Thermodynamics of scale factor dual universes

The thermodynamical aspects of the conformal time scale factor duality (CSFD) of cosmological models within Einstein gravity are investigated. We derive the CSFD transformations of the thermodynamical quantities describing the thermal evolution of the matter fluid and of the apparent horizon. The thermodynamical properties of the self-dual cosmological models with a modified Chaplygin gas are studied in detail. We deduce the restrictions on the equation of state parameters that allow us to extend scale factor duality as an UV/IR symmetry of the cosmological models consistent with their thermodynamical behavior.

Figure 1

Behavior of the speed of sound for different values of $\delta$: blue, $\delta >\frac{3}{2}$; brown, $1<\delta <\frac{3}{2}$; black, $\frac{3}{4}<\delta <1$; red, $0<\delta <\frac{3}{4}$.

Figure 2

Dual temperatures related by Eq. (20), for $\delta >0$. Dashed lines correspond to $0<\delta <\frac{3}{4}$ and dotted lines to $\delta >\frac{3}{4}$. The diagonal line corresponds to the limiting case $\delta =\frac{1}{2}$.