Volume Stabilization and Acceleration in Brane Gas Cosmology

TL;DR

This paper addresses the problem of stabilizing extra dimensions in brane gas cosmology by analyzing a toy $1+m+p$-dimensional model with a gas of $p$-branes wrapping the compact space. It computes the energy–momentum contributions of winding and momentum modes in a semiclassical setting and derives a self-dual radius solution that stabilizes the internal volume, with the observed space expanding as a power law $ds^2=-d\tau^2+(\alpha\tau)^{4/m}dx^idx^i+(R_{in}^0)^2 d\Sigma_p^2$; the internal radius is $R_{in}^0=[T_m(m+p-1)/(T_w(m-2)p)]^{1/(p+1)}$. The work also explores the effects of ordinary matter via equation-of-state parameters and demonstrates that acceleration can arise from brane winding or momentum modes, though with limited e-foldings and in some cases with singular endpoints. These results bolster brane gas cosmology as a moduli-stabilization mechanism and suggest avenues for addressing late-time acceleration and singularities, e.g., including the dilaton or quantum gravity corrections.

Abstract

We investigate toy cosmological models in (1+m+p)-dimensions with gas of p-branes wrapping over p-compact dimensions. In addition to winding modes, we consider the effects of momentum modes corresponding to small vibrations of branes and find that the extra dimensions are dynamically stabilized while the others expand. Adding matter, the compact volume may grow slowly depending on the equation of state. We also obtain solutions with winding and momentum modes where the observed space undergoes accelerated expansion.

Figures (3)

• Figure 1: The graphs of $R_{in}(\tau)$ for two different initial data set obeying (i). For convenience we take $m=3$, $p=6$, $T_w=8$ and $T_m=6$ so that the self-dual radius (\ref{['sd']}) is equal to 1. The initial conditions are: $R_{ob}(0)=1$, $R_{in}(0)=0.7$, $dR_{ob}/d\tau(0)=3.9761$, $dR_{in}/d\tau(0)=0.3$ and $R_{ob}(0)=1$, $R_{in}(0)=1.3$, $dR_{ob}/d\tau(0)=3.65135$, $dR_{in}/d\tau(0)=-0.7.$ Here, $dR_{ob}/d\tau(0)$ is solved from (\ref{['ini']}) given other conditions.
• Figure 2: The graphs of $R_{in}(\tau)$ for different values of $\omega$ and $\nu$. For convenience we take $m=3$, $p=6$, $T_w=8$, $T_m=6$, $R_{ob}(0)=2$. The initial conditions are: (a) $\left[\omega=0\right]$: $\nu=-0.9$, $R_{in}(0)=1.1$, $dR_{ob}/d\tau(0)=-1.41365$, $dR_{in}/d\tau(0)=1$; $\nu=0.5$, $R_{in}(0)=1.1$, $dR_{ob}/d\tau(0)=6.80001$, $dR_{in}/d\tau(0)=-0.7$, (b) $\left[\omega=0.5\right]$: $\nu=-0.6$, $R_{in}(0)=1.01$, $dR_{ob}/d\tau(0)=1.10393$, $dR_{in}/d\tau(0)=0.1$; $\nu=0.3$, $R_{in}(0)=0.8$, $dR_{ob}/d\tau(0)=1.07248$, $dR_{in}/d\tau(0)=0.3$, (c) $\left[\omega=-0.1\right]$: $\nu=-0.3$, $R_{in}(0)=1.7$, $dR_{ob}/d\tau(0)=-0.870317$, $dR_{in}/d\tau(0)=1$; $\nu=0.4$, $R_{in}(0)=1.1$, $dR_{ob}/d\tau(0)=-1.26295$, $dR_{in}/d\tau(0)=0.9.$ Here, $dR_{ob}/d\tau(0)$ is solved from the constraint on initial data.
• Figure 3: The graphs of $v_{ob}$ in (\ref{['vt']}) and $a_{ob}$ in (\ref{['at']}) with respect to the proper time $\tau$ in (\ref{['tt']}).