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

publication date

  • October 2022

issue

  • 8, 085003

volume

  • 106

International Standard Serial Number (ISSN)

  • 2470-0010

Electronic International Standard Serial Number (EISSN)

  • 2470-0029

abstract

  • It was recently pointed out that linear quantum fields phi(x) can be meaningfully propagated across the big renormalized observables ( phi 2(x))ren and ( Tab(x))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 spacetimes 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 ( phi(x) phi(x')); ( phi(x))ren and ( Tab(x))ren in closed and open universes for minimally coupled massless scalar fields and discuss the ambiguities in the definition of ( Tab(x))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 [L. H. Ford and L. Parker, Phys. Rev. D 16, 245 (1977)] 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 spacetime is not globally hyperbolic because of the singularity, and suggest directions for further work.

subjects

  • Astronomy
  • Mathematics
  • Physics

keywords

  • stress tensor; adiabatic regularization; quantum cosmology; functional analytical methods; mathematical physics methods