Decoupling Inflation From the String Scale

TL;DR

This paper explores how to maintain initial homogeneity in string theory inflation models by analyzing a pre-inflationary phase with compact negatively curved spaces, addressing stability and Casimir energy effects.

Contribution

It provides an estimate of the coupling suppression needed to stabilize pre-inflationary spacetime with Casimir energy in string theory models.

Findings

Pre-inflationary spacetime can be stable despite NEC violation.

Coupling suppression can mitigate Casimir energy effects.

Compact negatively curved spaces facilitate initial homogeneity.

Abstract

When Inflation is embedded in a fundamental theory, such as string theory, it typically begins when the Universe is already substantially larger than the fundamental scale [such as the one defined by the string length scale]. This is naturally explained by postulating a pre-inflationary era, during which the size of the Universe grew from the fundamental scale to the initial inflationary scale. The problem then arises of maintaining the [presumed] initial spatial homogeneity throughout this era, so that, when it terminates, Inflation is able to begin in its potential-dominated state. Linde has proposed that a spacetime with compact negatively curved spatial sections can achieve this, by means of chaotic mixing. Such a compactification will however lead to a Casimir energy, which can lead to effects that defeat the purpose unless the coupling to gravity is suppressed. We estimate the value of this coupling required by the proposal, and use it to show that the pre-inflationary spacetime is stable, despite the violation of the Null Energy Condition entailed by the Casimir energy.