Arrow of Time in String Theory

TL;DR

This paper proposes that string theory's concept of creation from nothing explains the Arrow of Time by ensuring initial spatial sections are locally isotropic, thus setting the inflaton in a minimal-entropy state and resolving classical divergence issues.

Contribution

It introduces a string-theoretic mechanism for the Arrow of Time that leverages deep geometric theorems to explain initial conditions and entropy states.

Findings

Initial spatial sections are forced to be locally isotropic.

The inflaton is set into a minimal-entropy state.

The theory accounts for the Arrow of Time in black holes and cosmic contraction.

Abstract

Inflation allows the problem of the Arrow of time to be understood as a question about the structure of spacetime: why was the intrinsic curvature of the earliest spatial sections so much better behaved than it might have been? This is really just the complement of a more familiar problem: what mechanism prevents the extrinsic curvature of the earliest spatial sections from diverging, as classical General Relativity suggests? We argue that the stringy version of "creation from nothing", sketched by Ooguri, Vafa, and Verlinde, solves both of these problems at once. The argument, while very simple, hinges on some of the deepest theorems in global differential geometry. These results imply that when a spatially toral spacetime is created from nothing, the earliest spatial sections are forced to be [quasi-classically] exactly locally isotropic. This local isotropy, in turn, forces the inflaton into its minimal-entropy state. The theory explains why the Arrow does not reverse in black holes or in a cosmic contraction, if any.