For example, in [3, 28], Maxwell-Boltzmann distribution functions are used to calculate the thermodynamics of photon gas. Reference [3] is based on model 1.

We must note that Camacho and Macias [30] have already visited the thermodynamics of photon gas within this model.

Thermodynamics of Photon Gas with Deformed Dispersion Relation in Model 1

The frequency distribution of the zero point energy is then reconsidered in Section 5, the cosmic equilibrium of a zero point energy photon gas is elaborated in Section 6, and the acceleration of the expansion is estimated in Section 7.

6 Equilibrium of a photon gas in its gravitational field

In a gas cloud of photons of zero point energy, there is an antigravity force due to the photon gas pressure gradient, and a gravitation force due to the intrinsic mass of the same photons as determined by the total energy according to Einstein's mass-energy relation.

Thermodynamics of photon gas has been investigated explicitly within the Magueijo-Smolin Lorentz invariant DSR model [24].

Photon Gas Thermodynamics in Noncommutative Spacetime

The only difference is that we are going to employ Bose-Einstein distribution function to solve the partition function for photon gas. As photons are spin-one massless quantum particles, it is mandatory to use Bose-Einstein distribution.

When subjecting local energy conservation in a Friedmann-Lemaitre-Robertson-Walker (FLRW) universe to this equation of state the numerical temperature (T)-redshift (z) relation (T(z)) of the CMB follows; see Figure 1 [27, 28], where a comparison with the conventional U(1)

photon gas is shown.

We consider two cases: ideal gas and photon gas. It is worth mentioning that a different version of GUP has been studied with ideal gas in [46, 47].

Using the partition functions, we determine all thermodynamical properties of the photon gas. Entropy and internal energy density, respectively, are as follows: