We discuss and clarify the validity of effective single field theories of inflation obtained by integrating out heavy degrees of freedom in the regime where adiabatic perturbations propagate with a suppressed speed of sound. We show by construction that it is indeed possible to have inflationary backgrounds where the speed of sound remains suppressed and slow-roll persists for long enough. In this class of models, heavy fields influence the evolution of adiabatic modes in a manner that is consistent with decoupling of physical low and high energy degrees of freedom. We emphasize the distinction between the effective masses of the isocurvature modes and the eigenfrequencies of the propagating high energy modes. Crucially, we find that the mass gap that defines the high frequency modes increases with the strength of the turn, even as the naive heavy (isocurvature) and light (curvature) modes become more strongly coupled. Adiabaticity is preserved throughout, and the derived effective field theory remains in the weakly coupled regime, satisfying all current observational constraints on the resulting primordial power spectrum. In addition, these models allow for an observably large equilateral non-Gaussianity.

We re-analyse current single-field inflationary models related to primordial black holes formation. We do so by taking into account recent developments on the estimations of their abundances and the influence of non-gaussianities. We show that, for all of them, the gaussian approximation, which is typically used to estimate the primordial black holes abundances, fails. However, in the case in which the inflaton potential has an inflection point, the contribution of non-gaussianities is only perturbative. Finally, we infer that only models featuring an inflection point in the inflationary potential, might predict, with a very good approximation, the desired abundances by the sole use of the gaussian statistics.

We study the dynamics of two-field models of inflation characterized by a hierarchy of masses between curvature and isocurvature modes. When the hierarchy is large, a low energy effective field theory (EFT) exists in which only curvature modes participate in the dynamics of perturbations. In this EFT heavy fields continue to have a significant role in the low energy dynamics, as their interaction with curvature modes reduces their speed of sound whenever the multi-field trajectory is subject to a sharp turn in target space. Here we analyze under which general conditions this EFT remains a reliable description for the linear evolution of curvature modes. We find that the main condition consists on demanding that the rate of change of the turn's angular velocity stays suppressed with respect to the masses of heavy modes. This adiabaticity condition allows the EFT to accurately describe a large variety of situations in which the multi-field trajectory is subject to sharp turns. To test this, we analyze several models with turns and show that, indeed, the power spectra obtained for both the original two-field theory and its single-field EFT are identical when the adiabaticity condition is satisfied. In particular, when turns are sharp and sudden, they are found to generate large features in the power spectrum, accurately reproduced by the EFT.arXiv:1201.4848v3 [hep-th]

We continue the study of mild transient reductions in the speed of sound of the adiabatic mode during inflation, of their effect on the primordial power spectrum and bispectrum, and of their detectability in the Cosmic Microwave Background (CMB). We focus on the regime of moderately sharp mild reductions in the speed of sound during uninterrupted slow-roll inflation, a theoretically well motivated and self-consistent regime that admits an effective single-field description. The signatures on the power spectrum and bispectrum were previously computed using a slow-roll Fourier transform (SRFT) approximation, and here we compare it with generalized slow-roll (GSR) and in-in methods, for which we derive new formulas that account for moderately sharp features. The agreement between them is excellent, and also with the power spectrum obtained from the numerical solution to the equation of motion. We show that, in this regime, the SRFT approximation correctly captures with simplicity the effect of higher derivatives of the speed of sound in the mode equation, and makes manifest the correlations between power spectrum and bispectrum features. In a previous paper we reported hints of these correlations in the Planck data and here we perform several consistency checks and further analyses of the best fits, such as polarization and local significance at different angular scales. For the data analysis, we show the excellent agreement between the CLASS and CAMB Boltzmann codes. Our results confirm that the theoretical framework is consistent, and they suggest that the predicted correlations are robust enough to be searched for in CMB and Large Scale Structure (LSS) surveys. I. INTRODUCTIONThe paradigm of inflation as the explanation for the origin of cosmic structures has entered a decisive new phase. The latest data releases by the Planck [1] and WMAP [2] collaborations point towards models of inflation that produce a slightly red-tilted primordial power spectrum and a negligible amount of scale-independent bispectra, as predicted [3][4][5] by the simplest models of cosmological inflation, 1 but with a mild deficit of power on large scales. There are also mild hints of scale-dependent features in the CMB power spectrum [2,6] and in the primordial bispectrum [7]. Besides this, the discovery of B-mode polarization by BICEP2 [8], if it is confirmed to be result of primordial tensor modes, would have striking implications and put inflation on a much firmer footing. A large tensor-to-scalar ratio of r ∼ O(0.1) suggests -again, in the context of canonical models -a high scale of inflation around 10 16 GeV, a Hubble parameter H ∼ 10 14 GeV during inflation and a large, transplanckian excursion in field space for the inflaton [9].According to [10], there is currently a "very significant tension" (around 0.1% unlikely) between the Planck temperature (r < 0.11 95%c.l.) and BICEP2 polarization (r = 0.2 +0.05 −0.07 ) results. The model-independent cubic spline reconstruction [11] result shows that the vanishing scalar index running (dn ...

Primordial black holes (PBHs) may result from high peaks in a random field of cosmological perturbations. In single field inflationary models, such perturbations can be seeded as the inflaton overshoots a small barrier on its way down the potential. PBHs are then produced through two distinct mechanisms, during the radiation era. The first one is the familiar collapse of large adiabatic overdensities. The second one is the collapse induced by relic bubbles where the inflaton field is trapped in a false vacuum. The latter are due to rare backward fluctuations of the inflaton which prevented it from overshooting the barrier in horizon sized regions. We consider (numerically and analytically) the effect of non-Gaussianities on the threshold for overdensities to collapse into a PBH. Since typical high peaks have some dispersion in their shape or profile, we also consider the effect of such dispersion on the corresponding threshold for collapse. With these results we estimate the most likely channel for PBH production as a function of the non-Gaussianity parameter f NL . We also compare the threshold for collapse coming from the perturbative versus the non perturbative template for the non-Gaussianity arising in this model. We show that i) for f NL 3.5, the population of PBH coming from false vacuum regions dominates over that which comes from the collapse of large adiabatic overdensities, ii) the non-perturbative template of the non-Gaussianities is important to get accurate results. iii) the effect of the dispersion is small in determining the threshold for the compaction function, although it can be appreciable in determining the threshold amplitude for the curvature perturbation at low f NL . We also confirm that the volume averaged compaction function provides a very accurate universal estimator for the threshold.3 These are sometimes refered to as black holes with a baby universe inside. Note, however, that the baby universe is not in the trapped region, or "interior" of the black hole. Rather, the trapped region separates two normal regions, one in the parent ambient universe and the other in the baby universe, which were once causally connected but are not anymore, after the trapped region forms.4 In a nutshell, the problems is that ζ diverges when the amplitude of ζg reaches a critical value µ * , and it is not even defined for larger amplitude of ζg, for which there is a finite probability.5 Refs. [44,[51][52][53] consider the non-Gaussianity in the density perturbation δ due to the non-linear relation between δ and ζ. Note that such discussion would be redundant in our approach, where the initial conditions for numerical evolution, as well as the threshold estimators for gravitational collapse, are expressed directly in terms of ζ.

In the context of transient constant-roll inflation near a local maximum, we derive the non-perturbative field redefinition that relates a Gaussian random field with the true non-Gaussian curvature perturbation. Our analysis shows the emergence of a new critical amplitude ζ * , corresponding to perturbations that prevent the inflaton from overshooting the local maximum, thus becoming trapped in the false minimum of the potential. For potentials with a mild curvature at the local maximum (and thus small non-Gaussianity), we recover the known perturbative field redefinition. We apply these results to the formation of primordial black holes, and discuss the cases for which ζ * is smaller or of the same order than the critical value for collapse of spherically symmetric overdensities. In the latter case, we present a simple potential for which the power spectrum needs an amplitude 10 times smaller that in the Gaussian case for producing a sizeable amount of primordial black holes.1 A notable exception, where no amplification of the power spectrum is needed, are models where PBH are formed from the collapse of domain walls created during inflation [7,8].2 The amplitude of non-Gaussianities in transient periods of CR is different from their amplitude in a pure CR [16][17][18]. The difference between both scenarios is that in the former the curvature perturbations eventually freeze.

In multi-field inflation one or more non-adiabatic modes may become light, potentially inducing large levels of isocurvature perturbations in the cosmic microwave background. If in addition these light modes are coupled to the adiabatic mode, they influence its evolution on super horizon scales. Here we consider the case in which a non-adiabatic mode becomes approximately massless ("ultralight") while still coupled to the adiabatic mode, a typical situation that arises with pseudo-Nambu-Goldstone bosons or moduli. This ultralight mode freezes on super-horizon scales and acts as a constant source for the curvature perturbation, making it grow linearly in time and effectively suppressing the isocurvature component. We identify a Stückelberg-like emergent shift symmetry that underlies this behavior. As inflation lasts for many e-folds, the integrated effect of this source enhances the power spectrum of the adiabatic mode, while keeping the non-adiabatic spectrum approximately untouched. In this case, towards the end of inflation all the fluctuations, adiabatic and non-adiabatic, are dominated by a single degree of freedom. arXiv:1607.08609v2 [astro-ph.CO] 18 Apr 2017 * For a complementary discussion on the construction of multi-field actions within the effective field theory approach of inflation [29] see ref. [30]. † More precisely, because of the non-diagonal couplingṘσ, the parameter mσ is not the mass of any propagating state [31][32][33][34].

The first year of observations by the Planck satellite mission shows that the cosmic microwave background (CMB) fluctuations are consistent with gaussian statistics in the primordial perturbations, a key prediction of the simplest models of inflation. However, there are hints of anomalies in the CMB power spectrum and bispectrum. We check for the possibility that some of these anomalous features have a common physical origin in a transient reduction of the inflaton speed of sound. We do this by exploiting predicted correlations between the power spectrum and bispectrum. Our results suggest that current data might already be sensitive enough to detect transient reductions in the speed of sound as mild as a few percent. Since this is a signature of interactions, it opens a new window for the detection of extra degrees of freedom during inflation. PACS numbers: 98.80.Cq, 98.70.VcThe paradigm of inflation [1][2][3][4][5][6] in its simplest realizations is consistent with the latest data releases from the Planck [7] and WMAP [8] satellites. However, hints of a primordial oscillatory signal in the CMB bispectrum [9] and of anomalies in the CMB power spectrum [8, 10] motivate a search for correlated features produced by inflationary scenarios beyond canonical single-field. 1 Such correlation is in general expected and will differ depending on its physical origin [11], so it can be used to discriminate among inflationary mechanisms.On the theory side, several mechanisms that produce oscillatory features are being investigated. As first noted in [12], a step in the inflaton potential causes features in the spectra [13][14][15][16][17][18][19][20][21][22][23], and novel methodologies have been developed in [24][25][26][27][28][29] for more generic transient slow-roll violations. The effect of a variable speed of sound has also been analyzed both in the power spectrum [30][31][32] (for sudden variations see [23,28,[33][34][35]) and bispectrum [29,32,36] (see [23,35] for sudden variations). Different initial vacuum states (see e.g. [37-40]) or multi-field dynamics [41][42][43][44] may also cause oscillations in the primordial spectra.On the observational side, searches in the CMB power spectrum data have been performed for a variety of scenarios, such as transient slow-roll violations [20,28,[45][46][47][48][49][50], superimposed oscillations in the primordial power spectrum [51-57] and more general parametric forms (see [10] and references therein). In addition, the Planck collaboration searched for features in the CMB bispectrum for a number of theoretically motivated templates [9]. In none of these cases the statistical significance of the extended models has been found high enough to claim a detection. Still, it is becoming clear that hints of new physics (if any) are most likely to be detected in the correlation between different observables.In this spirit, this is the first in a series of papers in which we search for transient reductions in the speed of sound of the adiabatic mode consistent with (effectively) single-...