Probing cosmological singularities with quantum fields: Open and closed FLRW universes

TL;DR

This paper extends the analysis of quantum fields across cosmological singularities from flat to open and closed FLRW universes, showing that quantum fields remain well-defined and exhibit simplified infrared behavior due to spatial curvature effects.

Contribution

It generalizes previous flat universe results to curved FLRW models, providing explicit expressions and analyzing the behavior of quantum fields at singularities in these settings.

Findings

Quantum fields can be propagated across big bang and crunch singularities in curved FLRW universes.

Infrared divergences are absent in open and closed universes due to spatial curvature acting as a natural cutoff.

Explicit formulas for renormalized quantum observables are derived in curved FLRW models.

Abstract

It was recently pointed out that linear quantum fields $\hat \phi(x)$ can be meaningfully propagated across the big bang (and the big crunch) singularities of spatially flat Friedmann, Lema\^itre, Robertson, Walker (FLRW) universes \cite{ADLS2021}. Recall that $\hat \phi(x)$, as well as renormalized observables $\langle\hat \phi(x)^2 \rangle_{ren}$ and $\langle \hat T_{ab}(x)\rangle_{ren}$, are distribution-valued already in Minkowskian quantum field theories. It was shown that they can be extended as well-defined distributions even when these space-times are enlarged to include the big-bang (or the big crunch). We generalize these results to spatially closed and open FLRW models, showing that this `tameness' of cosmological singularities is not an artifact of the technical simplifications due to spatial flatness. Our analysis also provides explicit expressions of $\langle\hat \phi(x) \hat \phi(x') \rangle_{ren}$, $\langle\hat \phi(x)^2 \rangle_{ren}$ and $\langle \hat T_{ab}(x)\rangle_{ren}$ in closed and open universes for minimally coupled massless scalar fields and discuss the ambiguities in the definition of $\langle \hat T_{ab}(x)\rangle_{ren}$ at the big-bang. While the technical expressions are more complicated than in the spatially flat case, there is also an unexpected conceptual simplification: the infrared divergence \cite{fp} is now absent because, in effect, the spatial curvature provides a natural cutoff. Finally, we further clarify the sense in which quantum field theory can continue to be well defined even though the extended space-time is not globally hyperbolic because of the singularity, and suggest directions for further work.