Five Dimensional Cosmology in Horava-Witten M-Theory

TL;DR

This paper investigates five-dimensional cosmology within Horava-Witten M-theory, analyzing how matter on branes affects the cosmological evolution and comparing it with Randall-Sundrum models, highlighting the need for non-perturbative potentials.

Contribution

It provides a detailed analysis of brane matter effects in five-dimensional Horava-Witten cosmology, including static and dynamic moduli, and compares with Randall-Sundrum phenomenology.

Findings

Relativistic matter yields four-dimensional cosmology with static moduli.

Non-relativistic matter cannot be accommodated with static moduli.

Varying brane distance helps include non-relativistic matter.

Abstract

The cosmology in the Hubble expansion era of the Horava-Witten M-theory compactified on a Calabi-Yau threefold is studied in the reduction to five-dimensions where the effects of the Calabi-Yau manifold are summarized by the volume modulus, and all perturbative potentials are included. Matter on the branes are treated as first order perturbations of the static vacuum solution, and all equations in the bulk and all boundary conditions on both end branes are imposed. It is found that for a static volume modulus and a static fifth dimension, y, one can recover the four dimensional Robertson Friedmann Walker cosmology for relativistic matter on the branes, but not for non-relativistic matter. In this case, the Hubble parameter H becomes independent of y to first order in matter density. This result holds also when an arbitrary number of 5-branes are included in the bulk. The five dimensional Horava-Witten model is compared with the Randall Sundrum phenomenology with a scalar field in the bulk where a bulk and brane potential are used so that the vacuum solutions can be rigorously obtained. (In the Appendix, the difficulty of obtaining approximate vacuum solutions for other potentials is discussed.) In this case non-relativistic matter is accommodated by allowing the distance between the branes to vary. It is suggested that non-perturbative potentials for the vacuum solution of Horava-Witten theory are needed to remove the inconsistency that non-relativistic matter creates.