The thermal backreaction of a scalar field in dS spacetime. II. Spectrum enhancement and holography

TL;DR

This paper analyzes a quasi-dS spacetime sourced by semiclassical thermal backreaction, casting the bulk scalar equation into a Whittaker form and performing canonical quantization. It finds a leading UV-enhanced curvature spectrum with a blue tilt $n_S\sim 2$, interpreted as a transient constant-roll–like phase that could seed PBH formation. On the holographic side, the authors compute the boundary CFT two-point function and develop a Wilsonian RG flow away from future infinity, deriving beta-functions for single- and double-trace deformations that align with a 3d $Sp(N)$ dual. Collectively, the results bolster a dS/CFT picture with a tractable holographic RG structure and reveal how thermal backreaction imprints bulk dynamics onto boundary correlators and RG flows, with potential observational and theoretical implications. The analysis integrates Whittaker-function mode solutions, BD-like normalization, and holographic renormalization to connect bulk quasi-dS physics with boundary CFT data and RG behavior.

Abstract

We study a spacetime obtained from the semi-classical backreaction computed via the Thermofield dynamics approach in the Poincare patch of de Sitter spacetime. The resulting bulk equation takes the Whittaker form and we examine two distinct applications. At leading order, the co-moving curvature perturbations are shown to match a constant-roll model in the frozen attractor regime, corresponding to a UV enhancement of the spectrum with $n_S \sim 2$. In the holographic context, we compute the CFT two-point function at the future boundary, and away from it we construct the flow-equation of the dual QFT that matches beta-function of the Sp(N ) model in three dimensions.