Classical resolution of singularities in dilaton cosmologies

TL;DR

This paper analyzes how cosmological solutions in dilaton-gravity models can be understood as trajectories in a 2D Milne space, revealing smooth continuations through singularities and connections to higher-dimensional black hole solutions.

Contribution

It demonstrates a novel geometric framework for resolving cosmological singularities in dilaton models using Milne space trajectories and constructs explicit solutions linking to higher-dimensional black holes.

Findings

Cosmological singularities correspond to Milne horizon crossings.

Trajectories can be smoothly continued through singularities to instanton solutions.

Some solutions lift to black holes in higher dimensions.

Abstract

For models of dilaton-gravity with a possible exponential potential, such as the tensor-scalar sector of IIA supergravity, we show how cosmological solutions correspond to trajectories in a 2D Milne space (parametrized by the dilaton and the scale factor). Cosmological singularities correspond to points at which a trajectory meets the Milne horizon, but the trajectories can be smoothly continued through the horizon to an instanton solution of the Euclidean theory. We find some exact cosmology/instanton solutions that lift to black holes in one higher dimension. For one such solution, the singularities of a big crunch to big bang transition mediated by an instanton phase lift to the black hole and cosmological horizons of de Sitter Schwarzschild spacetimes.