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M Theory Model of a Big Crunch/Big Bang Transition

Neil Turok, Malcolm Perry, Paul J. Steinhardt

TL;DR

This paper develops an M-theory framework for a big crunch/big bang transition using a compactified Milne background ${\cal M}_C \times \mathbb{R}^{d-1}$, focusing on p-branes that wind around the shrinking extra dimension. Winding M2-branes remain regular through the $t=0$ singularity, with finite quantum production and small gravitational back-reaction, and their dynamics are naturally described via a $1/\alpha'$ (inverse α′) expansion rather than the usual Einstein gravity regime. The analysis contrasts winding versus bulk modes to explain the pathologies seen in Lorentzian orbifolds and connects the results to ekpyrotic/cyclic cosmologies, offering a calculable route to evolve perturbations through the singularity. The work outlines several open tasks, including sigma-model quantization and consistent matching of high- and low-energy expansions, with potential implications for early-universe cosmology and singularity resolution.

Abstract

We consider a picture in which the transition from a big crunch to a big bang corresponds to the collision of two empty orbifold planes approaching each other at a constant non-relativistic speed in a locally flat background space-time, a situation relevant to recently proposed cosmological models. We show that $p$-brane states which wind around the extra dimension propagate smoothly and unambiguously across the orbifold plane collision. In particular we calculate the quantum mechanical production of winding M2-branes extending from one orbifold to the other. We find that the resulting density is finite and that the resulting gravitational back-reaction is small. These winding states, which include the string theory graviton, can be propagated smoothly across the transition using a perturbative expansion in the membrane tension, an expansion which from the point of view of string theory is an expansion in {\it inverse} powers of $α'$. We argue that interactions should be well-behaved because the string coupling tends to zero at the crunch. The production of massive Kaluza-Klein states should also be exponentially suppressed for small collision speeds. We contrast this good behavior with that found in previous studies of strings in Lorentzian orbifolds.

M Theory Model of a Big Crunch/Big Bang Transition

TL;DR

This paper develops an M-theory framework for a big crunch/big bang transition using a compactified Milne background , focusing on p-branes that wind around the shrinking extra dimension. Winding M2-branes remain regular through the singularity, with finite quantum production and small gravitational back-reaction, and their dynamics are naturally described via a (inverse α′) expansion rather than the usual Einstein gravity regime. The analysis contrasts winding versus bulk modes to explain the pathologies seen in Lorentzian orbifolds and connects the results to ekpyrotic/cyclic cosmologies, offering a calculable route to evolve perturbations through the singularity. The work outlines several open tasks, including sigma-model quantization and consistent matching of high- and low-energy expansions, with potential implications for early-universe cosmology and singularity resolution.

Abstract

We consider a picture in which the transition from a big crunch to a big bang corresponds to the collision of two empty orbifold planes approaching each other at a constant non-relativistic speed in a locally flat background space-time, a situation relevant to recently proposed cosmological models. We show that -brane states which wind around the extra dimension propagate smoothly and unambiguously across the orbifold plane collision. In particular we calculate the quantum mechanical production of winding M2-branes extending from one orbifold to the other. We find that the resulting density is finite and that the resulting gravitational back-reaction is small. These winding states, which include the string theory graviton, can be propagated smoothly across the transition using a perturbative expansion in the membrane tension, an expansion which from the point of view of string theory is an expansion in {\it inverse} powers of . We argue that interactions should be well-behaved because the string coupling tends to zero at the crunch. The production of massive Kaluza-Klein states should also be exponentially suppressed for small collision speeds. We contrast this good behavior with that found in previous studies of strings in Lorentzian orbifolds.

Paper Structure

This paper contains 11 sections, 66 equations, 1 figure.

Table of Contents

  1. Introduction
  2. The Background Big Crunch/Big Bang Space-time
  3. General Hamiltonian for $p$-Branes in Curved Space
  4. Winding $p$-Branes in ${\cal M}_C \times R^{d-1}$
  5. Winding states versus bulk states
  6. Toy Model: Winding Strings in ${\cal M}_C \times R^{d-1}$
  7. Dynamics of Winding M2-branes
  8. Einstein Gravity versus an Expansion in $1/\alpha'$
  9. Worldsheet Instanton Calculation of Loop Production
  10. Strings on Lorentzian Orbifolds are not regular
  11. Conclusions and Comments

Figures (1)

  • Figure 1: The contour for computation of Bogoliubov coefficients in string/membrane production.