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.Comment: LaTeX plus axodraw figures. v2: minor corrections; refs added. JHEP
style: 34 pages + 18 pages appendi