CMB energy

[Boud Roukema]

On Mon, 23 Feb 2004, Jarek Rzepecki wrote:

> Hi all,
>   CMB photons are red-shifted due to Universe expansion -> this means that
> the whole CMB energy gets smaller... where does it go?
> pozdrawiam
> 	Jarek


http://adjani.astro.uni.torun.pl/cgi-bin/twiki/view/Cosmo/CosmoFAQ

->

http://www.astro.ubc.ca/people/scott/faq_email.html


There's an FAQ on this but i'm not totally happy with it.


> The photons that are observed in CMB observations have presumably been
> traveling through space undisturbed since sometime after the big
> bang. But thay have apparently lost energy in the process, as their
> wavelength has changed. Where did this energy go? Did it go into the
> gravitational field?
>
> Submitted by jamont at visto.com 4/00
>
> I'm surprised I haven't been asked this before, since it's such a good
> question!
>
> There are several different ways of looking at this. One answer would
> be that the energy goes into the gravitational potential energy of the
> whole Universe.

Really this should be energy density, or energy within some fixed comoving
volume.

> Another answer is that it takes energy to expand the
> Universe, and that this "work" comes out of the contents which are
> expanding.


e.g. pp34, 35 Liddle 2000 polski

> Yet another answer is that the cooling of the CMB as the Universe
> expands is part of a simple relativisitic solution which describes the
> entire Universe, using the theoretical basis of General Relativity,
> which is a well tested theory of gravity. And if part of that solution
> appears to violate energy conservation, then tough!


i would add the special relativistic point of view - energy is not an
absolute quantity.

On scales where curvature is small (much less than a horizon radius),
SR (STW) is valid.

The amount of energy depends on which reference frame you use.

If you stick to one inertial frame, you can think of photons *not*
losing any energy.

E.g. Think of a UV photon which was emitted from a high redshift
galaxy X when (in constant cosmological time) the first amoebae
evolved on Earth and is today absorbed on the Earth.  In the reference
from of galaxy X, just using SR and not GR, the Earth is moving at
extremely high velocity away from galaxy X.

So when the UV photon is absorbed, the calculation for what physically
happens should be made between a UV photon moving at c, and a
spectrometer moving at, e.g. 0.9c.

If we take an alternative inertial frame, where the Earth is at rest,
then of course the energy of the photon in this frame is much lower -
just standard SR.

boud