle has some 'gaps' in it, which I can imagine WMAP falling thru as the wave 'washes' past.

Given those mental images, I'd imagine a sort of inherent resolution or pixellation to the CMBR itself (separate to any pixellation of the instrument).

I know that my everyday notions of a wave and particle are going to be severely lacking when applied to a photon, but still, I feel like I'm failing to grasp something important?

I would say the universe is not old enough for the CMB "resolution" to be virtually all "misses" from our corner of the woods.

KiwiBiggles, I think that, in trying to intuit this you have overlooked the numbers.

How many 'CMB photons' do you think pass through a cubic centimetre of space - somewhere beyond the Moon's orbit, say - every second? Compare that with the number of electrons (or protons) in that same cubic centimetre, whether free or bound to an atomic nucleus.

I would say the universe is not old enough for the CMB "resolution" to be virtually all "misses" from our corner of the woods.

It's interesting that pixellation from Hubble is apparent in some of the those images.

I'm not sure what to make of the effect expansion has had on the CMBR photons, aside from being reasonably comfortable (at a strictly layman's level) with redshift. Do you think there's any validity to these notions of an 'inherent' pixellation in the CMBR or the light from other cosomological objects? What say we lived in a much older period in the universe (horizons aside)?

KiwiBiggles, I think that, in trying to intuit this you have overlooked the numbers.

How many 'CMB photons' do you think pass through a cubic centimetre of space - somewhere beyond the Moon's orbit, say - every second? Compare that with the number of electrons (or protons) in that same cubic centimetre, whether free or bound to an atomic nucleus.

Hmmm. how many photons? I really don't have any idea. I was going to say thousands(?) but that seems too few on a gut level, so millions maybe? I haven't thought about the numbers except that there must be gazillions in the observable universe!

I'll go look it up.

Hmmm. how many photons? I really don't have any idea. I was going to say thousands(?) but that seems too few on a gut level, so millions maybe? I haven't thought about the numbers except that there must be gazillions in the observable universe!

I'll go look it up.

A billion is a good number to keep in mind the ratio of the number of photons to that of baryons is greater than a billion. For simplicity, the number of baryons is the same as the number of electrons (it's not, but at this level of approximation it's good enough).

a billion photons for every atom, in the entire universe, how does that change your intuitive picture?

Another way to think of this: the CMB is 'the surface of last scattering', it is 'when photons streamed free', or 'when radiation decoupled from matter'. Before this time, the universe was 'radiation dominated' afterwards, 'matter dominated'. Can you grok any of this?

There are 400 CMB photons in a cubic centimetre of the universe. I didn't think that sounded like a whole lot, my wife has a 8somethingmegapixel camera. I can count to 400 in a few minutes and a cubic centimetre isn't all that small after all.

But. then he mentions the speed of light.

"In terms of photons, or packets of light, there are quite a few of them in the microwave background -- about 400 per cubic centimeter. Since they travel at the speed of light that means quite a large number of them are whizzing through each patch of space each second."

10 trillion photons per second per squared centimeter.

I'm gonna have to think about that a minute!

Thanks folks. That has helped a lot. I think my problem was trying to understand how we measure the CMB from the perspective of a single photon. It turns out to be just a not-very-useful perspective.

When you consider sampling just some of the trillions of CMB photons streaming thru every centimetre of space every second. it's not so counter-intuitive after all. Nereid hit it on the head!

I think I can put that one to bed for now.

I do still have some vague questions rattling around about the nature of individual photons though, and quantum effects in the CMBR. Things to ponder another day!

In principal it is similar to how the light emitted by the sun is "here around us" and yet it is emitted by a distant object.

The CMBR that is detected by COBE, WMAP etc was emitted by matter that is not "here" around us - that stuff is all around us at a considerable distance (surface of last scattering) - that's what the famous CMB images show.

In popular literature it is often phrased as "CMB is everywhere around us", which is ambiguous because it says nothing about distance, and therefore is uninformative to lay persons.

Thanks Noncryptic and Glappkaeft.

I haven't done it yet, but I have on my to-do list to read up on the detectors onboard COBE and WMAP - I'm thinking it will help me 'visualise' better what's happening out there. I've always quite liked the history of science, and enjoy the 'stories' of the CMBR and the double-slit experiment, for example, very much. The more familiar I become with the 'stories', the more I find my interest in the technical side is piqued. I even find the orbital mechanics of these experiments exciting these days, not something I thought about a lot in the past. So much to learn.

It is also worth considering that, with the CMB, we aren't looking at something that was very far away at the time.

I saw a figure mentioned above of 70 billion light-years and I'm not sure where that figure came from - the surface of last scattering is currently only 46 billion light-years away and it marks the edge of the observable universe, which has expanded by a factor of around 1100 since those CMB photons were released. This means that those photons (the ones we currently detect) were released only around 40 million light-years away, 13.7 billion years ago!

The CMB was released throughout the universe at pretty much the same time, and as such has been passing this way, coming in from all directions, ever since. The CMB photons we detect today were originally released only a few tens of millions of light-years away, but the universe was expanding so fast at that time that the distance between those photons and "here" was increasing faster than light! It took billions of years of decelerating expansion before those CMB photons (the ones we currently detect!) could actually start to make any headway towards us against the expansion of the universe (from our viewpoint, that is. From the viewpoint of the place those CMB photons were released from, they have always been moving towards us!).

Of course, as I said, the CMB has been passing this way all along. The CMB has been coming in from all directions, released from an increasing distance away, throughout the history of the observable universe, and the universe has expanded by a factor of 1100 since the CMB was released.

So, when considering the "scale" of the WMAP projection of the CMB, remember that, as we see it, the surface of last scattering was only a few tens of millions of light-years away, and everything that CMB has passed on its journey was closer!

Thanks Speedfreek, that's a great summation!

Somewhere or other I've got a copy of the famous Davis/Lineweaver paper, I'll dust it off and have another look, at least some of it I can follow.

I don't know how old you are or whether you get television through a cable or antenna, but there is a common story about the CMB. If your TV is hooked up to an antenna, you can tune to a channel with no signal. Buried in the noise you see on the monitor, each "pixel" flashing on and off randomly, is the CMB. Approximately 1/100 pixel flashes is due to a photon from the CMB hitting your antenna. Not a great signal to noise ratio, but it's fun to think about it.

## Can we observe changes in the CMB (surface of last scattering) over time? - Astronomy

One of the foremost cosmological discoveries was the detection of the cosmic background radiation. The discovery of an expanding Universe by Hubble was critical to our understanding of the origin of the Universe, known as the Big Bang. However, a dynamic Universe can also be explained by the steady state theory.

The steady state theory avoids the idea of Creation by assuming that the Universe has been expanding forever. Since this would mean that the density of the Universe would get smaller and smaller with each passing year (and surveys of galaxies out to distant volumes shows this is not the case), the steady-state theory requires that new matter be produced to keep the density constant.

The creation of new matter would violate the conservation of matter principle, but the amount needed would only be one atom per cubic meter per 100 years to match the expansion rate given by Hubble's constant.

The discovery of the cosmic microwave background (CMB) confirmed the explosive nature to the origin of our Universe. For every matter particle in the Universe there are 10 billion more photons. This is the baryon number that reflects the asymmetry between matter and anti-matter in the early Universe. Looking around the Universe its obvious that there is a great deal of matter. By the same token, there are even many, many more photons from the initial annihilation of matter and anti-matter.

Most of the photons that you see with your naked eye at night come from the centers of stars. Photons created by nuclear fusion at the cores of stars then scatter their way out from a star's center to its surface, to shine in the night sky. But these photons only make up a very small fraction of the total number of photons in the Universe. Most photons in the Universe are cosmic background radiation, invisible to the eye.

Cosmic background photons have their origin at the matter/anti-matter annihilation era and, thus, were formed as gamma-rays. But, since then, they have found themselves scattering off particles during the radiation era. At recombination, these cosmic background photons escaped from the interaction with matter to travel freely through the Universe.

As the Universe continued to expanded over the last 15 billion years, these cosmic background photons also expanded', meaning their wavelengths increased. The original gamma-ray energies of cosmic background photons has since cooled to microwave wavelengths. Thus, this microwave radiation that we see today is an echo' of the Big Bang.

The discovery of the cosmic microwave background (CMB) in the early 1960's was powerful confirmation of the Big Bang theory. Since the time of recombination, cosmic background photons have been free to travel uninhibited by interactions with matter. Thus, we expect their distribution of energy to be a perfect blackbody curve. A blackbody is the curve expected from a thermal distribution of photons, in this case from the thermalization era before recombination.

Today, based on space-based observations because the microwave region of the spectrum is blocked by the Earth's atmosphere, we have an accurate map of the CMB's energy curve. The peak of the curve represents the mean temperature of the CMB, 2.7 degrees about absolute zero, the temperature the Universe has dropped to 15 billion years after the Big Bang.

Where are the CMB photons at the moment? The answer is `all around you'. CMB photons fill the Universe, and this lecture hall, but their energies are so weak after 15 billion years that they are difficult to detect without very sensitive microwave antennas.

The CMB is highly isotropy, uniform to better than 1 part in 100,000. Any deviations from uniformity are measuring the fluctuations that grew by gravitational instability into galaxies and clusters of galaxies.

Images of the CMB are a full sky image, meaning that it looks like a map of the Earth unfolded from a globe. In this case, the globe is the celestial sphere and we are looking at a flat map of the sphere.

Maps of the CMB have to go through three stages of analysis to reveal the fluctuations associated with the early Universe. The raw image of the sky looks like the following, where red is hotter and blue is cooler:

The above image has a typical dipole appearance because our Galaxy is moving in a particular direction. The result is one side of the sky will appear redshifted and the other side of the sky will appear blueshifted. In this case, redshifting means the photons are longer in wavelength = cooler (so backwards from their name, they look blue in the above diagram). Removing the Galaxy's motion produces the following map:

This map is dominated by the far-infrared emission from gas in our own Galaxy. This gas is predominately in the plane of our Galaxy's disk, thus the dark red strip around the equator. The gas emission can be removed, with some assumptions about the distribution of matter in our Galaxy, to reveal the following map:

This CMB image is a picture of the last scattering epoch, i.e. it is an image of the moment when matter and photons decoupled, literally an image of the recombination wall. This is the last barrier to our observations about the early Universe, where the early epochs behind this barrier are not visible to us.

The clumpiness of the CMB image is due to fluctuations in temperature of the CMB photons. Changes in temperature are due to changes in density of the gas at the moment of recombination (higher densities equal higher temperatures). Since these photons are coming to us from the last scattering epoch, they represent fluctuations in density at that time.

The origin of these fluctuations are primordial quantum fluctuations from the very earliest moments of are echo'ed in the CMB at recombination. Currently, we believe that these quantum fluctuations grew to greater than galaxy-size during the inflation epoch, and are the source of structure in the Universe.

When we look out in the sky, we're actually looking backwards in time. Light from more distant objects take longer to reach us and thus we are observing now how they appeared in the past. We can see back a few billion years with the light of galaxies. The microwave light of the background shines from long ago in an infant universe 300,000 years old (the epoch of "last scattering") and illuminates the particle soup that existed before this time. This soup has a very smooth consistency and is composed of fundamental particles like electrons, protons, helium nuclei, neutrinos.

The obvious questions are: how did the universe go from a smooth particle soup to a complex system of galaxies and large scale structure. Can we use the fact that we're seeing the surface of this soup in the microwave background to help us understand this question.

If we have small wrinkles or hills and valleys early on in the universe, matter will tend to fall into the valleys, eventually producing dense regions that become the sites of galaxies.

We represent these wrinkles by a sort of "top view" where the color coding refers to the density of matter (dark regions have more matter, light regions less).

Needless to say, this is a bit of an idealization for illustative purposes. Cosmologists actually run computer simulations to track how matter collects into valleys. For example, here is a simulation running forward in time which shows how particles collect and enhance small initially small wrinkles.

One question that remains unanswered is what is the origin of such large scale wrinkles in the first place. Inflation theory is that a period of rapid expansion takes very small scale fluctuations at the level of the particle soup and stretches them to cosmic proportions.

Here the blue bands are snapshots of the wrinkles in the density of the universe at various times. As time goes on, matter falls into these wrinkles and starts to build heavier and heavier objects. The crucial period when this process of gravitational attraction and infall can occur is related to an important concept in cosmology called the horizon. Like the horizon on the earth, it is the point beyond which we're unable to look. Unlike the earth's horizon, this distance is increasing with time because light from more distant regions has had more time to reach us. Heuristically, if there is a large clump in the universe we only know to fall toward it once it comes into the horizon.

A useful property of the microwave background is that when we look out across widely separated angles, we're looking at wrinkles on such large scales that this process of infall hasn't yet begun. We're looking at the primordial wrinkles themselves.

Small variations in the temperature of the background radiation from point to point on the sky are called anisotropies. These anisotropies were first detected by the COBE (NASA's COsmic Background Explorer) satellite in 1992. The current MAP (NASA's Microwave Anisotropy Probe mission) version of the CMB is:

COBE and MAP then has told us what the large scale ripples in the background radiation temperature look like. However there is much to be gained by examining the fine details of the ripples. Recall that on the large scales, the temperature ripples reflected the primordial ripples themselves. That is because on scales that are larger than the horizon there hasn't been enough time for matter to collect in the valleys and the process of structure formation to start. When we look at smaller scales than the horizon, we see the process of structure formation at work.

The goal of the current generation of experiments is to understand this process in detail by looking at the small scale ripples in the background radiation temperature.

What we see on small scales is actually sound. The photons behave as a gas just like air. Ordinary sound waves are just travelling compressions and rarefactions of the gas which we hear as sound as they strike our ear drum. The photons also carry sound waves as gravity tries to compress the gas and pressure resists it. The reason why we see it rather than hear it is that when we compress the gas it becomes hotter. We see the sound waves as hot and cold spots on the sky.

The result is a spectrum of sound waves that are useful in determining the origin, evolution and fate of objects in the universe.

The fluctuations originated from the inflation period of rapid expansion. Whether or not this actually happened can be "heard" in the microwave background. The fundamental tone of a musical system is related to its physical size - here the horizon size at last scattering.

There is also a pattern of overtones at integer multiples of the fundamental frequency.

In music, the pattern of overtones helps us distinguish one instrument from another: it is a kind of signature of the instrument that makes the sound. In the same way, the pattern of overtones in the sound spectrum of the microwave background ripples acts as a signature of inflation. Inflation's signatures are that the overtones follow a pure harmonic series with frequency ratios of 1:2:3.

COBE told us what the large-scale fluctuations in the background look like, but cosmologists today are more interested in the small-scale fluctuations. Astronomers divide up the sky into angular degrees, so that 90 degrees is the distance from the horizon to a point directly overhead. COBE measured temperature ripples from the 10 degree to 90 degree scale. This scale is so large that there has not been enough time for structures to evolve. Hence COBE sees the so-called initial conditions of the universe. At the degree scale, on the other hand, the process of structure formation imprints information in the ripples about conditions in the early universe.

Since the COBE discovery, many ground and balloon-based experiments have shown the ripples peak at the degree scale. What CMB experimentalists do is take a power spectrum of the temperature maps, much as you would if you wanted to measure background noise. The angular wavenumber, called a multipole l, of the power spectrum is related to the inverse of the angular scale (l=100 is approximately 1 degree). Recent experiments, noteably the Boomerang and Maxima experiments, have show that the power spectrum exhibits a sharp peak of exactly the right form to be the ringing or acoustic phenomena long awaited by cosmologists:

Fluctuations and the Origin of Galaxies :

The density fluctuations at recombination, as measured in the CMB, are too large and too low in amplitude to form galaxy sized clumps. Instead, they are the seeds for galaxy cluster-sized clouds that will then later break up into galaxies. However, in order to form cluster-sized lumps, they must grow in amplitude (and therefore mass) by gravitational instability, where the self-gravity of the fluctuation overcomes the gas pressure.

The CMB fluctuations are a link between Big Bang and the large scale structure of galaxies in the Universe, their distribution in terms of clusters of galaxies and filaments of galaxies that we observe around the Milky Way today.