Weyl Anomaly and Initial Singularity Crossing

TL;DR

This paper investigates how Weyl anomaly quantum corrections modify the initial singularity in FLRW cosmology, transforming it from a big bang to a sudden singularity and enabling a geodesically complete extension.

Contribution

It demonstrates that Weyl anomaly effects change the nature of the initial singularity and allows for a $C^1$ extension of spacetime, ensuring geodesic completeness in semiclassical gravity.

Findings

The singularity is weak and admits a geodesic extension.

Weyl anomaly converts the big bang into a sudden singularity.

The extended spacetime remains consistent with Friedmann and Raychaudhuri equations.

Abstract

We consider the role of quantum effects, mainly, Weyl anomaly in modifying FLRW model singular behavior at early times. Weyl anomaly corrections to FLRW models have been considered in the past, here we reconsider this model and show the following: The singularity of this model is weak according to Tipler and Krolak, therefore, the spacetime might admit a geodesic extension. Weyl anomaly corrections changes the nature of the initial singularity from a big bang singularity to a sudden singularity. The two branches of solutions consistent with the semiclassical treatment form a disconnected manifold. Joining these two parts at the singularity provides us with a $C^1$ extension to nonspacelike geodesics and leaves the spacetime geodesically complete. Using Gauss-Codazzi equations one can derive generalized junction conditions for this higher-derivative gravity. The extended spacetime obeys Friedmann and Raychaudhuri equations and the junction conditions. The junction does not generate Dirac delta functions in matter sources which keeps the equation of state unchanged.