Multiple-field Inflationary Models Research Articles

Numerical evaluation of inflationary 3-point functions on curved field space—with the transport method & CppTransport

We extend the public CPPTRANSPORT code to calculate the statistical properties of fluctuations in multiple-field inflationary models with curved field space. Our implementation accounts for all physical effects at tree-level in the `in-in' diagrammatic expansion. This includes particle production due to time-varying masses, but excludes scenarios where the curvature perturbation is generated by averaging over the decay of more than one particle. We test our implementation by comparing results in Cartesian and polar field-space coordinates, showing excellent numerical agreement and only minor degradation in compute time. We compare our results with the PYTRANSPORT 2.0 code, which uses the same computational approach but a different numerical implementation, finding good agreement. Finally, we use our tools to study a class of gelaton-like models which could produce an enhanced non-Gaussian signal on equilateral configurations of the Fourier bispectrum. We show this is difficult to achieve using hyperbolic field-space manifolds and simple inflationary potentials.

Influence of heavy modes on perturbations in multiple field inflation

We investigate linear cosmological perturbations in multiple field inflationary models where some of the directions are light while others are heavy (with respect to the Hubble parameter). By integrating out the massive degrees of freedom, we determine the multi-dimensional effective theory for the light degrees of freedom and give explicitly the propagation matrix that replaces the effective sound speed of the one-dimensional case. We then examine in detail the consequences of a sudden turn along the inflationary trajectory, in particular the possible breakdown of the low energy effective theory in case the heavy modes are excited. Resorting to a new basis in field space, instead of the usual adiabatic/entropic basis, we study the evolution of the perturbations during the turn. In particular, we compute the power spectrum and compare with the result obtained from the low energy effective theory.

Transport equations for the inflationary trispectrum

We use transport techniques to calculate the trispectrum produced in multiple-field inflationary models with canonical kinetic terms. Our method allows the time evolution of the local trispectrum parameters, τNL and gNL, to be tracked throughout the inflationary phase. We illustrate our approach using examples. We give a simplified method to calculate the superhorizon part of the relation between field fluctuations on spatially flat hypersurfaces and the curvature perturbation on uniform density slices, ζ, and obtain its third-order part for the first time. We clarify how the `backwards' formalism of Yokoyama et al. relates to our analysis and other recent work. We supply explicit formulae which enable each inflationary observable to be computed in any canonical model of interest, using a suitable first-order ODE solver.

EVOLUTION OF NON-GAUSSIANITY IN MULTI-SCALAR FIELD MODELS

We study the evolution of non-Gaussianity in multiple-field inflationary models, focusing on three fundamental questions: (a) How is the sign and peak magnitude of the non-linearity parameter f NL related to generic features in the inflationary potential? (b) How sensitive is f NL to the process by which an adiabatic limit is reached, where the curvature perturbation becomes conserved? (c) For a given model, what is the appropriate tool – analytic or numerical – to calculate f NL at the adiabatic limit? We summarise recent results obtained by the authors and further elucidate them by considering an inflection point model.

EVOLUTION OF NON-GAUSSIANITY IN MULTI-SCALAR FIELD MODELS

We study the evolution of non-Gaussianity in multiple-field inflationary models, focusing on three fundamental questions: (a) How is the sign and peak magnitude of the non-linearity parameter f NL related to generic features in the inflationary potential? (b) How sensitive is f NL to the process by which an adiabatic limit is reached, where the curvature perturbation becomes conserved? (c) For a given model, what is the appropriate tool – analytic or numerical – to calculate f NL at the adiabatic limit? We summarise recent results obtained by the authors and further elucidate them by considering an inflection point model.

On the primordial trispectrum from exchanging scalar modes in general multiple field inflationary models

We make a complementary investigation of the primordial trispectrum from exchanging intermediate scalar modes in multi-field inflationary models with generalized kinetic terms. Together with the calculation of irreducible contributions to the primordial trispectrum in ref. [104], we give the full leading-order primordial trispectrum in generalized multi-field models.

Primordial non-Gaussianities from the trispectra in multiple field inflationary models

We investigate the primordial non-Gaussianities from the trispectra in multi-field inflation models, which can be seen as generalization of multi-field k-inflation and multi-DBI inflation. We derive the full fourth-order perturbation action for the inflaton fields and evaluate the four-point correlation functions for the perturbations in the limit ca << 1 and ce << 1. There are three types of momentum-dependentshape functions which arise from three types of four-pointinteraction vertices. The final trispectrum of the curvature perturbation can be expressed in terms of the deformations and permutations of these three shape functions, and is determined by ca, ce, λ , Π which depend on the non-linear structure of the model and also the transfer function Tℛ\U0001d4ae. We also discuss the parameter space for the trispectrum and plot the shape diagrams for the trispectrum both for visualization and for distinguishing different shapes from each other.

Non-Gaussianities in extendedD-term inflation

We explore extensions of hybrid inflationary models in the context of supersymmetric $D$-term inflation. We point out that a large variety of inflationary scenarios can be encountered when the field content is extended. It is not only possible to get curvaton type models but also scenarios in which different fields, with nontrivial statistical properties, contribute to the primordial curvature fluctuations. We explore more particularly the parameter space of these multiple-field inflationary models. It is shown that there exists a large domain in which significant primordial non-Gaussianities can be produced while preserving a scale free power spectrum for the metric fluctuations. In particular we explicitly compute the expected bispectrum and trispectrum for such models and compared the results to the current and expected observational constraints. It is shown that it is necessary to use both the bispectra and trispectra of cosmic microwave background anisotropies to efficiently reduce their parameter space.

NON-GAUSSIANITY OF GENERAL MULTIPLE-FIELD INFLATIONARY MODELS

Using the "δN-formalism," we obtain the expression of the non-Gaussianity of multiple-field inflationary models with the non-trivial field-space metric. Further, we have rewritten the result by using the slow-rolling approximation.