Integrable Scalar Cosmologies I. Foundations and links with String Theory

TL;DR

This paper constructs and analyzes integrable scalar cosmological models with exponential potentials, exploring their behavior, links to string theory, and implications for inflation and spectral indices.

Contribution

It introduces new integrable scalar cosmologies, examines their dynamics, and connects them to string theory mechanisms like brane supersymmetry breaking.

Findings

Scalar fields emerge from singularities while climbing steep potentials.

Collapse occurs when scalar settles at negative potential extrema.

Wrapped branes can produce inflationary phases with spectral indices near 0.96.

Abstract

We build a number of integrable one--scalar spatially flat cosmologies, which play a natural role in inflationary scenarios, examine their behavior in several cases and draw from them some general lessons on this type of systems, whose potentials involve combinations of exponential functions, and on similar non--integrable ones. These include the need for the scalar to emerge from the initial singularity while climbing up sufficiently steep exponential potentials ("climbing phenomenon") and the inevitable collapse in a big Crunch whenever the scalar tries to settle at negative extrema of the potential. We also elaborate on the links between these types of potentials and "brane supersymmetry breaking", a mechanism that ties together string scale and scale of supersymmetry breaking in a class of orientifold models. We show that, under some assumptions that are spelled out in the text, the extended objects of these vacua can inject inflationary phases with discrete values of the spectral index that are determined by the number of unwrapped dimensions of the branes and by the inverse power with which the string coupling $g_s$ enters their world--volume actions. An NS fivebrane, which is interestingly unstable in this class of models, when wrapped on a small internal cycle would yield a spectral index that is amusingly close to the experimentally favored PLANCK value ns ~ 0.96.