Initial Conditions for Inflation

TL;DR

This work argues that the one-parameter family of de Sitter-invariant $|\alpha\rangle$ vacua, while well-defined for a free field in exact de Sitter space, becomes physically untenable once gravity is included in an inflationary setting. Through analyses of two-point functions, Unruh detector responses, and the quantum stress-energy tensor, the authors show that $|\alpha\rangle$ states have state-dependent short-distance structure, violate detailed balance, and yield UV divergences or infinite backreaction, effectively collapsing to the thermal vacuum. In an inflating universe, any departure from the thermal vacuum either inflates away quickly or demands extreme fine-tuning to leave observable imprints on the CMB, thereby reinforcing the conventional initial-state choice. The results challenge trans-Planckian initial-state proposals and emphasize that, under standard effective field theory with gravity, the thermal vacuum remains the consistent and natural starting point for inflationary perturbations.

Abstract

Free scalar fields in de Sitter space have a one-parameter family of states invariant under the de Sitter group, including the standard thermal vacuum. We show that, except for the thermal vacuum, these states are unphysical when gravitational interactions are included. We apply these observations to the quantum state of the inflaton, and find that, at best, dramatic fine tuning is required for states other than the thermal vacuum to lead to observable features in the CMBR anisotropy.