Gerasimos Rigopoulos

Separate universe approach and the evolution of nonlinear superhorizon cosmological perturbations

In this paper we review the separate universe approach for cosmological perturbations and point out that it is essentially the lowest order approximation to a gradient expansion. Using this approach, one can study the nonlinear evolution of inhomogeneous spacetimes and find the conditions under which the long wavelength curvature perturbation can vary with time. When there is one degree of freedom or a well-defined equation of state the nonlinear long wavelength curvature perturbation remains constant. With more degrees of freedom it can vary and this variation is determined by the nonadiabatic pressure perturbation, exactly as in linear theory. We identify combinations of spatial vectors characterizing the curvature perturbation which are invariant under a change of time hypersurfaces.

Large non-Gaussianity in multiple-field inflation

We investigate non-Gaussianity in general multiple-field inflation using the formalism we developed in earlier papers. We use a perturbative expansion of the nonlinear equations to calculate the three-point correlator of the curvature perturbation analytically. We derive a general expression that involves only a time integral over background and linear perturbation quantities. We work out this expression explicitly for the two-field slow-roll case, and find that non-Gaussianity can be orders of magnitude larger than in the single-field case. In particular, the bispectrum divided by the square of the power spectrum can easily be of

Nonlinear perturbations in multiple-field inflation

\mathcal{O}(1--10)

Quantitative bispectra from multifield inflation

, depending on the model. Our result also shows the explicit momentum dependence of the bispectrum. This conclusion of large non-Gaussianity is confirmed in a semianalytic investigation of a simple quadratic two-field model.

On the divergences of inflationary superhorizon perturbations

We develop a nonlinear framework for describing long-wavelength perturbations in multiple-field inflation. The basic variables describing inhomogeneities are defined in a nonperturbative manner, are invariant under changes of time slicing on large scales and include both matter and metric perturbations. They are combinations of spatial gradients generalizing the gauge-invariant variables of linear theory. Dynamical equations are derived and supplemented with stochastic source terms which provide the long-wavelength initial conditions determined from short-wavelength modes. Solutions can be readily obtained via numerical simulations or analytic perturbative expansions. The latter are much simpler than the usual second-order perturbation theory. Applications are given in a companion paper.

Non-linear inflationary perturbations

After simplifying and improving the non-Gaussian formalism we developed in previous work, we derive a quantitative expression for the three-point correlator (bispectrum) of the curvature perturbation in general multiple-field inflation models. Our result describes the evolution of non-Gaussianity on superhorizon scales caused by the nonlinear influence of isocurvature perturbations on the adiabatic perturbation during inflation. We then study a simple quadratic two-field potential and find that, when slow roll breaks down and the field trajectory changes direction in field space, the non-Gaussianity can become large. However, for the simple models studied to date, the magnitude of this non-Gaussianity decays away after the isocurvature mode is converted into the adiabatic mode.

The subdominant curvaton

We discuss the infrared divergences that appear to plague cosmological perturbation theory. We show that, within the stochastic framework, they are regulated by eternal inflation so that the theory predicts finite fluctuations. Using the ΔN formalism to one loop, we demonstrate that the infrared modes can be absorbed into additive constants and the coefficients of the diagrammatic expansion for the connected parts of two-and three-point functions of the curvature perturbation. As a result, the use of any infrared cutoff below the scale of eternal inflation is permitted, provided that the background fields are appropriately redefined. The natural choice for the infrared cutoff would, of course, be the present horizon; other choices manifest themselves in the running of the correlators. We also demonstrate that it is possible to define observables that are renormalization-group-invariant. As an example, we derive a non-perturbative, infrared finite and renormalization point-independent relation between the two-point correlators of the curvature perturbation for the case of the free single field.

Self-regulation of infrared correlations for massless scalar fields during inflation

We present a method by which cosmological perturbations can be quantitatively studied in single-field and multi-field inflationary models beyond linear perturbation theory. A non-linear generalization of the gauge-invariant Sasaki–Mukhanov variables is used in a long wavelength approximation. These generalized variables remain invariant under time slicing changes on long wavelengths. The equations they obey are relatively simple and can be formulated for a number of time slicing choices. Initial conditions are set after horizon crossing and the subsequent evolution is fully non-linear. We briefly discuss how these methods can be implemented numerically in the study of non-Gaussian signatures from specific inflationary models.

Simple route to non-Gaussianity in inflation

We present a systematic study of the amplitude of the primordial perturbation in curvaton models with self-interactions, treating both renormalizable and non-renormalizable interactions. In particular, we consider the possibility that the curvaton energy density is subdominant at the time of the curvaton decay. We find that large regions in the parameter space give rise to the observed amplitude of primordial perturbation even for non-renormalizable curvaton potentials, for which the curvaton energy density dilutes fast. At the time of its decay, the curvaton energy density may typically be subdominant by a relative factor of 10−3 and still produce the observed perturbation. Field dynamics turns out to be highly non-trivial, and for non-renormalizable potentials and certain regions of the parameter space we observe a non-monotonous relation between the final curvature perturbation and the initial curvaton value. In those cases, the time evolution of the primordial perturbation also displays an oscillatory behaviour before the curvaton decay.

Parametric decay of the curvaton

Self-energies of a minimally coupled scalar field with quartic and trilinear interactions are calculated in a de Sitter background, using a position space propagator. For quartic interactions, we recover earlier results for the seagull diagram, namely that it contributes an effective mass for the scalar field at leading order in the infrared enhancement in a steady-state de Sitter background. We further show that the sunset diagram also contributes to this effective mass and argue that these two contributions are sufficient in order to determine a self-consistent dynamical mass. In addition, trilinear interactions also induce a dynamical mass for the scalar field which we calculate. Since an interacting scalar field in de Sitter acquires a dynamical mass through these loop corrections, the infrared divergences of the two-point correlator are naturally self-regulated.