# Cosmology and gravity in the brane world

Abstract (Summary)

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. For relativistic matter, the Hubble parameter H becomes
independent of y to first order in matter density, and if a consistent solution for nonrelativistic
matter exists it would require H to be y dependent. These results hold 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 nonrelativistic
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.
Also considered is the problem of gravitational forces between point particles
on the branes in a Randall-Sundrum (R-S) two brane model with S1/Z2 symmetry.
Matter is assumed to produce a perturbation to the R-S vacuum metric and all the 5D
Einstein equations are solved to linearized order (for arbitrary matter on both branes).
We show that while the gauge condition hi5 = 0, i = 0, 1, 2, 3 can always be achieved
without brane bending, the condition h55 = 0 leads to large brane bending. The static
potential arising from the zero modes and the corrections due to the Kaluza-Klein
(KK) modes are calculated. Gravitational forces on the Planck (y1 = 0) brane recover
Newtonian physics with small KK corrections (in accord with other work). However,
forces on the TeV (y2) brane due to particles on that brane are strongly distorted
by large R-S exponentials, making the model in disagreement with experiment if the
TeV brane is the physical brane.
Bibliographical Information:

Advisor:Pope, Christopher; Arnowitt, Richard; Fulling, Stephen; Nanopoulos, Dimitri

School:Texas A&M University

School Location:USA - Texas

Source Type:Master's Thesis

Keywords:cosmology gravity

ISBN:

Date of Publication:08/01/2005