Isotropization in Brane Gas Cosmology
Scott Watson, Robert H. Brandenberger
TL;DR
Isotropization in Brane Gas Cosmology investigates whether the three large spatial dimensions can become isotropic within the Brane Gas Cosmology framework. The authors generalize BGC to anisotropic backgrounds by formulating the dilaton-gravity dynamics with winding and loop energies for a general metric, focusing on a 2+1 anisotropic case $ds^2=dt^2 - e^{2\lambda}(dx^2+dy^2) - e^{2\nu}dz^2$ and introducing $l=\dot\lambda$, $q=\dot\nu$, and $f=\dot\varphi$. They model winding-annihilation rates as $\dot N=-c_N t N^2 e^{-\lambda-\nu}$ and $\dot M=-c_M t M^2 e^{-2\lambda}$, and show numerically that winding numbers decay to zero while loop energy $g(t)$ saturates; the anisotropy parameter $\mathcal{A}$ peaks early and decays to zero as expansion rates converge, implying isotropization. The results demonstrate that isotropy emerges naturally in BGC, strengthening its viability as a non-inflationary route to a homogeneous, flat, $(3+1)$-dimensional cosmology and informing stabilization studies of extra dimensions.
Abstract
Brane Gas Cosmology (BGC) is an approach to unifying string theory and cosmology in which matter is described by a gas of strings and branes in a dilaton gravity background. The Universe is assumed to start out with all spatial dimensions compact and small. It has previously been shown that in this context, in the approximation of neglecting inhomogeneities and anisotropies, there is a dynamical mechanism which allows only three spatial dimensions to become large. However, previous studies do not lead to any conclusions concerning the isotropy or anisotropy of these three large spatial dimensions. Here, we generalize the equations of BGC to the anisotropic case, and find that isotropization is a natural consequence of the dynamics.