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Register a new userThe effects of a fast-turning trajectory in multiple-field inflation
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Added by
Krzysztof Turzynski
Publication date
2014
fields
Physics
and research's language is
English
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The latest results from PLANCK impose strong constraints on features in the spectrum of the curvature perturbations from inflation. We analyse the possibility of particle production induced by sharp turns of the trajectory in field space in inflation models with multiple fields. Although the evolution of the background fields can be altered by particle production, we find rather modest changes in the power spectrum even for the most extreme case in which the entire kinetic energy of the scalar fields is converted into particles.
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We present a complete framework for numerical calculation of the power spectrum and bispectrum in canonical inflation with an arbitrary number of light or heavy fields. Our method includes all relevant effects at tree-level in the loop expansion, including (i) interference between growing and decaying modes near horizon exit; (ii) correlation and coupling between species near horizon exit and on superhorizon scales; (iii) contributions from mass terms; and (iv) all contributions from coupling to gravity. We track the evolution of each correlation function from the vacuum state through horizon exit and the superhorizon regime, with no need to match quantum and classical parts of the calculation; when integrated, our approach corresponds exactly with the tree-level Schwinger or in-in formulation of quantum field theory. In this paper we give the equations necessary to evolve all two- and three-point correlation functions together with suitable initial conditions. The final formalism is suitable to compute the amplitude, shape, and scale dependence of the bispectrum in models with |fNL| of order unity or less, which are a target for future galaxy surveys such as Euclid, DESI and LSST. As an illustration we apply our framework to a number of examples, obtaining quantitatively accurate predictions for their bispectra for the first time. Two accompanying reports describe publicly-available software packages that implement the method.
We examine the momentum dependence of the bispectrum of two-field inflationary models within the long-wavelength formalism. We determine the sources of scale dependence in the expression for the parameter of non-Gaussianity fNL and study two types of variation of the momentum triangle: changing its size and changing its shape. We introduce two spectral indices that quantify the possible types of momentum dependence of the local type fNL and illustrate our results with examples.
We study the sensitivity of cosmological observables to the reheating phase following inflation driven by many scalar fields. We describe a method which allows semi-analytic treatment of the impact of perturbative reheating on cosmological perturbations using the sudden decay approximation. Focusing on $mathcal{N}$-quadratic inflation, we show how the scalar spectral index and tensor-to-scalar ratio are affected by the rates at which the scalar fields decay into radiation. We find that for certain choices of decay rates, reheating following multiple-field inflation can have a significant impact on the prediction of cosmological observables.
We calculate the conditions required to produce a large local trispectrum during two-field slow-roll inflation. This is done by extending and simplifying the heatmap approach developed by Byrnes et al. The conditions required to generate a large trispectrum are broadly the same as those that can produce a large bispectrum. We derive a simple relation between tauNL and fNL for models with separable potentials, and furthermore show that gNL and tauNL can be related in specific circumstances. Additionally, we interpret the heatmaps dynamically, showing how they can be used as qualitative tools to understand the evolution of non-Gaussianity during inflation. We also show how fNL, tauNL and gNL are sourced by generic shapes in the inflationary potential, namely ridges, valleys and inflection points.
We present a new class of two-field inflationary attractor models, known as `shift-symmetric orbital inflation, whose behaviour is strongly multi-field but whose predictions are remarkably close to those of single-field inflation. In these models, the field space metric and potential are such that the inflaton trajectory is along an `angular isometry direction whose `radius is constant but arbitrary. As a result, the radial (isocurvature) perturbations away from the trajectory are exactly massless and they freeze on superhorizon scales. These models are the first exact realization of the `ultra-light isocurvature scenario, previously described in the literature, where a combined shift symmetry emerges between the curvature and isocurvature perturbations and results in primordial perturbation spectra that are entirely consistent with current observations. Due to the turning trajectory, the radial perturbation sources the tangential (curvature) perturbation and makes it grow linearly in time. As a result, only one degree of freedom (i.e. the one from isocurvature modes) is responsible for the primordial observables at the end of inflation, which yields the same phenomenology as in single-field inflation. In particular, isocurvature perturbations and local non-Gaussianity are highly suppressed here, even if the inflationary dynamics is truly multi-field. We comment on the generalization to models with more than two fields.
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