Primordial non-Gaussianities after Planck 2015: an introductory review

Deviations from Gaussian statistics of the cosmological density fluctuations, so-called primordial non-Gaussianities (NG), are one of the most informative fingerprints of the origin of structures in the universe. Indeed, they can probe physics at energy scales inaccessible to laboratory experiments, and are sensitive to the interactions of the field(s) that generated the primordial fluctuations, contrary to the Gaussian linear theory. As a result, they can discriminate between inflationary models that are otherwise almost indistinguishable. In this short review, we explain how to compute the non-Gaussian properties in any inflationary scenario. We review the theoretical predictions of several important classes of models. We then describe the ways NG can be probed observationally, and we highlight the recent constraints from the Planck mission, as well as their implications. We finally identify well motivated theoretical targets for future experiments and discuss observational prospects.Comment: 23 pages + bibliography. 5 figures. Published in the French "Comptes Rendus de l'Acad\'emie des Sciences" on Inflatio

Perturbations in generalized multi-field inflation

We study the linear perturbations of multi-field inflationary models governed by a Lagrangian which is a general function of the scalar fields and of a global kinetic term combining their spacetime gradients with an arbitrary field space metric. Our analysis includes k-inflation, DBI inflation and its multi-field extensions which have been recently studied. For this general class of models, we calculate the action to second order in the linear perturbations. We decompose the perturbations into an (instantaneous) adiabatic mode, parallel to the background trajectory, and entropy modes. We show that all the entropy modes propagate with the speed of light whereas the adiabatic mode propagates with an effective speed of sound. We also identify the specific combination of entropy modes which sources the curvature perturbation on large scales. We then study in some detail the case of two scalar fields: we write explicitly the equations of motion for the adiabatic and entropy modes in a compact form and discuss their quantum fluctuations and primordial power spectra.Comment: 27 pages, typos corrected, published versio

Non-Gaussian inflationary shapes in G3G^3 theories beyond Horndeski

We consider the possible signatures of a recently introduced class of healthy theories beyond Horndeski models on higher-order correlators of the inflationary curvature fluctuation. Despite the apparent large number and complexity of the cubic interactions, we show that the leading-order bispectrum generated by the Generalized Horndeski (also called $G^3$) interactions can be reduced to a linear combination of two well known $k$-inflationary shapes. We conjecture that said behavior is not an accident of the cubic order but a consequence dictated by the requirements on the absence of Ostrogradski instability, the general covariance and the linear dispersion relation in these theories.Comment: 17 pages. Analysis expanded and some references adde

On reaching the adiabatic limit in multi-field inflation

We calculate the scalar spectral index $n_s$ and the tensor-to-scalar ratio $r$ in a class of recently proposed two-field no-scale inflationary models in supergravity. We show that, in order to obtain correct predictions, it is crucial to take into account the coupling between the curvature and the isocurvature perturbations induced by the noncanonical form of the kinetic terms. This coupling enhances the curvature perturbation and suppresses the resulting tensor-to-scalar ratio to the per mille level even for values of the slow-roll parameter $\epsilon \sim 0.01$. Beyond these particular models, we emphasise that multifield models of inflation are a priori not predictive, unless one supplies a prescription for the post-inflationary era, or an adiabatic limit is reached before the end of inflation. We examine the conditions that enabled us to actually derive predictions in the models under study, by analysing the various contributions to the effective isocurvature mass in general two-field inflationary models. In particular, we point out a universal geometrical contribution that is important at the end of inflation, and which can be directly extracted from the inflationary Lagrangian, independently of a specific trajectory. Eventually, we point out that spectator fields can lead to oscillatory features in the time-dependent power spectra at the end of inflation. We demonstrate how these features can be model semi-analytically as well as the theoretical uncertainties they can entail.Comment: 26 pages. 13 figures. One additional author. Substantially reworked and extende

Geometrical Destabilization of Inflation

We show the existence of a general mechanism by which heavy scalar fields can be destabilized during inflation, relying on the fact that the curvature of the field space manifold can dominate the stabilizing force from the potential and destabilize inflationary trajectories. We describe a simple and rather universal setup in which higher-order operators suppressed by a large energy scale trigger this instability. This phenomenon can prematurely end inflation, thereby leading to important observational consequences and sometimes excluding models that would otherwise perfectly fit the data. More generally, it modifies the interpretation of cosmological constraints in terms of fundamental physics. We also explain how the geometrical destabilization can lead to powerful selection criteria on the field space curvature of inflationary models.Comment: 5 pages, 1 figure. Extended discussion, additional results. Version published in PR

Multifield Cosmological Perturbations at Third Order and the Ekpyrotic Trispectrum

Using the covariant formalism, we derive the equations of motion for adiabatic and entropy perturbations at third order in perturbation theory for cosmological models involving two scalar fields. We use these equations to calculate the trispectrum of ekpyrotic and cyclic models in which the density perturbations are generated via the entropic mechanism. In these models, the conversion of entropy into curvature perturbations occurs just before the big bang, either during the ekpyrotic phase or during the subsequent kinetic energy dominated phase. In both cases, we find that the non-linearity parameters f_{NL} and g_{NL} combine to leave a very distinct observational imprint.Comment: 36 pages, 5 figures, replaced with published versio