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

TL;DR

This paper investigates the effects of scalar field backreaction in de Sitter spacetime, revealing spectrum enhancement during transient inflation and exploring holographic dualities with a three-dimensional QFT.

Contribution

It provides a detailed analysis of spectrum enhancement due to backreaction and establishes a connection between bulk dynamics and boundary QFT in de Sitter space.

Findings

UV spectrum is enhanced with a blue tilt (n_S ~ 2) during late-time inflation.

The spectrum enhancement does not impact CMB-scale perturbations.

A holographic duality is constructed linking bulk dynamics to a 3D Sp(N) model.

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 $n_S \sim 2$. This blue tilt arises only for modes exiting the horizon during a transient late-time phase of inflation and therefore does not affect perturbations in the CMB scale. 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 the beta-function of the Sp(N ) model in three dimensions.