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

TL;DR

This work tackles decoupling in FRW cosmologies by embedding vacuum/state choices into a boundary action and analyzing their evolution under Wilsonian RG flow. The authors identify the leading four dimension-four irrelevant boundary operators and show that they induce observable corrections to the inflationary power spectrum that scale as $H/M$, while backreaction remains under control for generic boundary choices. A key result is that the BD vacuum corresponds to a boundary condition that is effectively a fixed point of boundary RG flow in de Sitter space, with corrections being calculable and independent of the boundary location $y_0$. The framework provides a principled, covariant EFT approach to transplanckian physics in cosmology, clarifying the role of initial-state choices and offering a concrete link to potential CMB signatures, while also connecting to discussions around α-states.

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.