New Ekpyrotic Cosmology

TL;DR

New Ekpyrotic Cosmology presents a non-singular, 4d bouncing scenario that merges an ekpyrotic slow-contraction phase with NEC-violating ghost condensation to avoid singularities. A scale-invariant curvature perturbation is generated well before the bounce via conversion from scale-invariant entropy perturbations of two ekpyrotic fields, and this spectrum is preserved through the bounce. The model predicts an effectively vanishing gravitational-wave signal on observable scales and allows a red tilt through departures from exact exponential potentials, offering a concrete, testable alternative to inflation. Overall, the framework provides a complete, perturbation-consistent route from a contracting early universe to a hot big-bang phase within a controlled effective field theory.

Abstract

In this paper, we present a new scenario of the early Universe that contains a pre big bang Ekpyrotic phase. By combining this with a ghost condensate, the theory explicitly violates the null energy condition without developing any ghost-like instabilities. Thus the contracting universe goes through a non-singular bounce and evolves smoothly into the expanding post big bang phase. The curvature perturbation acquires a scale-invariant spectrum well before the bounce in this scenario. It is sourced by the scale-invariant entropy perturbation engendered by two ekpyrotic scalar fields, a mechanism recently proposed by Lehners et al. Since the background geometry is non-singular at all times, the curvature perturbation remains nearly constant on super horizon scales. It emerges from the bounce unscathed and imprints a scale-invariant spectrum of density fluctuations in the matter-radiation fluid at the onset of the hot big bang phase. The ekpyrotic potential can be chosen so that the spectrum has a ``red'' tilt, in accordance with the recent data from WMAP. As in the original Ekpyrotic scenario, the model predicts a negligible gravity wave signal on all observable scales. As such ``New Ekpyrotic Cosmology" provides a consistent and distinguishable alternative to inflation to account for the origin of the seeds of large scale structure.

Figures (4)

• Figure 1: Generic shape of the ekpyrotic scalar potential.
• Figure 2: Two possible choices for the global behavior of the kinetic function $P(X)$. In case a), the linear regime (ekpyrotic phase) lies at smaller $X$ than the ghost condensate point. This necessarily implies a maximum for $P(X)$ in between, signaling the presence of a real ghost. In case b), the linear regime lies at larger $X$, thereby avoiding real ghosts.
• Figure 3: Sketch of the dynamical evolution of the scalar field, in terms of $V$ and $P(X)$.
• Figure 4: Evolution of $\tilde{H}(\tilde{t})$ for $\beta=1$. We see that first $\dot{\tilde{H}}$ vanishes at some time, and later on $\tilde{H}$ itself vanishes, marking the reversal from contraction to expansion. Note that, in solving \ref{['master3']}, initial conditions were chosen such that $t=0$ corresponds to the beginning of the ghost condensation phase.