Cosmological Implications of Domain Walls due to Duality Invariant Moduli Sector of Superstring Vacua

TL;DR

This paper explores the cosmological effects of duality-invariant potentials in superstring vacua, focusing on domain walls related to symmetries of the moduli field T, and discusses their formation, stability, and implications for inflation.

Contribution

It introduces a detailed analysis of non-supersymmetric domain walls arising from duality symmetries in superstring models, highlighting their cosmological roles and constraints.

Findings

Two types of domain walls are identified: axionic and Z2 symmetry-related.

Domain walls are bounded by cosmic strings and have scales around 10^{16} GeV.

The study suggests inflation or initial string existence is necessary to resolve domain wall issues.

Abstract

We study cosmological implications of the duality ($PSL(2,{\bf Z})$) invariant potential for the compactification radius $T$, arising in a class of superstring vacua. We show that in spite of having only one minimum in the fundamental domain of the $T$ field there are two types of non-supersymmetric domain walls: one is associated with the discrete Peccei-Quinn symmetry $T\to T+i$, analogous to the axionic domain wall, and another one associated with the noncompact symmetry $T\to 1/T$, analogous to the $Z_2$ domain walls. The first one is bound by stringy cosmic strings. The scale of such domain walls is governed by the scale of gaugino condensation (${\cal O} (10^{16}$ GeV) in the case of hidden $E_8$ gauge group), while the separation between minima is of order $M_{pl}$. We discuss the formation of walls and their cosmological implications: the walls must be gotten rid of, either by chopping by stringy cosmic strings and/or inflation. Since there is no usual Kibble mechanism to create strings, either one must assume they exist $ab initio$, or one must conclude that string cosmologies require inflation. The non-perturbative potential dealt with here appears not to give the needed inflationary epoch.