The thermodynamic evolution of the cosmological event horizon

TL;DR

This paper derives a thermodynamic description of the cosmological event horizon in FRW universes, establishing relations between its radius, entropy, energy, and temperature during different cosmic epochs.

Contribution

It provides an analytical expression for the change in the horizon radius due to density fluctuations and links it to thermodynamic laws in a dynamic cosmological setting.

Findings

Temperature of CEH at any time is E_e/S_e, matching de Sitter temperature asymptotically.

CEH obeys the First Law T_e dS_e = P dV_e - dE_e during radiation dominance and late times.

Derived an analytical relation between horizon radius change and cosmic density fluctuations.

Abstract

By manipulating the integral expression for the proper radius $R_e$ of the cosmological event horizon (CEH) in a Friedmann-Robertson-Walker (FRW) universe, we obtain an analytical expression for the change $\dd R_e$ in response to a uniform fluctuation $\dd\rho$ in the average cosmic background density $\rho$. We stipulate that the fluctuation arises within a vanishing interval of proper time, during which the CEH is approximately stationary, and evolves subsequently such that $\dd\rho/\rho$ is constant. The respective variations $2\pi R_e \dd R_e$ and $\dd E_e$ in the horizon entropy $S_e$ and enclosed energy $E_e$ should be therefore related through the cosmological Clausius relation. In that manner we find that the temperature $T_e$ of the CEH at an arbitrary time in a flat FRW universe is $E_e/S_e$, which recovers asymptotically the usual static de Sitter temperature. Furthermore, it is proven that during radiation-dominance and in late times the CEH conforms to the fully dynamical First Law $T_e \drv S_e = P\drv V_e - \drv E_e$, where $V_e$ is the enclosed volume and $P$ is the average cosmic pressure.