Can Moduli Fields parametrize the Cosmological Constant?

TL;DR

This paper investigates whether string/M moduli fields can serve as a source of the cosmological constant or quintessence, analyzing their potential and evolution in the context of T-duality and superpotential functions.

Contribution

It demonstrates that moduli fields with polynomial superpotentials cannot produce an accelerating universe and explores the conditions under which moduli energy density can dominate cosmological evolution.

Findings

Moduli fields with polynomial superpotentials do not lead to acceleration.

The potential at large T behaves as a double exponential, causing rapid decay.

Finite moduli mass results in energy density redshifting faster or equal to matter.

Abstract

We study the cosmological evolution of string/M moduli fields T. We use T-duality to fix the potential and show that the superpotential W is a function of the duality invariant function j(T) only. If W is given as a finite polynomial of j then the moduli fields {\it do not} give an accelerating universe, i.e. they {\it cannot} be used as quintessence. Furthermore, at T >>1 the potential is given by a double exponential potential V \simeq e^{-a e^{\sqrt{2} T}} leading to a fast decaying behaviour at large times. For moduli potentials with a finite v.e.v. of T the energy density redshift is model dependent but if T has a finite mass, m < \infty, then the moduli energy density redshifts faster or equal to matter. Only if the moduli mass is infinite can the moduli energy density dominate the universe independently of the initial conditions.