The Geometry of The Entropic Principle and the Shape of the Universe

TL;DR

This paper develops a systematic framework for assigning Lorentzian spacetimes to Euclidean spaces in string cosmology, revealing that the universe's spatial sections must be flat and compact, advancing understanding of universe creation.

Contribution

It introduces a new framework for relating Euclidean and Lorentzian geometries in string cosmology, extending to higher dimensions and constraining universe shape.

Findings

Spatial sections must be flat and compact

Framework extends to higher-dimensional models

Supports the string-theoretic origin of universe creation

Abstract

Ooguri, Vafa, and Verlinde have outlined an approach to two-dimensional accelerating string cosmology which is based on topological string theory, the ultimate objective being to develop a string-theoretic understanding of "creating the Universe from nothing". The key technical idea here is to assign *two different* Lorentzian spacetimes to a certain Euclidean space. Here we give a simple framework which allows this to be done in a systematic way. This framework allows us to extend the construction to higher dimensions. We find then that the general shape of the spatial sections of the newly created Universe is constrained by the OVV formalism: the sections have to be flat and compact.