Holography, Diffeomorphisms, and Scaling Violations in the CMB

TL;DR

This work shows that a late-time boundary regulator in inflationary spacetimes necessitates local boundary counterterms to preserve diffeomorphism invariance. It derives the quadratic action for fluctuations in a gauge-invariant form, including boundary contributions, and frames inflation as a holographic RG flow governed by Callan-Symanzik equations. Solving these equations yields RG-improved expressions for the scalar and tensor power spectra, with the scalar index $n_s-1= -\beta^2-2\gamma$ and tensor index $n_t= -\beta^2$, matching standard slow-roll results when $\beta^2=2\bar{\epsilon}$ and $\gamma=\bar{\epsilon}-\bar{\eta}$. The approach provides a holographic perspective on cosmology, a method to resum large logs in the CMB spectrum, and a framework to explore infrared universality via boundary counterterms. It also establishes connections to AdS/CFT-like structures and clarifies how diffeomorphism invariance shapes cosmological observables.

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.