Searching for Inflation in Simple String Theory Models: An Astrophysical Perspective
Mark P. Hertzberg, Max Tegmark, Shamit Kachru, Jessie Shelton, Onur Ozcan
TL;DR
This work systematically probes whether slow-roll inflation can be embedded in simple string-theory constructions by deriving a 4D moduli-action from 10D Type IIA supergravity with fluxes and analyzing three explicit toroidal models (DGKT, VZ, IW). Despite an infinite landscape of flux vacua, the inflaton potentials share the same shape up to an overall scale, and comprehensive numerical scans yield no region with $oldsymbol{B5}<1$ and $oldsymbol{2}$ small enough for inflation; the vacua are predominantly AdS and the kinetic sector is governed by a logarithmic Kähler metric, making slow-roll difficult. The study identifies three obstacles to inflation in these simple models: the prevalence of AdS vacua, nontrivial moduli-space geometry, and flux-scaling symmetries that limit potential tuning. It suggests that more complex constructions—such as richer Calabi–Yau geometries, non-geometric fluxes, or non-perturbative effects—are likely required to realize viable string-theoretic inflation, and highlights directions for future multi-field or statistical analyses of the landscape. Overall, the results illustrate that embedding inflation in the string landscape is challenging and may require moving beyond the simplest toroidal, tree-level setups to capture realistic cosmology.
Abstract
Attempts to connect string theory with astrophysical observation are hampered by a jargon barrier, where an intimidating profusion of orientifolds, Kahler potentials, etc. dissuades cosmologists from attempting to work out the astrophysical observables of specific string theory solutions from the recent literature. We attempt to help bridge this gap by giving a pedagogical exposition with detailed examples, aimed at astrophysicists and high energy theorists alike, of how to compute predictions for familiar cosmological parameters when starting with a 10-dimensional string theory action. This is done by investigating inflation in string theory, since inflation is the dominant paradigm for how early universe physics determines cosmological parameters. We analyze three explicit string models from the recent literature, each containing an infinite number of "vacuum" solutions. Our numerical investigation of some natural candidate inflatons, the so-called "moduli fields", fails to find inflation. We also find in the simplest models that, after suitable field redefinitions, vast numbers of these vacua differ only in an overall constant multiplying the effective inflaton potential, a difference which affects neither the potential's shape nor its ability to support slow-roll inflation. This illustrates that even having an infinite number of vacua does not guarantee having inflating ones. This may be an artifact of the simplicity of the models that we study. Instead, more complicated string theory models appear to be required, suggesting that explicitly identifying the inflating subset of the string landscape will be challenging.