Maximal extensions and singularities in inflationary spacetimes

Abstract

Extendibility of inflationary spacetimes with flat spatial geometry is investigated. We find that the past boundary of an inflationary spacetime becomes a so-called parallely propagated curvature singularity if the ratioḢ/a 2 diverges at the boundary, whereḢ and a represent the time derivative of the Hubble parameter and the scale factor, respectively. On the other hand, if the ratioḢ/a 2 converges, then the past boundary is regular and continuously extendible. We also develop a method to judge the continuous (C 0 ) extendibility of spacetime in the case of slow-roll inflation driven by a canonical scalar field. As applications of this method, we find that Starobinsky inflation has a C 0 parallely propagated curvature singularity, but a small field inflation model with a Higgs-like potential does not. We also find that an inflationary solution in a modified gravity theory with limited curvature invariants is free of such a singularity and is smoothly extendible.

Dual spacetime and nonsingular string cosmology

“…If space-time is described by Einstein gravity and matter obeys energy conditions which are natural from the point of view of point particle theories, then singularities in homogeneous and isotropic cosmology are unavoidable [1]. These theorems in fact extend to inflationary cosmology [2][3][4].…”

Theories with limited extrinsic curvature and a nonsingular anisotropic universe

“…III. However, since we know that a large class of mimetic gravity, including the model (13a), is plagued by ghost/gradient instabilities [28,55,[63][64][65][66]], 5 we focus on the cuscuton-type theory (13b) in Sec. IV.…”

“…Although null geodesics are expected to be past incomplete as in the case of the flat de Sitter universe (see Refs. [4,5]), our formulation ensures that the past boundary is not a scalar curvature singularity at least up to Oð∂ 2 gÞ because the curvature invariants R, R μν R μν , and R μνρσ R μνρσ approach constant values.…”

“…As is well known, a decelerating and expanding universe inevitably has an initial big bang singularity. Even in an inflationary universe, there is a hard-to-avoid initial singularity [4][5][6]. Since classical Einstein gravity should be a low-energy effective theory of some more fundamental theory of quantum gravity, the presence of singularities is expected to be an artifact of the classical theory, and they should be removed if the effects of quantum gravity are taken into consideration.…”

Global spacetime structure of compactified inflationary universe

“…The extensibility of the past boundary due to the difference of scale factors was recently clarified by Ref. [8].…”