The Fate of the Alpha-Vacuum

TL;DR

This paper investigates the stability of different invariant vacua in de Sitter space for a scalar field, revealing that only the Euclidean vacuum avoids problematic divergences in interacting theories.

Contribution

It demonstrates that among the family of de Sitter invariant vacua, only the Euclidean vacuum remains free of linear divergences in one-loop corrections for interacting scalar fields.

Findings

Most vacua exhibit linear divergences in loop corrections

Only the Euclidean vacuum allows de Sitter invariant counterterms

Implications for selecting physical vacua in de Sitter space

Abstract

de Sitter space-time has a one complex parameter family of invariant vacua for the theory of a free, massive scalar field. For most of these vacua, in an interacting scalar theory the one loop corrections diverge linearly for large values of the loop momentum. These divergences are not of a form that can be removed by a de Sitter invariant counterterm, except in the case of the Euclidean, or Bunch-Davies, vacuum.