de Sitter Vacua, Renormalization and Locality

TL;DR

The paper analyzes renormalization in quantum field theory on de Sitter space across the family of α-vacua and shows that, except for the Euclidean vacuum ($\Re(\alpha)=a\to-\infty$) and the antipodal vacuum ($\alpha=0$), perturbation theory requires nonlocal counterterms such as $\delta S \propto \int \phi(x)\phi(x^A)$, rendering the theory nonlocal and likely unphysical. The Euclidean vacuum avoids these nonlocal divergences, while the antipodal vacuum can be interpreted as a theory on the antipodal orbifold related to an analytic continuation from $RP^d$, but it introduces unusual initial-state conditions and potential divergences at the origin of time, complicating the dynamics and backreaction in any quantum-gravitational context. Overall, the work argues that generic α-vacua are poorly behaved in perturbation theory, with the Euclidean vacuum most likely describing sensible physics in de Sitter space, while the antipodal construction remains intriguing but requires careful boundary renormalization and further study. The results have implications for inflationary cosmology and the viability of non-Euclidean vacua in curved spacetimes.

Abstract

We analyze the renormalization properties of quantum field theories in de Sitter space and show that only two of the maximally invariant vacuum states of free fields lead to consistent perturbation expansions. One is the Euclidean vacuum, and the other can be viewed as an analytic continuation of Euclidean functional integrals on $RP^d$. The corresponding Lorentzian manifold is the future half of global de Sitter space with boundary conditions on fields at the origin of time. We argue that the perturbation series in this case has divergences at the origin, which render the future evolution of the system indeterminate without a better understanding of high energy physics.