Renormalization of initial conditions and the trans-Planckian problem of inflation

TL;DR

This paper investigates how initial conditions in scalar field theories affect their renormalization, revealing that boundary divergences can be managed with counterterms, which influence the evolution of initial states during inflation.

Contribution

It demonstrates the renormalization process for nontrivial initial conditions in flat space and introduces boundary counterterms that control divergences and initial state evolution.

Findings

Boundary divergences are confined to initial condition surfaces.

Boundary counterterms effectively remove divergences.

Initial conditions undergo a renormalization group flow.

Abstract

Understanding how a field theory propagates the information contained in a given initial state is essential for quantifying the sensitivity of the cosmic microwave background to physics above the Hubble scale during inflation. Here we examine the renormalization of a scalar theory with nontrivial initial conditions in the simpler setting of flat space. The renormalization of the bulk theory proceeds exactly as for the standard vacuum state. However, the short distance features of the initial conditions can introduce new divergences which are confined to the surface on which the initial conditions are imposed. We show how the addition of boundary counterterms removes these divergences and induces a renormalization group flow in the space of initial conditions.