The Ekpyrotic Universe: Colliding Branes and the Origin of the Hot Big Bang

TL;DR

The paper introduces the ekpyrotic universe, a non-inflationary cosmology within heterotic M-theory in which a slowly moving bulk brane collides with the visible brane to trigger the hot big bang. It builds a moduli-space framework to derive the 4D effective action and analyzes how a pre-collision quasi-static, BPS state governs horizon and flatness while generating scale-invariant density perturbations from brane ripples; tensor perturbations, however, are predicted to be strongly blue, offering a distinctive observational signature. The authors provide explicit calculations for the ekpyrotic temperature, the collision dynamics, and the spectrum of scalar and tensor fluctuations, including an explicit exponential-potential example that yields near scale-invariance. They also discuss observational implications and contrasts with inflation, highlighting how a blue gravitational-wave spectrum would support or falsify the model. While promising, the framework leaves open questions about collision matching and moduli stabilization that require further theoretical development within M-theory.

Abstract

We propose a cosmological scenario in which the hot big bang universe is produced by the collision of a brane in the bulk space with a bounding orbifold plane, beginning from an otherwise cold, vacuous, static universe. The model addresses the cosmological horizon, flatness and monopole problems and generates a nearly scale-invariant spectrum of density perturbations without invoking superluminal expansion (inflation). The scenario relies, instead, on physical phenomena that arise naturally in theories based on extra dimensions and branes. As an example, we present our scenario predominantly within the context of heterotic M-theory. A prediction that distinguishes this scenario from standard inflationary cosmology is a strongly blue gravitational wave spectrum, which has consequences for microwave background polarization experiments and gravitational wave detectors.

Figures (4)

• Figure 1: One possible set of initial conditions of the ekpyrotic scenario has the universe beginning in a cold, vacuous, nearly BPS state consisting of two static massive orbifold planes and a warped geometry in the intervening bulk (a) in which the curvature is low near the rightmost orbifold plane (the hidden brane) and high near the leftmost orbifold plane (the visible brane). Spontaneously, a bulk brane peels away from the hidden brane over some region of space (b), forming a terrace. The edges of the terrace expand outwards at light speed, while the interior moves very slowly towards the opposing visible brane. Although the bulk brane is flat on average, quantum fluctuations produce ripples over a wide range of length scales as the brane traverses the bulk (c). When the bulk brane collides with the visible brane, the ripples result in different regions colliding and reheating at slightly different times (d), thereby impressing a spectrum of density fluctuations on the visible universe. The energy from the collision is translated into matter and radiation, heating the universe to a temperature a few orders of magnitude smaller than the unification scale.
• Figure 2: Sketch of the exponential potential $V(Y)=-ve^{-m \alpha Y}$ (the line of zero potential energy corresponds to the dotted line). The potential attracts the bulk brane towards the visible brane. The force is strongest near the visible brane and tends to zero at large distances.
• Figure 3: Evolution of scale factors in a three-brane system where a bulk brane is drawn across from the hidden brane to the visible brane. The solid lines show (from top to bottom) the scale factors on the hidden brane ($a_0$), the bulk brane ($a_B$) and the visible brane ($a_1$). At collision between the bulk brane and the visible brane, both boundary branes are expanding. The evolution of the 4d Einstein frame scale factor $a$ is also shown as a dashed line: it contracts throughout.
• Figure 4: Sketch comparing the generation of a super-horizon spectrum of perturbations in (a) inflationary cosmology versus (b) the ekpyrotic universe. During inflation, the Hubble radius is nearly fixed and the fluctuation wavelength grows exponentially fast, causing modes to be stretched outside the horizon. In the ekpyrotic scenario, modes correspond to ripples on the moving bulk brane. The perturbations have nearly constant wavelength but the effective Hubble radius shrinks, once again causing modes to cross outside the horizon.