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Brane gas cosmology in M-theory: late time behavior

Richard Easther, Brian R. Greene, Mark G. Jackson, Daniel Kabat

TL;DR

This work advances brane gas cosmology by embedding it in M-theory on $T^{10}$ and analyzing a gas of supergravity particles together with wrapped M2-branes described by a wrapping matrix. Through numerical simulations and analytic late-time analysis, it demonstrates that radii evolve toward power laws set by the wrapping pattern, producing hierarchies between unwrapped and wrapped dimensions and a potential three large dimensions via an attractor mechanism. Four regimes are identified depending on the relative importance of the supergravity gas and full-wrapping terms, with exponents and coefficients fixed by the wrapping data up to scale symmetries. A special string-winding limit recovers a Brandenberger–Vafa-like scenario in which the small 11th dimension shrinks in the M-theory frame, corresponding to a particular IIA/string-frame interpretation.

Abstract

We investigate the late-time behavior of a universe containing a supergravity gas and wrapped 2-branes in the context of M-theory compactified on T^10. The supergravity gas tends to drive uniform expansion, while the branes impede the expansion of the directions about which they are wrapped. Assuming spatial homogeneity, we study the dynamics both numerically and analytically. At late times the radii obey power laws which are determined by the brane wrapping numbers, leading to interesting hierarchies of scale between the wrapped and unwrapped dimensions. The biggest hierarchy that could evolve from an initial thermal fluctuation produces three large unwrapped dimensions. We also study configurations corresponding to string winding, in which the M2-branes are all wrapped around the (small) 11th dimension, and show that this recovers the scenario discussed by Brandenberger and Vafa.

Brane gas cosmology in M-theory: late time behavior

TL;DR

This work advances brane gas cosmology by embedding it in M-theory on and analyzing a gas of supergravity particles together with wrapped M2-branes described by a wrapping matrix. Through numerical simulations and analytic late-time analysis, it demonstrates that radii evolve toward power laws set by the wrapping pattern, producing hierarchies between unwrapped and wrapped dimensions and a potential three large dimensions via an attractor mechanism. Four regimes are identified depending on the relative importance of the supergravity gas and full-wrapping terms, with exponents and coefficients fixed by the wrapping data up to scale symmetries. A special string-winding limit recovers a Brandenberger–Vafa-like scenario in which the small 11th dimension shrinks in the M-theory frame, corresponding to a particular IIA/string-frame interpretation.

Abstract

We investigate the late-time behavior of a universe containing a supergravity gas and wrapped 2-branes in the context of M-theory compactified on T^10. The supergravity gas tends to drive uniform expansion, while the branes impede the expansion of the directions about which they are wrapped. Assuming spatial homogeneity, we study the dynamics both numerically and analytically. At late times the radii obey power laws which are determined by the brane wrapping numbers, leading to interesting hierarchies of scale between the wrapped and unwrapped dimensions. The biggest hierarchy that could evolve from an initial thermal fluctuation produces three large unwrapped dimensions. We also study configurations corresponding to string winding, in which the M2-branes are all wrapped around the (small) 11th dimension, and show that this recovers the scenario discussed by Brandenberger and Vafa.

Paper Structure

This paper contains 12 sections, 58 equations, 2 figures, 1 table.

Table of Contents

  1. Introduction
  2. Homogeneous brane gas dynamics
  3. Some exact solutions
  4. General features
  5. Numerical results
  6. Late time behavior
  7. Neglect $\rho_{\rm S}$
  8. Neglect $\rho_{\rm S}$ and full-full wrapping
  9. Neglect full-full wrapping
  10. All terms important
  11. String gas cosmology
  12. Conclusions

Figures (2)

  • Figure 1: Radii vs. time for three unwrapped dimensions (solid red curves), two partially wrapped dimensions (dotted green curves) and five fully wrapped dimensions (dashed blue curves). Distances and and times measured in Planck units.
  • Figure 2: A plot with three unwrapped dimensions (solid red curves), four partially wrapped dimensions (dotted green curves) and three fully wrapped dimensions (dashed blue curves).