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]

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

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]

Yes but how do photons lead to expansion pressure?

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]

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.

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 http://en.wikipedia.org/wiki/Thermodynamics_of_the_universe - as radiation energy drops with the 4th power of space expansion, we "lose" energy if space expands.

 

[Chalnoth]

Yes but how do photons lead to expansion pressure?

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]

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.

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

 

[Chalnoth]

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

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

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

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

By contrast, with photons, $p = \rho/3$, so that we pick up an extra factor reducing the expansion, leading to a photon gas reducing the expansion by $-8\pi \rho G/3$, 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]

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

Yes.

 

[bcrowell]

We have a FAQ about this: https://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 $\rho/3$.

Now, what happens if we cause this box to expand in size? Well, if the box expands by a factor of $a$, 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]

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 $\rho/3$.

Now, what happens if we cause this box to expand in size? Well, if the box expands by a factor of $a$, 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.

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.

 

[atyy]

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.

It seems a not uncommon analogy:
http://books.google.com/books?id=kN...ce=gbs_ge_summary_r&cad=0#v=onepage&q&f=false (p343)
http://www.astro.caltech.edu/~george/ay21/readings/peacock_cosmology_notes.pdf
http://www2.ph.ed.ac.uk/teaching/course-notes/documents/118/1703-AstrophysicalCosmology.pdf

 

[julcab12]

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 $\rho/3$.

Now, what happens if we cause this box to expand in size? Well, if the box expands by a factor of $a$, 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.

Good analogy but for noobies like me. It would be a good thing if you mention such limitations, conditions and a brief elaboration of each component first to avoid misconceptions. :shy:

 

[Chalnoth]

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.

It is a different system, but I think it is rather interesting that the math works out identically.

 

[Chalnoth]

Good analogy but for noobies like me. It would be a good thing if you mention such limitations, conditions and a brief elaboration of each component first to avoid misconceptions. :shy:

It's not really an analogy. It's a slightly different system that behaves in the exact same way mathematically. This is at least suggestive that we can think of gravity as soaking up the lost energy in the expanding photon field.

 

[atyy]

In the Harrison textbook I linked to #18 there is an extensive discussion of the analogy (p349-350). He says it's ok for things that don't depend on spatial curvature. He contrasts two physicists, one doing the full GR calculation and one doing the box calculation. He does say that the GR physicist will be surprised that after evaluating all the difficult integrals, that he gets the same answer as the simple minded box physicist. He also says that energy is not conserved in the box. He does say that the analogy fails in that in the box, energy is still conserved in box + surroundings, whereas in the universe, energy is simply not conserved.

 

[JuanCasado]

The analogy described seems reasonable and clarifying to me. However, the amount of ordinary matter within the observable universe results to be similar to the amount of energy lost by CBR since decoupling...
Just an accident by mere chance? or perhaps a kind of new coincidence problem in cosmology?

 

[Chalnoth]

The analogy described seems reasonable and clarifying to me. However, the amount of ordinary matter within the observable universe results to be similar to the amount of energy lost by CBR since decoupling...
Just an accident by mere chance? or perhaps a kind of new coincidence problem in cosmology?

I don't think there can be anything particularly special here, at least not anything pointing to new physics.

The issue is that the radiation energy density at decoupling is fixed by the fact that a hydrogen-helium plasma turns to a gas at around 2970K. The baryon energy density, on the other hand, was set by the amount of imbalance between normal matter and anti-matter in the very early universe, which was decided by physics at extremely high temperatures when the radiation energy density was vastly, vastly higher than the matter energy density.

Now, since the baryon asymmetry was determined in the very early universe, as the temperature dropped and various forms of matter became non-relativistic, they dumped their energy into photons. But the various times that occurred also happened at much higher temperatures when the photon and baryon energy densities were extremely different.

So no, I don't think there's anything particularly special here.