Cosmological three-coupled scalar theory for the dS/LCFT correspondence

TL;DR

This paper explores the dS/LCFT correspondence in a three-coupled scalar theory during de Sitter inflation, demonstrating how LCFT correlators relate to cosmological power spectra and discussing unitarity via field truncation.

Contribution

It introduces a three-coupled scalar model for higher-order derivatives and applies the dS/LCFT correspondence to connect cosmological perturbations with LCFT correlators.

Findings

Power spectra match LCFT correlators in the superhorizon limit.

The dS/LCFT correspondence is validated for this scalar theory.

A bulk truncation process yields a unitary CFT in the LCFT framework.

Abstract

We investigate cosmological perturbations generated during de Sitter inflation in the three-coupled scalar theory. This theory is composed of three coupled scalars ($\phi_p,p=1,2,3$) to give a sixth-order derivative scalar theory for $\phi_3$, in addition to tensor. Recovering the power spectra between scalars from the LCFT correlators in momentum space indicates that the de Sitter/logarithmic conformal field theory (dS/LCFT) correspondence works in the superhorizon limit. We use LCFT correlators derived from the dS/LCFT differentiate dictionary to compare cosmological correlators (power spectra) and find also LCFT correlators by making use of extrapolate dictionary. This is because the former approach is more conventional than the latter. A bulk version dual to the truncation process to find a unitary CFT in the LCFT corresponds to selecting a physical field $\phi_2$ with positive norm propagating on the dS spacetime.