Decoupling in an expanding universe: backreaction barely constrains short distance effectsin the cosmic microwave background

Abstract

We clarify the status of trans-Planckian effects on the cosmic microwave background (CMB)anisotropy. We do so using the boundary effective action formalism of hep-th/0401164 whichaccounts quantitatively for the cosmological vacuum ambiguity. In this formalismwe can clearly (1) delineate the validity of cosmological effective actions in anexpanding universe. The corollary of the initial state ambiguity is the existence of anearliest time. The inability of an effective action to describe physics before this timedemands that one sets initial conditions on the earliest time hypersurface. Acalculation then shows that CMB anisotropy measurements are generically sensitive tohigh energy corrections to the initial conditions. (2) We compute the one-loopcontribution to the stress tensor due to high energy physics corrections to anarbitrary cosmological initial state. We find that phenomenological bounds on thebackreaction do not lead to strong constraints on the coefficient of the leadingboundary irrelevant operator. Rather, we find that the power spectrum itself isthe quantity most sensitive to initial state corrections. (3) The computation ofthe one-loop backreaction confirms arguments that irrelevant corrections to theBunch–Davies initial state yield non-adiabatic vacua characterized by an energyexcess at some earlier time. However, this excess only dominates over the classicalbackground at times before the ‘earliest time’ at which the effective action is valid.We conclude that the cosmological effective action with boundaries is a fullyself-consistent and quantitative approach to trans-Planckian corrections to the CMB.