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Brane Gases in the Early Universe

S. Alexander, R. Brandenberger, D. Easson

TL;DR

The paper generalizes Brandenberger–Vafa brane-gas cosmology by including D-branes in a toroidal, dilaton-gravity early Universe, derived from M-theory compactification to Type II-A. It derives the equation of state for brane winding and non-winding modes and shows that t-duality continues to avoid the cosmological singularity while winding modes still cap the expansion to a maximum of three large spatial dimensions; higher-p branes can induce a hierarchical structure among the extra dimensions (e.g., leading to a $T^5$ and then a $T^3$ subspace). It also discusses a brane-domain-wall problem and proposes loitering or inflation as possible resolutions, noting that the horizon problem is absent but flatness and structure-formation issues remain. Overall, the work strengthens the viability of string-theory-inspired, non-singular early-Universe scenarios and highlights concrete mechanisms for dimensionality selection and potential observational consequences.

Abstract

Over the past decade it has become clear that fundamental strings are not the only fundamental degrees of freedom in string theory. D-branes are also part of the spectrum of fundamental states. In this paper we explore some possible effects of D-branes on early Universe string cosmology, starting with two key assumptions: firstly that the initial state of the Universe corresponded to a dense, hot gas in which all degrees of freedom were in thermal equilibrium, and secondly that the topology of the background space admits one-cycles. We argue by t-duality that in this context the cosmological singularities are not present. We derive the equation of state of the brane gases and apply the results to suggest that, in an expanding background, the winding modes of fundamental strings will play the most important role at late times. In particular, we argue that the string winding modes will only allow four space-time dimensions to become large. The presence of brane winding modes with $p > 1$ may lead to a hierarchy in the sizes of the extra dimensions.

Brane Gases in the Early Universe

TL;DR

The paper generalizes Brandenberger–Vafa brane-gas cosmology by including D-branes in a toroidal, dilaton-gravity early Universe, derived from M-theory compactification to Type II-A. It derives the equation of state for brane winding and non-winding modes and shows that t-duality continues to avoid the cosmological singularity while winding modes still cap the expansion to a maximum of three large spatial dimensions; higher-p branes can induce a hierarchical structure among the extra dimensions (e.g., leading to a and then a subspace). It also discusses a brane-domain-wall problem and proposes loitering or inflation as possible resolutions, noting that the horizon problem is absent but flatness and structure-formation issues remain. Overall, the work strengthens the viability of string-theory-inspired, non-singular early-Universe scenarios and highlights concrete mechanisms for dimensionality selection and potential observational consequences.

Abstract

Over the past decade it has become clear that fundamental strings are not the only fundamental degrees of freedom in string theory. D-branes are also part of the spectrum of fundamental states. In this paper we explore some possible effects of D-branes on early Universe string cosmology, starting with two key assumptions: firstly that the initial state of the Universe corresponded to a dense, hot gas in which all degrees of freedom were in thermal equilibrium, and secondly that the topology of the background space admits one-cycles. We argue by t-duality that in this context the cosmological singularities are not present. We derive the equation of state of the brane gases and apply the results to suggest that, in an expanding background, the winding modes of fundamental strings will play the most important role at late times. In particular, we argue that the string winding modes will only allow four space-time dimensions to become large. The presence of brane winding modes with may lead to a hierarchy in the sizes of the extra dimensions.

Paper Structure

This paper contains 4 sections, 24 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Equation of State of Brane Gases
  3. Brane Gases in the Early Universe
  4. Discussion and Conclusions

Figures (1)

  • 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 $l/f = p/d$.