The non-minimal ekpyrotic trispectrum

Abstract

Employing the covariant formalism, we derive the evolution equations for two scalar fields with non-canonical field space metric up to third order in perturbation theory. These equations can be used to derive predictions for local bi-and trispectra of multi-field cosmological models. Our main application is to ekpyrotic models in which the primordial curvature perturbations are generated via the non-minimal entropic mechanism. In these models, nearly scale-invariant entropy perturbations are generated first due to a non-minimal kinetic coupling between two scalar fields, and subsequently these perturbations are converted into curvature perturbations.Remarkably, the entropy perturbations have vanishing bi-and trispectra during the ekpyrotic phase. However, as we show, the conversion process to curvature perturbations induces local non-Gaussianity parameters f N L and g N L at levels that should be detectable by near-future observations. In fact, in order to obtain a large enough amplitude and small enough bispectrum of the curvature perturbations, as seen in current measurements, the conversion process must be very efficient. Interestingly, for such efficient conversions the trispectrum parameter g N L remains negative and typically of a magnitude O(10 2 ) − O(10 3 ), resulting in a distinguishing feature of non-minimally coupled ekpyrotic models.

BeyondΛCDM: Problems, solutions, and the road ahead

“…In addition to these different predictions for the tensor spectrum, there are other observables that are also expected to be different in inflation compared to its alternatives. These include expectations for the running of the scalar spectral index in ekpyrotic and matter bounce models [428], and predictions for the bi-and tri-spectra in ekpyrotic models [429,430].…”

Notes on the post-bounce background dynamics in bouncing cosmologies

“…In either case the final amplitude of curvature perturbations is proportional to the amplitude δs B− of the entropic fluctuation at the end of the ekpyrotic contraction [15,38,42,43], with the proportionality factor F ranging from O(10 −1 ) to O(10 4 ), which depends on the conversion efficiency as well as whether the conversion occurs after the bounce or not [15]. What is more, it follows from the (nearly) scale-invariance that |δs B− | 2 is of the same order of magnitude as the potential V (φ B− ) at the end of the ekpyrotic phase, namely [15,38]…”

No-go theorems for ekpyrosis from ten-dimensional supergravity

“…The occurrence of blueshift scalar perturbation is nonetheless a minor flaw of ekpyrotic theory which can be easily corrected. Hence, new ekpyrotic theory considers multiple scalar field and successfully generated a scalar spectrum which is scale invariant and slightly redshifted [16][17][18][19][20][21][22][23][24][25][26][27][28][29][30]. Producing primordial gravitational waves sourced by the gauge field in the ekpyrotic scenario was also studied in [31].…”