Moduli stabilisation in early superstring cosmology

TL;DR

This paper investigates how thermal effects in early universe string cosmology can stabilize moduli fields, avoiding the cosmological moduli problem by dynamically attracting moduli to local minima at enhanced symmetry points.

Contribution

It demonstrates moduli stabilization via thermal effects in heterotic and type II string models, identifying specific points in moduli space where minima occur, and explores duality relations for stabilization.

Findings

Thermal effects induce effective potentials with local minima at symmetry points.

Moduli acquire decreasing masses, diluting scalar oscillations before nucleosynthesis.

Stabilization occurs at enhanced gauge symmetry or shrinking cycle loci in Calabi-Yau spaces.

Abstract

We study moduli stabilization by thermal effects in the cosmological context. The implementation of finite temperature, which spontaneously breaks supersymmetry, induces an effective potential at one loop level. At the points where extra massless states appear in the string spectrum, the potential develops local minima whose depth depends on the temperature. Moduli attracted to these points acquire dynamical masses which decrease with cosmological evolution. This makes the coherent scalar oscillations dilute before nucleosynthesis, and the cosmological moduli problem is avoided. In particular, we study the effective potential induced by a maximally supersymmetric heterotic string gas for spacetime dimension D>=4, and a gas of type II strings compactified on Calabi-Yau three-folds (D=4). In the former case, the local minima of the potential arise at enhanced gauge symmetry points, which can stabilize all moduli but the dilaton. In the latter case, the local minima are reached at the loci where 2-cycles or 3-cycles in the Calabi-Yau space shrink to zero size, accompanied with either conifold transitions or non Abelian gauge symmetries. This stabilizes the type II moduli which characterize the deformation of these shrinking cycles. Moduli stabilization in the dual string models is also investigated by heterotic/type I S-dualities and type II/heterotic dualities.