Decoupling in an expanding universe: boundary RG-flow affects initial conditions for inflation

TL;DR

This paper develops an effective field theory framework for inflationary initial conditions in expanding universes, showing how high-energy physics influences boundary conditions and observable power spectra through RG flow and irrelevant operators.

Contribution

It introduces a Lagrangian approach to boundary conditions in cosmology, incorporating vacuum ambiguity and RG flow effects, and derives high-energy corrections to inflationary power spectra.

Findings

Boundary conditions are sensitive to high-energy physics via irrelevant boundary operators.

Known vacua like Bunch-Davies are consistent with decoupling in this framework.

High-energy corrections to the power spectrum are proportional to Hubble scale and new physics scale.

Abstract

We study decoupling in FRW spacetimes, emphasizing a Lagrangian description throughout. To account for the vacuum choice ambiguity in cosmological settings, we introduce an arbitrary boundary action representing the initial conditions. RG flow in these spacetimes naturally affects the boundary interactions. As a consequence the boundary conditions are sensitive to high-energy physics through irrelevant terms in the boundary action. Using scalar field theory as an example, we derive the leading dimension four irrelevant boundary operators. We discuss how the known vacuum choices, e.g. the Bunch-Davies vacuum, appear in the Lagrangian description and square with decoupling. For all choices of boundary conditions encoded by relevant boundary operators, of which the known ones are a subset, backreaction is under control. All, moreover, will generically feel the influence of high-energy physics through irrelevant (dimension four) boundary corrections. Having established a coherent effective field theory framework including the vacuum choice ambiguity, we derive an explicit expression for the power spectrum of inflationary density perturbations including the leading high energy corrections. In accordance with the dimensionality of the leading irrelevant operators, the effect of high energy physics is linearly proportional to the Hubble radius H and the scale of new physics L= 1/M.