Trans-Planckian Censorship and Spacetime Singularities

We study the effects of trans-Planckian censorship conjecture (TCC) bounds on geodesic completeness of spacetime and the associated existence for an infinite proper time. Using Gronwall’s lemma, TCC bounds can be derived directly, leading to a result about the absence of blowup solutions. We show that the TCC provides part of the required criteria for geodesic completeness, and we then provide the remaining ones, the norm of the extrinsic curvature being bounded away from zero. We also discuss the importance of these results for the classical evolution of Friedmann universes under the assumptions of global and regular hyperbolicity. © 2023 by the authors.