Erratum: Non-Gaussian density fluctuations from entropically generated curvature perturbations in ekpyrotic models [Phys. Rev. D77, 063533 (2008)]

Abstract

We analyze the non-gaussian density perturbations generated in ekpyrotic/cyclic models based on heterotic M-theory. In this picture, two scalar fields produce nearly scale-invariant entropic perturbations during an ekpyrotic phase that are converted into curvature modes after the ekpyrotic phase is complete and just before the big bang. Both intrinsic non-linearity in the entropy perturbation and the conversion process contribute to non-gaussianity. The range of the non-gaussianity parameter fNL depends on the details of the scalar field potential during the ekpyrotic phase, and on how gradual the conversion process is. Although a wider range is possible, in principle, natural values of the parameters of the potential combined with a gradual conversion process lead to values of −60 fNL +80, typically much greater than slow-roll inflation but within the current observational bounds.Ekpyrotic [1] and cyclic [2] models of the universe use quantum fluctuations of scalar fields produced during a slowly contracting phase with equation of state w > 1 to generate the observed nearly scale-invariant spectrum of curvature (energy density) fluctuations after the big bang. One mechanism considered for converting the fluctuations of a scalar field into cosmological curvature perturbations relies on higher-dimensional effects at the collision between orbifold planes (branes) along an extra dimension [3]. Recently, however, a new "entropic" mechanism [4,5] has been proposed that relies on two (or more) scalar fields and ordinary 4d physics, stimulating new approaches to ekpyrotic and cyclic cosmology that may not require branes or extra dimensions at all [6][7][8][9].In this paper, we wish to consider an important byproduct of the entropic mechanism: a non-gaussian contribution to the density fluctuation spectrum that is more than an order of magnitude greater than for conventional inflationary models and that can satisfy current observational bounds, including the recently claimed detection of non-gaussianity [10]. Our results differ significantly from the cases considered by Koyama et al. [11] and Buchbinder et al. [12] in which they assumed an ekpyrotic (w ≫ 1) phase that continues all the way to the conversion of entropic to curvature fluctuations, as in the "new ekpyrotic" model [6]; for these cases, the non-gaussianity is amplified by the non-linear evolution on super-horizon scales to the point where f N L , the parameter characterizing the non-linear curvature perturbation [13], reaches magnitude O(c 2 1 ), where c 1 ≈ 2 √ w + 1 parameterizes the steepness of the scalar field potential during the ekpyrotic phase. A potential problem is that a minimum of c 1 ≥ 10 is required just to satisfy the current upper bound constraints on n s , the spectral tilt of the scalar (energy density) perturbation spectrum [5]; and c 1 ≥ 30 is needed to reach the best-fit value n s ≈ 0.97. Yet, excluding finelytuned cancellations, the resulting value of f N L obtained in Ref. [6][7][8][9] is marginally consistent with current observationa...

A critical review of classical bouncing cosmologies

“…In that regard, it should be noted that different aspects are highlighted in the literature: before the improved constraints by PLANCK, Lehners et al [166][167][168] highlighted the generic prediction of observably large non-Gaussianities of f local NL of order 10 or bigger for the conversion mechanism in [161,162]. However, after the publication of PLANCK, the emphasis was put onto the possibility to counterbalance different contributions to non-Gaussianities to enable f local NL of order 1 [152].…”

Probing Inflation with CMB Polarization

“…An important prediction of this new mechanism for generating density perturbations in the ekpyrotic model is a substantial level of non-Gaussianity [77,[197][198][199]379]. This is a consequence of the self-interactions in the steep exponential potential and of the mechanism of conversion to adiabatic perturbations.…”

“…As this conversion happens outside of the horizon, when gradients are irrelevant, one generates non-linearities of the form (64). Specific models of this type include multi-field inflation [183][184][185][186][187][188][189][190][191][192][193][194][195], the curvaton scenario [132,196], inhomogeneous reheating [129,130], and New Ekpyrotic models [77,[197][198][199][200][201][202]. In these cases, |/NL al | is model-dependent but generically larger than 5 -10.…”

Planck2015 results

“…Models based on a conversion taking place during the ekpyrotic phase (the so called "ekpyrotic conversion mechanism") are already ruled out (Koyama et al 2007;Planck Collaboration XXIV 2014). Ekpyrotic models where "kinetic conversion" occurs after the ekpyrotic phase predict a local bispectrum with f local NL = (3/2) κ 3 √ ± 5, where the sign depends on the details of the conversion process (Lehners & Steinhardt 2008, 2013Lehners 2010), where 50 or greater are typical values. If we take 100 and a uniform prior on −5 < κ 3 < 5 the constraints on f local NL from T-only (see Table 11), yield −0.91 < κ 3 < 0.58 and −0.25 < κ 3 < 1.2 at 95% CL, for the plus and minus sign in f local NL respectively.…”