The thermodynamic evolution of the cosmological event horizon

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 δR e in response to a uniform fluctuation δρ in the average cosmic background density ρ. 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 δρ/ρ is constant. The respective variations 2πR e δR e and δE 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 dS e =PdV e −dE e , where V e is the enclosed volume and P is the average cosmic pressure.