Instanton Cosmology and Domain Walls from M-theory and String Theory

TL;DR

This work derives exact lower-dimensional Lagrangians from sphere compactifications of M-theory and string theory, focusing on breathing and squashing modes to obtain scalar potentials that drive cosmological dynamics. It demonstrates that the resulting theories harbor supersymmetric domain-wall (membrane) solutions, which oxidize to familiar extremal p-branes, and also admit cosmological instanton solutions obtainable via Wick rotation or AdS reductions. While some solutions resemble Hawking–Turok scenarios, detailed analysis reveals important distinctions rooted in the specific exponential potentials and higher-dimensional origins, with domain-wall patching providing a mechanism to tame singularities. Collectively, the paper establishes a concrete bridge between higher-dimensional supergravity compactifications and lower-dimensional cosmological/brane configurations, enriching the toolkit for open-universe and inflationary model-building within a string/M-theory framework.

Abstract

The recent proposal by Hawking and Turok for obtaining an open inflationary universe from singular instantons makes use of low-energy effective Lagrangians describing gravity coupled to scalars and non-propagating antisymmetric tensors. In this paper we derive some exact results for Lagrangians of this type, obtained from spherical compactifications of M-theory and string theory. In the case of the S^7 compactification of M-theory, we give a detailed discussion of the cosmological solutions. We also show that the lower-dimensional Lagrangians admit domain-wall solutions, which preserve one half of the supersymmetry, and which approach AdS spacetimes near their horizons.