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arXiv · 1803.07085

Maximal extensions and singularities in inflationary spacetimes

Daisuke Yoshida·Jerome Quintin
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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 ratio $\dot{H}/a^2$ diverges at the boundary, where $\dot{H}$ and $a$ represent the time derivative of the Hubble parameter and the scale factor, respectively. On the other hand, if the ratio $\dot{H}/a^2$ 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.

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Daisuke Yoshida, Jerome Quintin. 2018-03-19. Maximal extensions and singularities in inflationary spacetimes. https://doi.org/10.1088/1361-6382%2Faacf4b

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