Toward a Unified de Sitter Holography: A Composite $T\bar{T}$ and $T\bar{T}+\Lambda_2$ Flow

TL;DR

This paper proposes a unified holographic framework for de Sitter space by combining $T\bar{T}$ and $T\bar{T}+\Lambda_2$ deformations, supported by energy and entanglement entropy calculations.

Contribution

It introduces a composite flow that unifies two dS holographic models through a novel boundary motion concept, bridging different boundary conditions.

Findings

Computed quasi-local energy in dS static spacetime.

Analyzed holographic entanglement entropy in the extended geometry.

Supported the unified framework with these holographic calculations.

Abstract

In de Sitter (dS) holography, both the dS/CFT correspondence and the dS static patch holography have been extensively studied. In these two holographic frameworks, the dual field theories are defined on spacelike and timelike boundaries, respectively, where the inward motion of the holographic boundary into the bulk corresponds to the $T\bar{T}$ and $T\bar{T}+\Lambda_2$ deformations in the respective dual field theories. In this work, we develop a unified framework for these two dS holographic models by introducing a composite flow that incorporates both $T\bar{T}$ and $T\bar{T}+\Lambda_2$ deformations. We propose that this composite flow corresponds to the inward motion of a spacelike boundary from the asymptotic infinity of dS spacetime, traversing the cosmological horizon and approaching the worldline of a static observer. This proposal is supported by the computation of the quasi-local energy and the holographic entanglement entropy within the dS static spacetime and its extended geometry.