Asymptotic Scalar Field Cosmology in String Theory

TL;DR

This paper investigates the late-time behavior of scalar field cosmologies in string theory, providing bounds on parameters that ensure decelerated expansion and consistency with the Distance Conjecture.

Contribution

It establishes inequalities relating the decay rates of potentials and particle masses, supporting the consistency of asymptotic scalar field cosmology with string theory conjectures.

Findings

The Hubble scale decays exponentially with the scalar field.

Light particle towers remain at or above the Hubble scale at late times.

The cosmology satisfies strong and dominant energy conditions.

Abstract

Asymptotic (late-time) cosmology depends on the asymptotic (infinite-distance) limits of scalar field space in string theory. Such limits feature an exponentially decaying potential $V \sim \exp(- c \phi)$ with corresponding Hubble scale $H \sim \sqrt{\dot \phi^2 + 2 V} \sim \exp(- \lambda_H \phi)$, and at least one tower of particles whose masses scale as $m \sim \exp( - \lambda \phi)$, as required by the Distance Conjecture. In this paper, we provide evidence that these coefficients satisfy the inequalities $\sqrt{(d-1)/(d-2)} \geq \lambda_H \geq \lambda_{\text{lightest}} \geq 1/\sqrt{d-2}$ in $d$ spacetime dimensions, where $\lambda_{\text{lightest}}$ is the $\lambda$ coefficient of the lightest tower. This means that at late times, as the scalar field rolls to $\phi \rightarrow \infty$, the low-energy theory remains a $d$-dimensional FRW cosmology with decelerated expansion, the light towers of particles predicted by the Distance Conjecture remain at or above the Hubble scale, and both the strong energy condition and the dominant energy condition are satisfied.