Diversity in the Phoenix Universe

It has recently been argued by Copeland et al. that in eleven dimensions two orbifold planes can collide and bounce in a regular way, even when the bulk metric is perturbed away from Milne spacetime to a Kasner solution. In this paper, we point out that as a consequence the global "phoenix" structure of the cyclic universe is significantly enriched. Spatially separated regions, with different density fluctuation amplitudes as well as different non-gaussian characteristics, are all physically realized. Those regions containing by far the most structure are specified by a fluctuation amplitude of Q ~ 10^{-4.5} and local non-gaussianity parameters f_{NL} ~ O(+/- 10) and g_{NL} ~ O(-10^3), in agreement with current observations.Comment: 20 pages, 3 figure

New Ekpyrotic Quantum Cosmology

Ekpyrotic instantons describe the emergence of classical contracting universes out of the no-boundary quantum state. However, up to now these instantons ended in a big crunch singularity. We remedy this by adding a higher-derivative term, allowing a ghost condensate to form. This causes a smooth, non-singular bounce from the contracting phase into an expanding, kinetic-dominated phase. Remarkably, and although there is a non-trivial evolution during the bounce, the wavefunction of the universe is "classical" in a WKB sense just as much after the bounce as before. These new non-singular instantons can thus form the basis for a fully non-singular and calculable ekpyrotic history of the universe, from creation until now.Comment: 6 pages, 9 figure

Small-Field and Scale-Free: Inflation and Ekpyrosis at their Extremes

There is increasing evidence from string theory that effective field theories are only reliable over approximately sub-Planckian field excursions. The two most promising effective models for early universe cosmology, inflation and ekpyrosis, are mechanisms that, in order to address cosmological puzzles, must operate over vast expansion/energy ranges. This suggests that it might be appropriate to describe them using scaling laws. Here we combine these two ideas and demonstrate that they drive inflation and ekpyrosis to their extremes: inflation must start at ultra-slow-roll, and ekpyrosis at ultra-fast-roll. At face value, the implied spectra are overly tilted to the red, although in both cases minor departures from pure scale freedom bring the spectral indices within current observational bounds. These models predict a significant spectral running at a level detectable in the near future ($\alpha_s \approx -10^{-3}$). Ekpyrotic models with minimal coupling are nevertheless ruled out, as they lead to levels of non-Gaussianity that are at least an order of magnitude too large. No such restrictions apply to models with a kinetic coupling between the two ekpyrotic scalar fields, and these remain the most promising ekpyrotic models. An additional swampland criterion that was recently proposed for the slope of the scalar field potential would however rule out all ultra-slow-roll models of inflation. Finally, we speculate on the existence of corresponding restrictions on the slope at negative potential values, which might lead to similarly severe constraints on ekpyrotic models.Comment: 22 pages, v2: references update

Ekpyrotic Non-Gaussianity -- A Review

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.Comment: 39 pages, 10 figures. Invited review, replaced with version published in Advances in Astronom

Classical Inflationary and Ekpyrotic Universes in the No-Boundary Wavefunction

This paper investigates the manner in which classical universes are obtained in the no-boundary quantum state. In this context, universes can be characterised as classical (in a WKB sense) when the wavefunction is highly oscillatory, i.e. when the ratio of the change in the amplitude of the wavefunction becomes small compared to the change in the phase. In the presence of a positive or negative exponential potential, the WKB condition is satisfied in proportion to a factor $e^{-(\epsilon - 3)N/(\epsilon -1)},$ where $\epsilon$ is the (constant) slow-roll/fast-roll parameter and $N$ designates the number of e-folds. Thus classicality is reached exponentially fast in $N$, but only when $\epsilon 3$ (ekpyrosis). Furthermore, when the potential switches off and the ekpyrotic phase goes over into a phase of kinetic domination, the level of classicality obtained up to that point is preserved. Similar results are obtained in a cyclic potential, where a dark energy plateau is added. Finally, for a potential of the form $-\phi^n$ (with $n=4,6,8$), where the classical solution becomes increasingly kinetic-dominated, there is an initial burst of classicalisation which then quickly levels off. These results demonstrate that inflation and ekpyrosis, which are the only dynamical mechanisms known for smoothing the universe, share the perhaps even more fundamental property of rendering space and time classical in the first place.Comment: 35 pages, 19 figures, v2: replaced with version to be published in PR

On the Quantum-To-Classical Transition for Ekpyrotic Perturbations

We examine the processes of quantum squeezing and decoherence of density perturbations produced during a slowly contracting ekpyrotic phase in which entropic perturbations are converted to curvature perturbations before the bounce to an expanding phase. During the generation phase, the entropic fluctuations evolve into a highly squeezed quantum state, analogous to the evolution of inflationary perturbations. Subsequently, during the conversion phase, quantum coherence is lost very efficiently due to the interactions of entropy and adiabatic modes. Moreover, while decoherence occurs, the adiabatic curvature perturbations inherit their semi-classicality from the entropic perturbations. Our results confirm that, just as for inflation, an ekpyrotic phase can generate nearly scale-invariant curvature perturbations which may be treated as a statistical ensemble of classical density perturbations, in agreement with observations of the cosmic background radiation.Comment: 32 pages, 4 figure

On the No-Boundary Proposal for Ekpyrotic and Cyclic Cosmologies

The no-boundary proposal provides a compelling theory for the initial conditions of our universe. We study the implications of such initial conditions for ekpyrotic and cyclic cosmologies. These cosmologies allow for the existence of a new type of "ekpyrotic instanton", which describes the creation of a universe in the ekpyrotic contraction phase. Remarkably, we find that the ekpyrotic attractor can explain how the universe became classical. In a cyclic context, in addition to the ekpyrotic instantons there exist de Sitter-like instantons describing the emergence of the universe in the dark energy phase. Our results show that typically the ekpyrotic instantons yield a higher probability. In fact, in a potential energy landscape allowing both inflationary and cyclic cosmologies, the no-boundary proposal implies that the probability for ekpyrotic and cyclic initial conditions is vastly higher than that for inflationary ones.Comment: 46 pages, 24 figures, v3: updated with version to be published in JCA

Non-Canonical Inflation in Supergravity

We investigate the effect of non-canonical kinetic terms on inflation in supergravity. We find that the biggest impact of such higher-derivative kinetic terms is due to the corrections to the potential that they induce via their effect on the auxiliary fields, which now have a cubic equation of motion. This is in contrast to the usual (non-supersymmetric) effective field theory expansion which assumes that mass-suppressed higher-derivative terms do not affect the lower-derivative terms already present. We demonstrate with several examples that such changes in the potential can significantly modify the inflationary dynamics. Our results have immediate implications for effective descriptions of inflation derived from string theory, where higher-derivative kinetic terms are generally present. In addition we elucidate the structure of the theory in the parameter range where there are three real solutions to the auxiliary field's equation of motion, studying the resulting three branches of the theory, and finding that one of them suffers from a singularity in the speed of propagation of fluctuations.Comment: 22 pages + Appendix, 16 figure

On the Creation of the Universe via Ekpyrotic Instantons

We present a new class of complex instantons in the context of ekpyrotic cosmological theories. These instantons, which satisfy the "no-boundary" boundary conditions, describe the emergence of a classical, contracting universe out of nothing. The ekpyrotic attractor is essential in guaranteeing an evolution towards a real, Lorentzian history of the universe. In the context of the no-boundary proposal, the relative probability for such ekpyrotic histories compared to inflationary ones is very high -- in fact, assuming a bounce can be incorporated, these new instantons currently describe the most likely origin of the universe.Comment: 5 page

Eternal Inflation With Non-Inflationary Pocket Universes

Eternal inflation produces pocket universes with all physically allowed vacua and histories. Some of these pocket universes might contain a phase of slow-roll inflation, some might undergo cycles of cosmological evolution and some might look like the galilean genesis or other "emergent" universe scenarios. Which one of these types of universe we are most likely to inhabit depends on the measure we choose in order to regulate the infinities inherent in eternal inflation. We show that the currently leading measure proposals, namely the global light-cone cut-off and its local counterpart, the causal diamond measure, as well as closely related proposals, all predict that we should live in a pocket universe that starts out with a small Hubble rate, thus favoring emergent and cyclic models. Pocket universes which undergo cycles are further preferred, because they produce habitable conditions repeatedly inside each pocket.Comment: 13 pages, 2 figures, v2: replaced with PRD versio