Ekpyrotic Non-Gaussianity -- A Review

TL;DR

The paper surveys non-Gaussianity in ekpyrotic and cyclic cosmologies, focusing on the entropic mechanism that first generates nearly scale-invariant entropy perturbations and then converts them to curvature perturbations. It presents explicit predictions for higher-order statistics under two conversion scenarios: ekpyrotic conversion yields $f_{NL}=-\frac{5}{12}c_1^2$ and $g_{NL}=\frac{25}{108}c_1^4$, while kinetic conversion yields $f_{NL} \approx \frac{3}{2}\kappa_3\sqrt{\epsilon}+5$ and $g_{NL} \approx 100\big(\frac{\kappa_4}{60}+\frac{\kappa_3^2}{80}-\frac{2}{5}\big)\epsilon$, with $\tau_{NL}=\frac{36}{25}f_{NL}^2$. The tilt of the entropy spectrum is $n_s-1=\frac{2}{\epsilon}-\frac{\epsilon_{,N}}{\epsilon^2}$, allowing $0.97\lesssim n_s\lesssim 1.02$, and the paper discusses how these predictions compare with current and near-future observational constraints. The results show that kinetic conversion could yield observable local non-Gaussianity, while ekpyrotic conversion is currently increasingly constrained, and the overall framework provides a critical test for distinguishing ekpyrotic/cyclic cosmology from inflationary models, especially in the absence or presence of primordial gravitational waves.

Abstract

Ekpyrotic models and their cyclic extensions solve the standard cosmological flatness, horizon and homogeneity puzzles by postulating a slowly contracting phase of the universe prior to the big bang. This ekpyrotic phase also manages to produce a nearly scale-invariant spectrum of scalar density fluctuations, but, crucially, with significant non-gaussian corrections. In fact, some versions of ekpyrosis are on the borderline of being ruled out by observations, while, interestingly, the best-motivated models predict levels of non-gaussianity that will be measurable by near-future experiments. Here, we review these predictions in detail, and comment on their implications.

Figures (8)

• Figure 1: The potential during ekpyrosis is negative and steeply falling; it can be modeled by the exponential form $V(\phi)=-V_0 e^{-c\phi}.$
• Figure 2: The braneworld picture of our universe. Think of a sandwich: the 5-dimensinonal bulk spacetime is bounded by two 4-dimensional boundary branes. There is no space "outside" of the sandwich, but the branes can be infinite in all directions perpendicular to the line segment (orbifold). In the M-theory embedding, there are 6 additional internal dimensions at each point of the sandwich.
• Figure 3: The potential for the cyclic universe integrates the ekpyrotic part and a quintessence epoch, but is irrelevant at the brane collision. A possible form for the potential is $V(\phi)=V_0(e^{b\phi}-e^{-c\phi})F(\phi),$ with $b\ll 1, \, c\gg 1$ and $F(\phi)$ tends to unity for $\phi>\phi_{end}$ and to zero for $\phi < \phi_{end}.$ Reproduced with permission from Erickson:2006wc.
• Figure 4: After a rotation in field space, the two-field ekpyrotic potential can be viewed as composed of an ekpyrotic direction ($\sigma$) and a transverse tachyonic direction ($s$). The ekpyrotic scaling solution corresponds to motion along the ridge of the potential. Perturbations along the direction of the trajectory are adiabatic/curvature perturbations, while perturbations transverse to the trajectory are entropy/isocurvature perturbations.
• Figure 5: After the ekpyrotic phase, the trajectory in scalar field space enters the kinetic phase and bends - this bending is described by the existence of an effective repulsive potential (the potentials are indicated by their contour lines). A trajectory adjacent to the background evolution can be characterized by the entropy perturbation $\delta s(t_{ek-end})$ at the end of the ekpyrotic phase, leading to a corresponding off-set $\delta s(t_{bend}),$ or equivalently $\delta V(t_{bend}),$ at the time of bending.