Inflation and de Sitter Thermodynamics

TL;DR

This paper explores the thermodynamics of quasi-de Sitter space during inflation, showing how energy flux and metric perturbations relate to Einstein equations and horizon entropy, with implications for holography and inflation stability.

Contribution

It demonstrates that the thermodynamic law dE=TdS reproduces Friedmann and Einstein equations during inflation, linking horizon thermodynamics with quantum field fluctuations.

Findings

Thermodynamic law reproduces Friedmann equations during inflation.

Metric perturbations cause horizon area fluctuations consistent with Einstein equations.

Horizon entropy variations relate to quantum fluctuations and stochastic inflation.

Abstract

We consider the quasi-de Sitter geometry of the inflationary universe. We calculate the energy flux of the slowly rolling background scalar field through the quasi-de Sitter apparent horizon and set it equal to the change of the entropy (1/4 of the area) multiplied by the temperature, dE=TdS. Remarkably, this thermodynamic law reproduces the Friedmann equation for the rolling scalar field. The flux of the slowly rolling field through the horizon of the quasi-de Sitter geometry is similar to the accretion of a rolling scalar field onto a black hole, which we also analyze. Next we add inflaton fluctuations which generate scalar metric perturbations. Metric perturbations result in a variation of the area entropy. Again, the equation dE=TdS with fluctuations reproduces the linearized Einstein equations. In this picture as long as the Einstein equations hold, holography does not put limits on the quantum field theory during inflation. Due to the accumulating metric perturbations, the horizon area during inflation randomly wiggles with dispersion increasing with time. We discuss this in connection with the stochastic decsription of inflation. We also address the issue of the instability of inflaton fluctuations in the ``hot tin can'' picture of de Sitter horizon.