M-theory resolution of four-dimensional cosmological singularities via U-duality

TL;DR

This paper demonstrates that U-duality transformations in M-theory can resolve four-dimensional cosmological singularities by lifting solutions to higher dimensions where singularities are absent, especially in non-closed universes.

Contribution

It introduces a method to construct four-dimensional cosmologies from vacuum solutions and shows how U-duality can remove singularities by analyzing higher-dimensional lifts.

Findings

Singularities can be resolved in higher dimensions when only one extra dimension varies with time.

U-duality transformations map singular cosmologies to non-singular ones.

Non-closed Friedmann-Robertson-Walker universes can have their singularities removed in higher-dimensional models.

Abstract

We consider cosmological solutions of string and M-theory compactified to four dimensions by giving a general prescription to construct four-dimensional modular cosmologies with two commuting Killing vectors from vacuum solutions. By lifting these solutions to higher dimensions we analyze the existence of cosmological singularities and find that, in the case of non-closed Friedmann-Robertson-Walker universes, singularities can be removed from the higher-dimensional model when only one of the extra dimensions is time-varying. By studying the moduli space of compactifications of M-theory resulting in homogeneous cosmologies in four dimensions we show that U-duality transformations map singular cosmologies into non-singular ones.