An effective theory of initial conditions in inflation

TL;DR

This paper develops a renormalization framework for initial conditions in inflationary cosmology, showing how to include effects of new physics in the cosmic microwave background calculations by adding boundary counterterms.

Contribution

It introduces a method to renormalize divergences from initial state modifications in inflation, distinguishing between bulk and boundary divergences and providing a systematic way to handle them.

Findings

Bulk divergences match standard vacuum renormalization.

Boundary divergences are renormalized with boundary counterterms.

States close to vacuum require only relevant or marginal counterterms.

Abstract

We examine the renormalization of an effective theory description of a general initial state set in an isotropically expanding space-time, which is done to understand how to include the effects of new physics in the calculation of the cosmic microwave background power spectrum. The divergences that arise in a perturbative treatment of the theory are of two forms: those associated with the properties of a field propagating through the bulk of space-time, which are unaffected by the choice of the initial state, and those that result from summing over the short-distance structure of the initial state. We show that the former have the same renormalization and produce the same subsequent scale dependence as for the standard vacuum state, while the latter correspond to divergences that are localized at precisely the initial time hypersurface on which the state is defined. This class of divergences is therefore renormalized by adding initial-boundary counterterms, which render all of the perturbative corrections small and finite. Initial states that approach the standard vacuum at short distances require, at worst, relevant or marginal boundary counterterms. States that differ from the vacuum at distances below that at which any new, potentially trans-Planckian, physics becomes important are renormalized with irrelevant boundary counterterms.