Loitering Phase in Brane Gas Cosmology

TL;DR

The paper investigates a loitering phase in Brane Gas Cosmology as a noninflationary route to resolve horizon and initial-singularity issues. It extends the dilaton-gravity background with winding-to-loop annihilation dynamics and analyzes phase-space trajectories, showing a short contracting loitering period where winding modes self-annihilate, followed by a transition to expansion. A detailed unwinding/loop-production framework in 3+1 dimensions yields a matter-dominated era after the dilaton stabilizes, with the scale factor evolving as $a(t) \sim t^{2/3}$. The work argues that brane winding modes can dynamically select three large spatial dimensions, address the brane/horizon problems without inflation, and hints at deeper connections between SUSY breaking and T-duality breaking in the late Universe.

Abstract

Brane Gas Cosmology (BGC) is an approach to M-theory cosmology in which the initial state of the Universe is taken to be small, dense and hot, with all fundamental degrees of freedom near thermal equilibrium. Such a starting point is in close analogy with the Standard Big Bang (SBB) model. The topology of the Universe is assumed to be toroidal in all nine spatial dimensions and is filled with a gas of p-branes. The dynamics of winding modes allow, at most, three spatial dimensions to become large, thus explaining the origin of our macroscopic 3+1-dimensional Universe. Here we conduct a detailed analysis of the loitering phase of BGC. We do so by including into the equations of motion that describe the dilaton gravity background some new equations which determine the annihilation of string winding modes into string loops. Specific solutions are found within the model that exhibit loitering, i.e. the Universe experiences a short phase of slow contraction during which the Hubble radius grows larger than the physical extent of the Universe. As a result the brane problem (generalized domain wall problem) in BGC is solved. The initial singularity and horizon problems of the SBB scenario are solved without relying on an inflationary phase.

Figures (6)

• Figure 1: Phase space trajectories of the solutions of the background equations (\ref{['EOMback1']} - \ref{['EOMback3']}) for the values $p = 2$ and $d = 9$. The energetically allowed region lies near the $l = 0$ axis between the special lines a and c, which are the lines given by $l/f = \pm 1 / \sqrt{d}$. The trajectory followed in the scenario investigated in this paper starts out in the upper left quadrant close to the special line c (corresponding to an expanding background), crosses the $l = 0$ axis at some finite value of $f$ (at this point entering a contracting phase), and then approaches the loitering point $(l, f) = (0, 0)$ along the phase space line b which corresponds to $l/f = p/d$.
• Figure 2: A solution of the background equations (\ref{['eoml']}) and (\ref{['eomf']}) including the effects of loop production. This depicts a typical solution which starts in the energetically allowed region of the phase space. The solution crosses the $l = 0$ axis at some finite value of $f$ (at which point the Universe enters a contracting phase), and then crosses the $l=0$ line a second time when the winding modes have fully annihilated. At this point the Universe begins to expand, is matter dominated and the dilaton is assumed to become massive.
• Figure 3: The time evolution of $H = l$. The loitering phase begins when $l(t)$ crosses the $l =0$ line for the first time and ends when $l(t)$ crosses back over the $l=0$ line.
• Figure 4: The time evolution of the scale factor $a$. By comparing this plot with Fig. 3 we see that the loitering phase lasts long enough to allow all winding modes to self-annihilate in the large three-dimensional Universe.
• Figure 5: Time evolution of $\tilde{\nu}$. Initially, $\tilde{\nu}$ increases as the Universe contracts. The winding modes begin to self-annihilate ($\tilde{\nu}$ decreases) and eventually vanish ($\tilde{\nu} \rightarrow 0$).