Classical Propagation of Strings across a Big Crunch/Big Bang Singularity

TL;DR

This paper investigates the classical and semi-classical quantum evolution of fundamental strings crossing a cosmological big crunch/big bang singularity in M theory, showing regular behavior and quantum excitation production.

Contribution

It provides a detailed analysis of string dynamics across a cosmological singularity and introduces a semi-classical method to compute quantum effects during the transition.

Findings

Strings remain regular across the singularity without blue-shift.

Quantum excitations are produced during the transition.

Classical solutions are well-behaved through the big crunch/big bang.

Abstract

One of the simplest time-dependent solutions of M theory consists of nine-dimensional Euclidean space times 1+1-dimensional compactified Milne space-time. With a further modding out by Z_2, the space-time represents two orbifold planes which collide and re-emerge, a process proposed as an explanation of the hot big bang. When the two planes are near, the light states of the theory consist of winding M2-branes, describing fundamental strings in a particular ten-dimensional background. They suffer no blue-shift as the M theory dimension collapses, and their equations of motion are regular across the transition from big crunch to big bang. In this paper, we study the classical evolution of fundamental strings across the singularity in some detail. We also develop a simple semi-classical approximation to the quantum evolution which allows one to compute the quantum production of excitations on the string and implement it in a simplified example.