Holography, Diffeomorphisms, and Scaling Violations in the CMB

TL;DR

This paper investigates how diffeomorphism invariance affects inflationary spacetime models with a boundary, deriving gauge-invariant actions and connecting boundary correlation functions to CMB spectral predictions.

Contribution

It provides a detailed analysis of boundary conditions and counterterms in inflationary models, linking bulk symmetries to observable CMB scaling violations.

Findings

Gauge invariance achieved with proper counterterms

Correlation functions follow Callan-Symanzik equations

Predicted spectral indices match standard inflationary results

Abstract

We analyze diffeomorphism invariance in inflationary spacetimes regulated by a boundary at late time. We present the action for quadratic fluctuations in the presence of a boundary, and verify that it is gauge invariant precisely when the correct local counterterms are included. The scaling behavior of bulk correlation functions at the boundary is determined by Callan-Symanzik equations which predict scaling violations in agreement with the standard inflationary predictions for spectral indices of the CMB.