Testing and comparing tachyon inflation to single standard field inflation

We compare the standard single scalar field inflationary predictions with those of an inflationary phase driven by a tachyon field. A slow-roll formalism is defined for tachyon inflation and we derive the spectra of scalar and tensor perturbations as well as the consistency relations. At lowest order the predictions of standard and tachyon inflation are the same. Higher order deviations are present and their observational relevance is discussed. We discuss the observational consequences of some typical inflationary tachyon potentials and compare them with recent data. All the models predict a negative and very small running of the scalar spectral index, and they consistently lie within the 1$\sigma$ contour of the data set. However, the regime of blue scalar spectral index and large gravity waves is not explored by these models.Comment: Proceedings of the 10th Marcel Grossmann Meeting, Rio de Janeiro, July 2003, 6 pages, 1 figur

A geometrical approach to nonlinear perturbations in relativistic cosmology

We give a pedagogical review of a covariant and fully non-perturbative approach to study nonlinear perturbations in cosmology. In the first part, devoted to cosmological fluids, we define a nonlinear extension of the uniform-density curvature perturbation and derive its evolution equation. In the second part, we focus our attention on multiple scalar fields and present a nonlinear description in terms of adiabatic and entropy perturbations. In both cases, we show how the formalism presented here enables one to easily obtain equations up to second, third and higher orders.Comment: 16 pages; invited review article for Classical and Quantum Gravity issue on non-linear cosmolog

Effective Field Theory of Cosmological Perturbations

The effective field theory of cosmological perturbations stems from considering a cosmological background solution as a state displaying spontaneous breaking of time translations and (adiabatic) perturbations as the related Nambu-Goldstone modes. With this insight, one can systematically develop a theory for the cosmological perturbations during inflation and, with minor modifications, also describe in full generality the gravitational interactions of dark energy, which are relevant for late-time cosmology. The formalism displays a unique set of Lagrangian operators containing an increasing number of cosmological perturbations and derivatives. We give an introductory description of the unitary gauge formalism for theories with broken gauge symmetry---that allows to write down the most general Lagrangian---and of the Stueckelberg "trick"---that allows to recover gauge invariance and to make the scalar field explicit. We show how to apply this formalism to gravity and cosmology and we reproduce the detailed analysis of the action in the ADM variables. We also review some basic applications to inflation and dark energy.Comment: 27 pages, references added, matches published version as special issue article in Classical and Quantum Gravit

Full-sky lensing shear at second order

We compute the reduced cosmic shear up to second order in the gravitational potential without relying on the small angle or thin-lens approximation. This is obtained by solving the Sachs equation which describes the deformation of the infinitesimal cross-section of light bundle in the optical limit, and maps galaxy intrinsic shapes into their angular images. The calculation is done in the Poisson gauge without a specific matter content, including vector and tensor perturbations generated at second order and taking account of the inhomogeneities of a fixed redshift source plane. Our final result is expressed in terms of spin-2 operators on the sphere and is valid on the full sky. Beside the well known lens-lens and Born corrections that dominate on small angular scales, we find new non-linear couplings. These are a purely general relativistic intrinsic contribution, a coupling between the gravitational potential at the source with the lens, couplings between the time delay with the lens, couplings between two photon deflections, as well as non-linear couplings due to the second-order vector and tensor components. The inhomogeneity in the redshift of the source induces a coupling between the photon redshift with the lens. All these corrections become important on large angular scales and should thus be included when computing higher-order observables such as the bispectrum, in full or partially full-sky surveys.Comment: 29 pages, discussion about the first-order convergence added, matches published versio

δN\delta N formalism from superpotential and holography

We consider the superpotential formalism to describe the evolution of scalar fields during inflation, generalizing it to include the case with non-canonical kinetic terms. We provide a characterization of the attractor behaviour of the background evolution in terms of first and second slow-roll parameters (which need not be small). We find that the superpotential is useful in justifying the separate universe approximation from the gradient expansion, and also in computing the spectra of primordial perturbations around attractor solutions in the $\delta N$ formalism. As an application, we consider a class of models where the background trajectories for the inflaton fields are derived from a product separable superpotential. In the perspective of the holographic inflation scenario, such models are dual to a deformed CFT boundary theory, with $D$ mutually uncorrelated deformation operators. We compute the bulk power spectra of primordial adiabatic and entropy cosmological perturbations, and show that the results agree with the ones obtained by using conformal perturbation theory in the dual picture.Comment: 37 page

Weakly Broken Galileon Symmetry

Effective theories of a scalar $\phi$ invariant under the internal \textit{galileon symmetry} $\phi\to\phi+b_\mu x^\mu$ have been extensively studied due to their special theoretical and phenomenological properties. In this paper, we introduce the notion of \textit{weakly broken galileon invariance}, which characterizes the unique class of couplings of such theories to gravity that maximally retain their defining symmetry. The curved-space remnant of the galileon's quantum properties allows to construct (quasi) de Sitter backgrounds largely insensitive to loop corrections. We exploit this fact to build novel cosmological models with interesting phenomenology, relevant for both inflation and late-time acceleration of the universe.Comment: 26+8 pages, 2 figures, 2 table

Healthy theories beyond Horndeski

We introduce a new class of scalar-tensor theories that extend Horndeski, or "generalized galileon", models. Despite possessing equations of motion of higher order in derivatives, we show that the true propagating degrees of freedom obey well-behaved second-order equations and are thus free from Ostrogradski instabilities, in contrast to the standard lore. Remarkably, the covariant versions of the original galileon Lagrangians-obtained by direct replacement of derivatives with covariant derivatives-belong to this class of theories. These extensions of Horndeski theories exhibit an uncommon, interesting phenomenology: the scalar degree of freedom affects the speed of sound of matter, even when the latter is minimally coupled to gravity.Comment: 5 pages, version accepted in PR

Resilience of the standard predictions for primordial tensor modes

We show that the prediction for the primordial tensor power spectrum cannot be modified at leading order in derivatives. Indeed, one can always set to unity the speed of propagation of gravitational waves during inflation by a suitable disformal transformation of the metric, while a conformal one can make the Planck mass time-independent. Therefore, the tensor amplitude unambiguously fixes the energy scale of inflation. Using the Effective Field Theory of Inflation, we check that predictions are independent of the choice of frame, as expected. The first corrections to the standard prediction come from two parity violating operators with three derivatives. Also the correlator $$ is standard and only receives higher derivative corrections. These results hold also in multifield models of inflation and in alternatives to inflation and make the connection between a (quasi) scale-invariant tensor spectrum and inflation completely robust.Comment: 5 pages, reference added, version accepted in PR