Squeezed States in the de Sitter Vacuum

TL;DR

This work reexamines squeezed-state excitations in the de Sitter vacuum by contrasting them with alpha-vacua. It shows that alpha-vacua are problematic in interacting theories, whereas squeezed states can be consistently renormalized using the same local counterterms as the Euclidean vacuum, effectively treating them as excited states rather than true vacua. The authors derive how squeezed-state correlators relate to Euclidean ones through Bogoliubov transformations, analyze free-field propagators with antipodal contributions, and formulate interacting-theory Feynman rules that preserve locality. They further discuss Hadamard conditions and cosmological implications, arguing that such excited-state constructions could yield viable initial conditions for inflation and potentially leave imprints in in-in correlation functions. Overall, the paper provides a coherent framework in which squeezed states are physically acceptable in curved space QFT and clarifies their distinction from alpha-vacua in both theory and cosmology.

Abstract

We discuss the treatment of squeezed states as excitations in the Euclidean vacuum of de Sitter space. A comparison with the treatment of these states as candidate no-particle states, or alpha-vacua, shows important differences already in the free theory. At the interacting level alpha-vacua are inconsistent, but squeezed state excitations seem perfectly acceptable. Indeed, matrix elements can be renormalized in the excited states using precisely the standard local counterterms of the Euclidean vacuum. Implications for inflationary scenarios in cosmology are discussed.