Temperature evolution of the FRW universe filled with modified Chaplygin gas

The thermodynamical evolution of the modified Chaplygin gas (MCG) with equation of state p=Bρ−Aρ−α is studied in the context of the Friedmann flat cosmological model. The temperature as a function of redshift z is obtained. In order to describe the universe since the radiation era, the constant B is chosen to be B=1/3. Today's temperature of 2.7 K and the temperature at decoupling (z≈1100) are used to fix the values of the parameters A and α, yielding α=1/4 and A=(B+1)ΩXρ0α+1=(4/3)0.7ρ05/4. With these values, the redshift of the transition from positive to negative acceleration is calculated to be zc=0.18. Using observational data for the redshift at a¨=0 and fixing B=1/3, the best values for the other parameters are α=1/4 and ΩX=0.75, yielding T(z=1100)≈4000K and zc=0.25.