Stochastic inflation and entropy bound in de Sitter spacetime

We analyze the entropy behavior of the de Sitter spacetime during the inflationary phase. In the de Sitter spacetime, a cosmological horizon that constrains the causal accessible region of an observer, exhibits thermal properties analogous to the event horizon of a black hole. From the principle of holography, the entropy within the causally connected region for an observer is constrained by the area of its boundary. This entropy bound is violated in the late stage of inflation. To address the issue of entropy bound violation from a perspective of quantum information, we adopt the stochastic approach to cosmic inflation. To reformulate the issue of entropy bound in the inflation, we follow the derivation of the Page curve in the black hole context. By adopting the volume-weighted probability distribution for the inflaton field, we obtain a meaningful entropy behavior in the de Sitter spacetime.