Pre-big bang geometric extensions of inflationary cosmologies

TL;DR

This paper introduces geometric extensions of Robertson-Walker spacetimes that include a lightlike big bang, providing a continuous and differentiable structure across the initial singularity, aligning with quantum gravity insights.

Contribution

It presents a novel geometric extension of cosmologies with a lightlike big bang, incorporating continuous metrics and geodesics across the singularity.

Findings

Spacelike geodesics are continuous across the big bang.

The extended big bang is lightlike and inherits geometric structure.

The extension aligns with quantum gravity perspectives.

Abstract

Robertson-Walker spacetimes within a large class are geometrically extended to larger cosmologies that include spacetime points with zero and negative cosmological times. In the extended cosmologies, the big bang is lightlike, and though singular, it inherits some geometric structure from the original spacetime. Spacelike geodesics are continuous across the cosmological time zero submanifold which is parameterized by the radius of Fermi space slices, i.e, by the proper distances along spacelike geodesics from a comoving observer to the big bang. The continuous extension of the metric, and the continuously differentiable extension of the leading Fermi metric coefficient $g_{\tau\tau}$ of the observer, restrict the geometry of spacetime points with pre-big bang cosmological time coordinates. In our extensions the big bang is two dimensional in a certain sense, consistent with some findings in quantum gravity.