The computation of the primordial power spectrum in multi-field inflation models requires us to correctly account for all relevant interactions between adiabatic and non-adiabatic modes around and after horizon crossing. One specific complication arises from derivative interactions induced by the curvilinear trajectory of the inflaton in a multi-dimensional field space. In this work we compute the power spectrum in general multi-field models and show that certain inflaton trajectories may lead to observationally significant imprints of 'heavy' physics in the primordial power spectrum if the inflaton trajectory turns, that is, traverses a bend, sufficiently fast (without interrupting slow roll), even in cases where the normal modes have masses approaching the cutoff of our theory. We emphasise that turning is defined with respect to the geodesics of the sigma model metric, irrespective of whether this is canonical or non-trivial. The imprints generically take the form of damped superimposed oscillations on the power spectrum. In the particular case of two-field models, if one of the fields is sufficiently massive compared to the scale of inflation, we are able to compute an effective low energy theory for the adiabatic mode encapsulating certain relevant operators of the full multi-field dynamics. As expected, a particular characteristic of this effective theory is a modified speed of sound for the adiabatic mode which is a functional of the background inflaton trajectory and the turns traversed during inflation. Hence in addition, we expect non-Gaussian signatures directly related to the features imprinted in the power spectrum.

Abstract. We investigate inflationary scenarios driven by a class of potentials which are similar in form to those that arise in certain minimal supersymmetric extensions of the standard model. We find that these potentials allow a brief period of departure from inflation sandwiched between two stages of slow roll inflation. We show that such a background behavior leads to a step like feature in the scalar power spectrum. We set the scales such that the drop in the power spectrum occurs at a length scale that corresponds to the Hubble radius today-a feature that seems necessary to explain the lower power observed in the quadrupole moment of the Cosmic Microwave Background (CMB) anisotropies. We perform a Markov Chain Monte Carlo analysis to determine the values of the model parameters that provide the best fit to the recent WMAP 5-year data for the CMB angular power spectrum. We find that an inflationary spectrum with a suppression of power at large scales that we obtain leads to a much better fit (with just one extra parameter, χ 2 eff improves by 6.62) of the observed data when compared to the best fit reference ΛCDM model with a featureless, power law, primordial spectrum.

The effect of self-interactions of heavy scalar fields during inflation on the primordial non-Gaussianity is studied. We take a specific constant-turn quasi-single field inflation as an example. We derive an effective theory with emphasis on non-linear self-interactions of heavy fields and calculate the corresponding non-Gaussianity, which is of equilateral type and can be as relevant as those computed previously in the literature. We also derive the non-Gaussianity by directly using the in-in formalism, and verify the equivalence of these two approaches. 98.90.Cq

We discuss the effect of local type non-Gaussianity on the abundance of primordial black holes based on the peak theory. It is explicitly shown that the value of non-linear parameter |f NL | ∼ 1 induces a similar effect to a few factors of difference in the amplitude of the power spectrum.Primordial black holes (PBHs) repeatedly come up as a hot topic in cosmology and astrophysics since the pioneering works of Zel'dovich and Novikov [1] and Hawking [2]. For instance, PBHs are still fascinating candidate for dark matter (e.g., see [3][4][5][6][7][8][9][10][11][12][13][14] and references therein), and observational constraints are frequently updated (see e.g. [10,15]). Number of interesting scenarios which produce substantial number of PBHs are proposed (see e.g. a recent review [16] and references therein).One of inevitable issues is the estimation of PBH abundance. Simplest conventional way to estimate PBH abundance is the Press-Schechter (PS) formalism [17], where the Gaussian distribution of a perturbation variable and its threshold for PBH formation are assumed. The validity of these assumptions has been under discussion for a long time (see e.g. [4,[18][19][20][21][22][23][24][25][26][27][28][29][30][31][32]). Recently, a more plausible procedure for PBH formation in a radiation dominated era is proposed [33], where an enhanced feature is assumed in the primordial power spectrum around some specific scale which enters the horizon in a radiation dominated era. Another important assumption is the random Gaussian distribution of the curvature perturbation. Then, a reliable procedure for the estimation of PBH abundance is derived based on the peak theory [34,35] of the curvature perturbation, by taking the non-linear effect between the curvature perturbation and the density perturbation into account (see e.g. [36][37][38] for the significance of the non-linearity).The purpose of this article is to show the impact of the local type non-Gaussianity of the curvature perturbation extending the procedure given in [33]. The effect of non-Gaussianity on the PBH abundance and the spatial distribution of PBHs have been discussed in [39][40][41][42][43][44][45][46][47][48][49][50][51][52][53][54][55][56][57]. However, since a new plausible procedure is proposed, it is important to check how the previously reported effect of the non-Gaussianity works in the new procedure. Providing a method to estimate PBH abundance including the local type non-Gaussianity, we demonstrate the effect of the non-Gaussianity of the curvature perturbation.This article is organized as follows. In Section 2, the typical profile of the curvature perturbation is derived for a given scale and amplitude of the peak with the non-linear parameter f NL . The general implicit expression for the PBH fraction is derived in Section 3. Two specific primordial power spectra are shown as examples to present the impact of non-Gaussianity in Section 4. Section 5 is devoted to a short summary. Some technical detail is given in the appendices. Throughout this arti...

We show that in the single component situation all perturbation variables in the comoving gauge are conformally invariant to all perturbation orders. Generally we identify a special time slicing, the uniform-conformal transformation slicing, where all perturbations are again conformally invariant to all perturbation orders. We apply this result to the δN formalism, and show its conformal invariance. a jinn-ouk.gong@cern.ch

We provide a concise review on multi-field inflation and cosmological perturbations. We discuss convenient and physically meaningful bases in terms of which perturbations can be systematically studied. We give formal accounts on the gauge fixing conditions and present the perturbation action in two gauges. We also briefly review non-linear perturbations.arXiv:1606.06971v2 [gr-qc]

We present the growing mode solutions of cosmological perturbations to the second order in the matter dominated era. We also present several gauge-invariant combinations of perturbation variables to the second order in most general fluid context. Based on the solutions we study the Newtonian correspondence of relativistic perturbations to the second order. In addition to the previously known exact relativistic/Newtonian correspondence of density and velocity perturbations to the second order in the comoving gauge, here we show that in the sub-horizon limit we have the correspondences for density, velocity and potential perturbations in the zero-shear gauge and in the uniform-expansion gauge to the second order. Density perturbation in the uniform curvature gauge also shows the correspondence to the second order in the sub-horizon scale. We also identify the relativistic gravitational potential which shows exact correspondence to the Newtonian one to the second order. Subject headings: cosmology: theory -large scale structure of universe

We derive the power spectrum P ψ (k) of the gravitational waves produced during general classes of inflation with second order corrections. Using this result, we also derive the spectrum and the spectral index in the standard slow-roll approximation with new higher order corrections.