Sébastien Renaux-Petel

Primordial perturbations and non-Gaussianities in DBI and general multifield inflation

We study cosmological perturbations in general inflation models with multiple scalar fields and arbitrary kinetic terms, with special emphasis on the multifield extension of Dirac-Born-Infeld (DBI) inflation. We compute the second-order action governing the dynamics of linear perturbations in the most general case. Specializing to DBI inflation, we show that the adiabatic and entropy modes propagate with a common effective sound speed and are thus amplified at sound horizon crossing. In the small sound speed limit, we find that the amplitude of the entropy modes is much higher than that of the adiabatic modes. We also derive, in the general case, the third-order action which is useful for studying primordial non-Gaussianities generated during inflation. In the DBI case, we compute the dominant contributions to non-Gaussianities, which depend on both the adiabatic and entropy modes.

Primordial Fluctuations and Non-Gaussianities in Multifield Dirac-Born-Infeld Inflation

We study Dirac-Born-Infeld inflation models with multiple scalar fields. We show that the adiabatic and entropy modes propagate with a common effective sound speed and are thus amplified at the sound horizon crossing. In the small sound speed limit, we find that the amplitude of the entropy modes is much higher than that of the adiabatic modes. We show that this could strongly affect the observable curvature power spectrum as well as the amplitude of non-Gaussianities, although their shape remains as in the single-field Dirac-Born-Infeld case.

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.

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 nonlinearity parameters f{sub NL} and g{sub NL} combine to leave a very distinct observational imprint.

Multi-field DBI inflation: introducing bulk forms and revisiting the gravitational wave constraints

We study multi-field Dirac-Born-Infeld (DBI) inflation models, taking into account the NS-NS and R-R bulk fields present in generic flux compactifications. We compute the second-order action, which governs the behaviour of linear cosmological perturbations, as well as the third-order action, which can be used to calculate non-Gaussianities in these models. Remarkably, for scalar-type perturbations, we show that the contributions due to the various form fields exactly cancel in both the second- and third-order actions. Primordial perturbations and their non-Gaussianities are therefore unaffected by the presence of form fields and our previous results are unmodified. We also study vector-type perturbations associated with the U(1) gauge field confined on the D3-brane, and discuss whether their quantum fluctuations can be amplified. Finally, we revisit the gravitational wave constraints on DBI inflation and show that an ultra-violet DBI multi-field scenario is still compatible with data, in contrast with the single field case, provided there is a transfer from entropy into adiabatic perturbations.

Nonlinear perturbations of cosmological scalar fields with non-standard kinetic terms

We adopt a covariant formalism to derive exact evolution equations for nonlinear perturbations, in a universe dominated by two scalar fields. These scalar fields are characterized by non-canonical kinetic terms and an arbitrary field space metric, a situation typically encountered in inflationary models inspired by string theory. We decompose the nonlinear scalar perturbations into adiabatic and entropy modes, generalizing the definition adopted in the linear theory, and we derive the corresponding exact evolution equations. We also obtain a nonlinear generalization of the curvature perturbation on uniform density hypersurfaces, showing that on large scales it is sourced only by the nonlinear version of the entropy perturbation. We then expand these equations to second order in the perturbations, using a coordinate based formalism. Our results are relatively compact and elegant and enable one to identify the new effects coming from the non-canonical structure of the scalar fields Lagrangian. We also explain how to analyze, in our formalism, the interesting scenario of multi-field Dirac-Born-Infeld inflation.

Non-gaussian inflationary shapes in G3 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 G3) 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.

DBI Galileon in the effective field theory of inflation: orthogonal non-Gaussianities and constraints from the Trispectrum

Very few explicit inflationary scenarios are known to generate a large bispectrum of orthogonal shape. Dirac-Born-Infeld Galileon inflation, in which an induced gravity term is added to the DBI action, is one such model. We formulate it in the language of the effective field theory of inflation by identifying the unitary gauge operators that govern the behavior of its cosmological fluctuations. We show how to recover rather easily from this its power spectrum and bispectrum, which we calculated previously using standard cosmological perturbation theory. We push our calculations up to the determination of the fourth-order action and of the trispectrum, in which shapes absent in k-inflation arise due to the presence of higher-order derivative operators. We finally discuss the combined constraints set on this model by current observational bounds on the bispectrum and trispectrum.

A modal approach to the numerical calculation of primordial non-Gaussianities

We propose a new method to numerically calculate higher-order correlation functions of primordial fluctuations generated from any early-universe scenario. Our key-starting point is the realization that the tree-level In-In formalism is intrinsically separable. This enables us to use modal techniques to efficiently calculate and represent non-Gaussian shapes in a separable form well suited to data analysis. We prove the feasibility and the accuracy of our method by applying it to simple single-field inflationary models in which analytical results are available, and we perform non-trivial consistency checks like the verification of the single field consistency relation. We also point out that the i prescription is automatically taken into account in our method, preventing the need for ad-hoc tricks to implement it numerically.

The trispectrum as a diagnostic of primordial orthogonal non-Gaussianities

In single-field inflationary models with a low sound speed, the orthogonal shape of the primordial bispectrum arises due to partial cancellations between equilateral-type shapes. This fact allows for a speed of sound cs as low as about 0.01, which is actually weakly preferred by WMAP data. For such values, the trispectrum, scaling like 1/cs4, is of order 108 and is therefore comparable to, and greater than, the 1σ observational bound tNLeq = (−3.11±7.5) × 106. Hence, the trispectrum is already constraining inflationary mechanisms candidates for generating an orthogonal bispectrum at the level hinted in WMAP data. If this signal persists in imminent Planck data, most of the parameter space of the simplest effective field theory of inflation will be under observational pressure, while a dedicated analysis will be needed for the substantial fraction of parameter space where we show that a qualitatively new, orthogonal, trispectrum naturally arises.