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Big Bang Models in String Theory

Ben Craps

TL;DR

These proceedings survey how general relativity's spacetime singularities can be addressed within string theory, focusing on static orbifold/ALE singularities and cosmological singularities such as the Milne orbifold and the matrix big bang. The analysis combines perturbative string methods (twisted strings, D-branes, and tachyon effects) with non-perturbative tools (AdS/CFT, matrix theory, and DLCQ) to understand whether singularities can be resolved or whether spacetime itself can emerge from underlying degrees of freedom. A key finding is that Milne-type cosmologies exhibit divergences in tree-level amplitudes signaling breakdown of perturbation theory, while non-perturbative mechanisms, including winding condensates, tachyon phases, and holographic descriptions, offer potential resolutions. The matrix big bang proposal provides a concrete non-perturbative description in which late-time dynamics imply emergent spacetime as off-diagonal modes decouple, highlighting a pathway from singular early-times to classical spacetime and raising important questions about higher-loop effects, observables, and large-$N$ limits in cosmological string theory $g_s$-dependent settings.

Abstract

These proceedings are based on lectures delivered at the "RTN Winter School on Strings, Supergravity and Gauge Theories", CERN, January 16 - January 20, 2006. The school was mainly aimed at Ph.D. students and young postdocs. The lectures start with a brief introduction to spacetime singularities and the string theory resolution of certain static singularities. Then they discuss attempts to resolve cosmological singularities in string theory, mainly focusing on two specific examples: the Milne orbifold and the matrix big bang.

Big Bang Models in String Theory

TL;DR

These proceedings survey how general relativity's spacetime singularities can be addressed within string theory, focusing on static orbifold/ALE singularities and cosmological singularities such as the Milne orbifold and the matrix big bang. The analysis combines perturbative string methods (twisted strings, D-branes, and tachyon effects) with non-perturbative tools (AdS/CFT, matrix theory, and DLCQ) to understand whether singularities can be resolved or whether spacetime itself can emerge from underlying degrees of freedom. A key finding is that Milne-type cosmologies exhibit divergences in tree-level amplitudes signaling breakdown of perturbation theory, while non-perturbative mechanisms, including winding condensates, tachyon phases, and holographic descriptions, offer potential resolutions. The matrix big bang proposal provides a concrete non-perturbative description in which late-time dynamics imply emergent spacetime as off-diagonal modes decouple, highlighting a pathway from singular early-times to classical spacetime and raising important questions about higher-loop effects, observables, and large- limits in cosmological string theory -dependent settings.

Abstract

These proceedings are based on lectures delivered at the "RTN Winter School on Strings, Supergravity and Gauge Theories", CERN, January 16 - January 20, 2006. The school was mainly aimed at Ph.D. students and young postdocs. The lectures start with a brief introduction to spacetime singularities and the string theory resolution of certain static singularities. Then they discuss attempts to resolve cosmological singularities in string theory, mainly focusing on two specific examples: the Milne orbifold and the matrix big bang.

Paper Structure

This paper contains 15 sections, 92 equations, 18 figures.

Table of Contents

  1. Lecture I: Introduction and outline
  2. General relativity and spacetime singularities
  3. Static singularities in string theory
  4. A first look at cosmological singularities in string theory
  5. Lecture II: Time-dependent orbifolds and AdS/CFT
  6. Tree-level amplitudes of untwisted states in the Milne orbifold
  7. Can winding modes resolve the singularity?
  8. Using the AdS/CFT correspondence
  9. Lecture III: Light-like linear dilaton and matrix theory
  10. Light-like linear dilaton
  11. Matrix theory in flat spacetime
  12. A first look at matrix theory in the lightlike linear dilaton background
  13. Lecture IV: Matrix big bang
  14. Derivation of the matrix big bang via DLCQ
  15. The one-loop effective potential

Figures (18)

  • Figure 1: Can string theory make sense of spacetime singularities?
  • Figure 2: A geodesic ending in a singularity.
  • Figure 3: Four fermion interaction replaced by a W-boson exchange diagram.
  • Figure 4: Scalar fields from open strings describe the position and profile of a D-brane in its transverse dimensions $X^i$.
  • Figure 5: Open strings stretching between two different D-branes give rise to off-diagonal matrix degrees of freedom.
  • ...and 13 more figures