## Redshift of CMB temperature

Syksy Rasanen
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Joined: March 02 2005
Affiliation: University of Helsinki

### Redshift of CMB temperature

What kind of constraints are there on the CMB temperature (or the energy of any other photons, for that matter) behaving differently from 1/a at late times? In other words, what are the constraints on the radiation energy density evolving differently from 1/a^4? We have sensitive data on the behaviour of the energy density during BBN, but what about later eras, especially after last scattering?

Simon DeDeo
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### Redshift of CMB temperature

That's a curious question. I suppose for the redshift relationship to break down you would have to violate Lorentz invariance? In other words, the relationship between energy and momentum of the photon would have to become unusual? (e.g., a massive photon, LV couplings, etc. etc.)

Having thought about this in the past (no guarantee of being correct!) -- probably the strongest cosmological contraint would be in the expansion history. Since the FRW has those spacelike Killing vectors, one would expect the momentum of the photon to decrease in the usual 1/a fashion, but a breakdown in the E-p relationship would lead to an unexpected energy density and thus funny behavior in the Einstein equation.

By symmetry, I don't think you can violate the 1/a redshift of the photon momentum (wavelength.) By which I mean, I don't know how (or if it is even conceptually possible) to test that.

Probably there would be stronger constraints coming from lab/satellite tests looking at the gravitational redshift in the Earth's field -- I don't think it's natural to be able to hide one of the effects from the other.

Niayesh Afshordi
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### Redshift of CMB temperature

Theoretically, I think Simon is right that it is very hard to break the 1/a scaling in FRW/homogeneous cosmologies. However, I think Syksy is interested in inhomogenous cosmologies, where this scaling breaks down generically.

On the other hand, not many people know that 1/a scaling of CMB temperature is one of the less appreciated observational sucesses of big bang/FRW cosmology. The CMB temperature can be measured from the ionization state of some IGM/ISM atoms at high redshifts, and then compared against the 1/a scaling. I cannot recall the original reference for this observation, but you could look at:

as well as its citations and references. As far as I know, there is no significant discrepancy with 1+z scaling, but I wouldn't be surprised if some discrepancies have been swept under the rug ...

Dragan Huterer
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### Redshift of CMB temperature

Constraints on T(z)/T(0) have been imposed using measurements of temperatures of clusters via the SZ effect, though at modest z=0.2 last I checked (see Battistelli et al, astro-ph/0208027). Not surprisingly, things are consistent with the standard (1+z) scaling.

For people interested in prospects of doing this better, and getting at the inhomogeneity constraints, this seems to be of relevance: LoSecco, Matthews and Wang, astro-ph/0108260.

Syksy Rasanen
Posts: 119
Joined: March 02 2005
Affiliation: University of Helsinki

### Redshift of CMB temperature

Thanks, these look useful. (I had a vague recollection of having heard about the SZ constraints, but no reference.)

As Niayesh says, my interest is mainly due to inhomogeneous cosmologies, where there can be a contribution to the redshift which is not given by the expansion of space. The 1/a scaling can also break down in extra-dimensional models, where the energy density of radiation depends on the size of extra dimensions, and those dimensions expand or contract. So one can perhaps also use these observations to put limits on such models.

Anze Slosar
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### Redshift of CMB temperature

A slightly related joke is estimating tcmb from WMAP power spectrum alone. Taking cosmomc and letting T_{cmb} be a free parameter, WMAP power spectra alone gives Tcmb=3.1+-0.2 at one sigma. It is degenerate with all kinds of stuff, most importantly amplitude (I assumed that WMAP measure muK^2 spectrum and not power/tcmb^2 spectrum, but this is debatable due to how they calibrate the instrument), so puting a prior on say sigma8 should take it bang on 2.7. It also weakens constraints to the point that h0=0.5 Omega_m=1 is fine again, provided tcmb=3.2... :)

Simon DeDeo
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### Redshift of CMB temperature

I think for effects in inhomogenous cosmologies the breakdown of the 1/a would definitely show up in lab-based experiments (it's possible for it not to break the lab results in the "pure" case of comparing homogenous FRW with static Schwartzschild.)

The extra-dimensional case is interesting, I hadn't thought of that, but I think that somewhere hidden in there is a case of Lorentz violation (e.g., in fixing a brane in the higher dimensional case.)

Syksy Rasanen
Posts: 119
Joined: March 02 2005
Affiliation: University of Helsinki

### Redshift of CMB temperature

What kind of laboratory experiments do you mean?

I don't understand the comment about Lorentz-invariance. The FRW solutions already break Lorentz-invariance. For an example of what I had in mind with regard to extra dimensions, see hep-th/0509225, where there are toroidal extra dimensions (and no branes).

Simon DeDeo
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### Redshift of CMB temperature

FRW breaks Lorentz invariance, but the photon doesn't couple to it (well, not after recombination, at least.) You want to break the relationship between the energy and momentum of the photon, you are going to have to break Lorentz invariance. If you have a brane, and the photon's propagation changes depending on whether it is in our out of the brane, then you are producing a kind of Lorentz violation that will get you off the ground.

If you are going to break the redshifting relationship through inhomogeneites (while leaving the relationship unchanged in the homogenous case), this has to happen because something funny is happening when photons propagate in a field without spacelike Killing vectors, i.e., up and down gravitational field gradients, and this would show up in say GPS, or anything Pound-Rebka-esque.

I guess it's tricky, however, for me to know what to think without a specific model! I may be missing the point of your question.

[Edit: just saw you linked a compact-no-brane example, I will have to read it this weekend.]

Syksy Rasanen
Posts: 119
Joined: March 02 2005
Affiliation: University of Helsinki

### Redshift of CMB temperature

I don't follow you on Lorentz invariance. What do you mean when you say that the photon does not couple to the FRW spacetime? In FRW models, redshift is due to expansion, which implies breaking of Lorentz invariance.

For a general inhomogeneous spacetime, however, the redshift (i.e. change in photon energy) is not solely due to expansion. E.g. when photons climb out ot gravitational potential wells, they lose energy and thus gain redshift. In perturbed FRW universes, this is of course covered by the well-known ISW and RS effects. In a non-perturbatively inhomogeneous space, the situation is more complicated, and e.g. the redshift-luminosity distance relatioship can be very different from that given just by a scale factor (see e.g. astro-ph/0609120). (Let me say, though, that I expect the contribution to the redshift which does not come from the scale factor to be small for a realistic model of the universe, modulo the effect of spatial curvature).

In fact, for a general inhomogeneous space, the emergence of the scale factor average description is an unsolved problem; see my comments, and references, in thread http://cosmocoffee.info/viewtopic.php?t=684&highlight= .

Simon DeDeo
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### Redshift of CMB temperature

I see what you are aiming at; we seem to have two totally different things in mind.

I was thinking of an upset to the time-changes-wavelength-changes-energy-changes-gravity relationship by upsetting the the "wavelength-changes-energy" part. You are thinking about doing it by upsetting the "time-changes-wavelength" part.

This is why I was going on and on about Lorentz violation and you were like what are you going on about! In the homogenous universe, you can upset the "wavelength-changes-energy" part without futzing QED and violating lab tests, but if you want to try to do it using climbing in and out of wells, keeping the homogenous case standard, then you will violate GPS, e.g..

On the other hand, if you want to upset the expansion history (or what have you) by fiddling the time-changes-wavelength part, you can have a completely standard QED photon.

I think this clarifies why we've been missing each other's points!

Syksy Rasanen
Posts: 119
Joined: March 02 2005
Affiliation: University of Helsinki

### Redshift of CMB temperature

Right, right...

Martin Landriau
Posts: 1
Joined: June 04 2007
Affiliation: Max-Planck-Institut für extraterrestrische Physik

### Redshift of CMB temperature

Many of the papers mentioned only put constraints on $T_{cmb}$ at $z>0$. However, there is a paper measuring it at $z=2.34$ to be between 6 and 14K, which is consistent with $1/a$ evolution. The reference is:

Srianand, Petitjean & Ledoux, Nature, 408, 931-935 (2000).

Martin