The lost energy of Cosmic Background Radiation

JuanCasado

Could anyone clarify where is gone the energy lost by CBR as the universe expands?
Thank you in advance and happy new year

mfb

General relativity has no global energy conservation, energy can get lost.

Those photons lead to a pressure, which influences expansion of the universe - you could view this as "the energy went into expansion of space".

Drakkith

I've never seen it put quite like that MFB. Can you elaborate? Are you referring to dark energy or something else?

phinds

My understanding is that the universe is expanding because of the pressure of all the energy in the early universe up to and including the surface of last scattering. Dark energy is not believed to cause the expansion, it is causing the ACCELERATION of the expansion.

That is, the current expansion has what you could think of as a base value which has nothing to do with dark energy and then acceleration due to dark energy.

It is the presence of dark energy that was such a surprise when first discovered because the belief was that only the base expansion existed and it would have been slowing down.

Drakkith

Yes but how do photons lead to expansion pressure?

phinds

I don't think it IS now, just that it was prior to the surface of last scattering. The expansion since then has been sort of a ballistic remnant of the expansion at that time. I am NOT sure about that, though. I could be just making it up, but I think that's what I've read.

Drakkith

Ok, but still, how does photon pressure lead to expansion if it's coming from everywhere?

mfb

The FLRW metric depends - apart from initial conditions - on a cosmological constant, energy density and pressure (see section "solution") only. Both energy density and pressure slow expansion - but in the current universe, pressure is negligible.
Energy density and pressure are related via thermodynamics - as radiation energy drops with the 4th power of space expansion, we "lose" energy if space expands.

Chalnoth

The photons don't lead to expansion pressure. The pressure that a photon gas exerts, however, gravitates (there is as much attractive gravity caused by the energy density of photons as by their pressure). This is what makes it so that a universe dominated by photons slows its expansion much more rapidly than one dominated by normal matter, and also what makes photons lose energy as the universe expands.

Drakkith

So photons don't lead to an increase in expansion rate then? They slow it down?

Chalnoth

Yes. They are more efficient at slowing the expansion than normal matter. You can see this in the second Friedmann equation:

[tex]\dot{H} + H^2 = {\ddot{a} \over a}= -{4 \pi G \over 3}\left(\rho + 3p\right)[/tex]

For normal matter, the pressure [itex]p = 0[/itex], and the energy density [itex]\rho[/itex] is positive. So the right hand side is always negative: normal matter always acts to slow the expansion by a factor of [itex]-4\pi \rho G / 3[/itex].

By contrast, with photons, [itex]p = \rho/3[/itex], so that we pick up an extra factor reducing the expansion, leading to a photon gas reducing the expansion by [itex]-8\pi \rho G/3[/itex], or twice as rapid a deceleration compared with normal matter for the same energy density.

Drakkith

What exactly is meant by "photon pressure"? Is this the same thing as normal Radiation pressure?

Mordred

As far as I can tell yes every search I do using Photon pressure returns radiation pressure

Chalnoth

Yes.

bcrowell

We have a FAQ about this: http://www.physicsforums.com/showthread.php?t=506985

Chalnoth

One way to understand why it has this effect is to consider a somewhat different scenario:

Imagine that we have an enclosed box, and within that box is a gas of photons (you can simply imagine the box as having some temperature, which causes it to be filled with radiation). That gas of photons exerts radiation pressure on each wall of the box equal to [itex]\rho/3[/itex].

Now, what happens if we cause this box to expand in size? Well, if the box expands by a factor of [itex]a[/itex], then the photon pressure on each side of the box exerts work on the box. Because the work is in the direction of the motion of the walls of the box, this amounts to a transfer of energy from the photon gas to the walls of the box. In fact, if you calculate the energy transfer, you exactly get the loss of energy of the photon gas that we see as a redshift.

As to why this pressure leads to a faster slowdown of the expansion, well, that's a bit harder to explain. But suffice it to say that pressure is sort of a kind of energy density, and gravity responds just as well to this sort of energy density as it responds to mass energy.

bcrowell

This is incorrect. You're comparing (1) a cosmological spacetime with (2) a system consisting of a box with photons inside. In case 1, energy isn't conserved (as explained in the FAQ linked to in #15). In case 2, energy is conserved.