de Sitter Duality and Holographic Renormalization

TL;DR

This paper explores the duality between quantum stochastic physics on the boundary and classical thermodynamics in the bulk of de Sitter space, deriving fundamental equations and discussing implications for early universe inflation.

Contribution

It introduces a duality framework for de Sitter space, deriving the Universe equation from renormalization group and thermodynamics, linking quantum stochastic physics and classical thermodynamics.

Findings

Derivation of the Universe equation (EqU) with an ultraviolet fixed point.

Establishment of de Sitter duality between boundary quantum physics and bulk thermodynamics.

Discussion of inflationary scenarios with decreasing epsilon and entropy maximization.

Abstract

We perform the resummation of the infrared logarithms in the inflationary universe. Applying the renormalization group, we derive the stochastic equations as the effective theory at the horizon. We focus on the conformal zero mode to respect local Lorentz symmetry. Under Gaussian approximation, we derive the fundamental equation for the Universe (EqU). We also derive the identical equation from the first law of thermodynamics in a dual geometric picture. We believe it is a convincing evidence for de Sitter duality between quantum stochastic physics on the boundary and classical thermodynamics in the bulk. The equation for the Universe (EqU) possesses the solution with the ultraviolet fixed point. It also contains the inflationary universe with the power potentials. We discuss possible scenarios for the very early universe with decreasing epsilon. We argue inflationary universe subsequently dominates to maximize the entropy and epsilon problem is naturally solved.