Does a rigid box of gas cool over cosmological timescales?

[jcap]

According to standard cosmology theory the physical momentum $p$ of both massive and massless particles decay like:
$$p \propto \frac{1}{a(t)}$$
where $a(t)$ is the scale factor as function of cosmological time $t$ (for a derivation see page 12 in the following lecture notes: http://www.damtp.cam.ac.uk/user/db275/Cosmology/Lectures.pdf).

Does this imply that a gas inside a rigid box cools over cosmological timescales (in addition to the effect of external blackbody radiation from the box itself)?

As I understand it one can model a particle with rest mass as a rigid box with massless particles confined inside it (cf. proton mass mostly due to confined gluons). If the momentum of the massless particles decay then that implies that the system itself loses energy as the Universe expands. I presume that the massless particles will no longer redshift once their wavengths are comparable to the size of the box. Therefore the energy of the system as a whole will tend towards a constant value with increasing cosmological time. Does rest mass decay with cosmological time? I presume not as we would have seen the observational consequences of this effect.

 

[PeterDonis]

According to standard cosmology theory the physical momentum $p$ of both massive and massless particles decay

This assumes that the particles are moving freely. If they are confined inside a rigid box, they are not moving freely.

Does this imply that a gas inside a rigid box cools over cosmological timescales (in addition to the effect of external blackbody radiation from the box itself)?

No. See above.