From Big Crunch to Big Bang

TL;DR

The paper investigates whether a contracting universe can transition to expansion via a bounce at $a=0$, using a $d$-dimensional gravity–scalar framework with a massless modulus and embedding the bounce in string/M-theory. It introduces moduli-space variables that remain finite across the bounce, analyzes elastic and inelastic bounce scenarios, and argues that a UV-complete string-theoretic description is essential to pass through the singularity, potentially connecting contracting and expanding phases through conifold/flop–like transitions. The work contrasts this bounce mechanism with the pre-big bang model and proposes a modified ekpyrotic scenario where boundary-brane collisions suffice to generate the hot big bang, removing the need for bulk branes. Overall, it opens a route to non-singular cosmologies that can address horizon and flatness puzzles without conventional inflation and provides a framework for transferring perturbations across the bounce. The findings suggest new cosmological models where string theory resolves the big crunch/big bang transition and reshapes the role of ekpyrotic scenarios in early-universe physics.

Abstract

We consider conditions under which a universe contracting towards a big crunch can make a transition to an expanding big bang universe. A promising example is 11-dimensional M-theory in which the eleventh dimension collapses, bounces, and re-expands. At the bounce, the model can reduce to a weakly coupled heterotic string theory and, we conjecture, it may be possible to follow the transition from contraction to expansion. The possibility opens the door to new classes of cosmological models. For example, we discuss how it suggests a major simplification and modification of the recently proposed ekpyrotic scenario.

Figures (3)

• Figure 1: Phase diagrams for $d=4$ comparing the (a) pre-big bang (PBB) model with (b) the bounce scenario considered here. The four rays connected at the origin represent the four solutions to the potential-less equations of motion. The large arrows indicate the two solutions that are joined together in each of the two cosmologies. Reversal from contraction to expansion connects the two weak coupling regimes in (b).
• Figure 2: Sketch of the compactified Milne universe (hatched region) embedded in a Minkowski background, where $x^0$ and $x^1$ are the time and space coordinates. The dashed surfaces are surfaces of constant $t$.
• Figure 3: The moduli space in $a_0$ and $a_1$ or, equivalently, light-cone coordinates $a_{\pm}$. The physical regime is the upper light-cone (quadrant). The two trajectories correspond to the exact solutions for the potential discussed in the text for $t >0$. The bounce occurs at $t=0$. By construction the solutions are time-symmetric. The dashed solution corresponds to $\epsilon =+1$ and the dotted corresponds to $\epsilon=-1$.