A Cosmological Super-Bounce

TL;DR

The paper demonstrates that a non-singular cosmological bounce can be embedded in ${\cal N}=1$ supergravity by combining ghost-condensate and Galileon-type higher-derivative terms. It first reviews a non-supersymmetric bounce model with a short NEC-violating phase and then provides a supergravity embedding in which the bounce and an preceding ekpyrotic contraction are realized consistently, with precise identifications linking the supergravity couplings to the ghost-condensate sector. A thorough perturbation analysis shows the background can be ghost-free and largely stable, though a stabilizing term is needed to control the transverse scalar $\xi$; an entropic mechanism for generating nearly scale-invariant perturbations requires additional tuning or alternative couplings. Overall, the work provides a proof-of-principle that non-singular bounces are viable within supergravity and offers a framework for exploring cyclic/ekpyrotic cosmologies compatible with high-energy theory.

Abstract

We study a model for a non-singular cosmic bounce in N=1 supergravity, based on supergravity versions of the ghost condensate and cubic Galileon scalar field theories. The bounce is preceded by an ekpyrotic contracting phase which prevents the growth of anisotropies in the approach to the bounce, and allows for the generation of scale-invariant density perturbations that carry over into the expanding phase of the universe. We present the conditions required for the bounce to be free of ghost excitations, as well as the tunings that are necessary in order for the model to be in agreement with cosmological observations. All of these conditions can be met. Our model thus provides a proof-of-principle that non-singular bounces are viable in supergravity, despite the fact that during the bounce the null energy condition is violated.

Figures (13)

• Figure 1: The solid curve shows $k(\phi)$ while the dashed curve shows the normalized functions $\tau(\phi)/\bar{\tau},g(\phi)/\bar{g}$, all with $\kappa=1/4.$
• Figure 2: The ekpyrotic potential. The ekpyrotic phase starts at large positive $\phi,$ with the field rolling down the potential towards smaller values of the field. Around $\phi_{ek-end}\approx 15$ the potential starts to come back up to zero, and is irrelevant from then on. The bounce occurs at small values, $\phi \approx 0$.
• Figure 3: The scale factor around the time of the bounce. Our numerical evaluation starts at $\phi_0=17/2$ with $\dot\phi_0=-10^{-5},$$a_0=1$ and $H_0$ is determined by the Friedmann equation. We are using the parameters $\kappa=1/4,\bar{\tau}=1,\bar{g}=1/100.$ The figure shows a zoom-in on the most interesting time period, namely that of the bounce. One can clearly see that the bounce is smooth. The next three figures plot the evolution of various quantities during that same time period.
• Figure 4: The evolution of the scalar field $\phi$ during the bounce phase. The approximately linear evolution near $\phi=0$ corresponds to the ghost condensate phase which is responsible for the bounce.
• Figure 5: The sum of energy density and pressure during the bounce phase. When this quantity goes negative, the null energy condition is violated -- this is a necessary condition for a non-singular bounce in a flat FLRW universe.