On the power spectrum of inflationary cosmologies dual to a deformed CFT

TL;DR

This paper demonstrates that the inflationary power spectrum in certain holographic cosmologies can be precisely derived from the spectral density of a deformed CFT, confirming the duality's predictive power.

Contribution

It provides an exact holographic computation of the inflationary power spectrum using conformal perturbation theory, linking cosmological observables to CFT correlators.

Findings

Power spectrum inversely proportional to stress tensor trace spectral density

Exact agreement with inflationary predictions to second order in slow roll

Validates holographic duality as a tool for cosmological calculations

Abstract

We analyse slow-roll inflationary cosmologies that are holographically dual to a three-dimensional conformal field theory deformed by a nearly marginal scalar operator. We show the cosmological power spectrum is inversely proportional to the spectral density associated with the 2-point function of the trace of the stress tensor in the deformed CFT. Computing this quantity using second-order conformal perturbation theory, we obtain a holographic power spectrum in exact agreement with the expected inflationary power spectrum to second order in slow roll.