General Single-field Inflation Research Articles

Anatomy of bispectra in general single-field inflation — Modal expansions

We discuss bispectra of single-field inflationary models described by general Lorentz invariant Lagrangians that are at most first order in field derivatives, including the fast-roll models investigated by Noller and Magueijo. Based on a factor analysis, we identify the least correlated basic contributions to the general shape and show quantitatively which templates provide a good approximation. We compute how relative contributions of basic shapes to the total bispectrum scale as slow roll is relaxed. To enable future comparison with CMB observations, we provide a modal expansion of these non-separable bispectra in Fourier space, employing the formalism by Fergusson et al. Convergence is rapid, usually better than ninety-five percent with less than thirty modes, due to the smoothness of these primordial shapes. Truncated polynomial modal expansions have restrictions, which we highlight using an example with slow convergence. The particular shape originates from particle production during inflation (common in trapped inflation) and entails both localized and oscillatory features. We show that this shape can be recovered efficiently using a Fourier basis and outline the prospect of future model parameter extraction and N-body simulations based on modal techniques.

Primordial Non-Gaussianities of Gravitational Waves in the Most General Single-Field Inflation Model with Second-Order Field Equations

We completely clarify the feature of primordial non-Gaussianities of tensor perturbations in the most general single-field inflation model with second-order field equations. It is shown that the most general cubic action for the tensor perturbation h(ij) is composed only of two contributions, one with two spacial derivatives and the other with one time derivative on each h(ij). The former is essentially identical to the cubic term that appears in Einstein gravity and predicts a squeezed shape, while the latter newly appears in the presence of the kinetic coupling to the Einstein tensor and predicts an equilateral shape. Thus, only two shapes appear in the graviton bispectrum of the most general single-field inflation model, which could open a new clue to the identification of inflationary gravitational waves in observations of cosmic microwave background anisotropies as well as direct detection experiments.

Generalized G-Inflation: --Inflation with the Most General Second-Order Field Equations--

We study generalized Galileons as a framework to develop the most general single-field inflation models ever, Generalized G-inflation, containing yet further generalization of G-inflation, as well as previous examples such as k-inflation, extended inflation, and new Higgs inflation as special cases. We investigate the background and perturbation evolution in this model, calculating the most general quadratic actions for tensor and scalar cosmological perturbations to give the stability criteria and the power spectra of primordial fluctuations. It is pointed out in the Appendix that the Horndeski theory and the generalized Galileons are equivalent. In particular, even the non-minimal coupling to the Gauss-Bonnet term is included in the generalized Galileons in a non-trivial manner.

Non-Gaussianity in single field models without slow-roll conditions

We investigate non-Gaussianity in general single field models without assuming slow-roll conditions or the exact scale-invariance of the scalar power spectrum. The models considered include general single field inflation (e.g. DBI and canonical inflation) as well as bimetric models. We compute the full non-Gaussian amplitude, its size fnl, its shape, and the running with scale n_{NG}. In doing so we show that observational constraints allow significant violations of slow roll conditions and we derive explicit bounds on slow-roll parameters for fast-roll single field scenarios. A variety of new observational signatures is found for models respecting these bounds. We also explicitly construct concrete model implementations giving rise to this new phenomenology.

Folded resonant non-Gaussianity in general single field inflation

We compute a novel type of large non-Gaussianity due to small periodic features in general single field inflationary models. We show that the non-Bunch-Davies vacuum component generated by features, although has a very small amplitude, can have significant impact on the non-Gaussianity. Three mechanisms are turned on simultaneously in such models, namely the resonant effect, non-Bunch-Davies vacuum and higher derivative kinetic terms, resulting in a bispectrum with distinctive shapes and running. The size can be equal to or larger than that previously found in each single mechanism. Our full results, including the resonant and folded resonant non-Gaussianities, give the leading order bispectra due to general periodic features in general single field inflation.

One-loop corrections to the power spectrum in general single-field inflation

We perfom a thorough computation of the one-loop corrections from both scalar and tensor degrees of freedom to the power spectrum of curvature fluctuations for non-canonical Lagrangians in single-field inflation. We consider models characterized by a small sound speed cs, which produce large non-Gaussianities. As expected, the corrections turn out to be inversely proportional to powers of cs; evaluating their amplitudes it is then possible to derive some theoretical bounds on the sound speed by requesting the conditions necessary for perturbation theory to hold.

On the squeezed limit of the bispectrum in general single field inflation

We investigate the consistency relation relating the squeezed limit of the bispectrum to the scalar spectral index in single field models of inflation. We give a simple integral formula for the bispectrum in the squeezed limit in terms of the free mode functions of the primordial curvature perturbation, in any Lorentz invariant single field model of inflation and without resorting to any approximation, generalizing a recent result obtained by Ganc and Komatsu in the case of canonical kinetic terms. We use our result to verify the consistency relation in an exactly solvable class of models with a non-trivial speed of sound. We then verify the consistency relation at the first non-trivial order in the slow-varying approximation in general single field inflation (a known result) and at second order in this approximation in canonical single field inflation.

Non-Gaussianity of quantum fields during inflation

In this paper, we discuss how non-Gaussianity of cosmological perturbations arises from inflation. After introducing the in–in formalism to calculate the n-point correlation function of quantum fields, we present the computation of the bispectrum of the curvature perturbation generated in general single-field inflation models. The shapes of the bispectrum are compared with the local-type non-Gaussianity that arises from nonlinear dynamics on super-horizon scales.

Large primordial trispectra in general single field inflation

We compute the large scalar four-point correlation functionsin general single field inflation models, where the inflatonLagrangian is anarbitrary function of the inflaton and its first derivative.We find that theleading order trispectra have four different shapes determined bythree parameters. We study features in these shapes that can be used todistinguish among themselves, and between them and the trispectra of the local form. For thepurpose of data analyses, we give two simple representative formsfor these ``equilateral trispectra''. Wealso study the effects on the trispectra if the initial state of inflationdeviates from the standard Bunch-Daviesvacuum.

Cosmological constraints on general, single field inflation

Inflation is now an accepted paradigm in standard cosmology, with its predictions consistent with observations of the cosmic microwave background. It lacks, however, a firm physical theory, with many possible theoretical origins beyond the simplest, canonical, slow-roll inflation, including Dirac-Born-Infeld inflation and k-inflation. We discuss how a hierarchy of Hubble flow parameters, extended to include the evolution of the inflationary sound speed, can be applied to compare a general, single field inflationary action with cosmological observational data. We show that it is important to calculate the precise scalar and tensor primordial power spectra by integrating the full flow and perturbation equations, since values of observables can deviate appreciably from those obtained using typical second-order Taylor expanded approximations in flow parameters. As part of this, we find that a commonly applied approximation for the tensor-to-scalar ratio, $r\ensuremath{\approx}16{c}_{s}ϵ$, becomes poor (deviating by as much as 50%) as ${c}_{s}$ deviates from 1 and hence the Taylor expansion including next-to-leading order contribution terms involving ${c}_{s}$ is required. By integrating the full flow equations, we use a Monte-Carlo-Markov-Chain approach to impose constraints on the parameter space of general single field inflation, and reconstruct the properties of such an underlying theory in light of recent cosmic microwave background and large-scale structure observations.

Non-Gaussianity from the trispectrum in general single field inflation

We compute the fourth order action in perturbation theory for scalar and second order tensor perturbations for a minimally coupled single field inflationary model, where the inflaton's Lagrangian is a general function of the field's value and its kinetic energy. We obtain the fourth order interaction Hamiltonian in two gauges, the comoving gauge and the uniform curvature gauge. Using the comoving gauge action we calculate the trispectrum at leading order in slow roll, finding agreement with a previously known result in the literature. We point out that, in general, to obtain the correct leading order trispectrum one cannot ignore second order tensor perturbations as previously done by others. The next-to-leading order corrections may become detectable depending on the shape, and we provide the necessary formalism to calculate them.

General single field inflation with large positive non-Gaussianity

Recent analysis of the WMAP three-year data suggests in the WMAP convention. It is necessary to make surewhether general single field inflation can produce a large positivefNL before turning to other scenarios. We give some examples to generate a large positivefNLequil in general single field inflation. Our models are different from ghost inflation. Due to theappearance of non-conventional kinetic terms, can be realized in single field inflation.

Observational signatures and non-Gaussianities of general single-field inflation

We perform a general study of primordial scalar non-Gaussianities in single-fieldinflationary models in Einstein gravity. We consider models where the inflaton Lagrangianis an arbitrary function of the scalar field and its first derivative, and the sound speed isarbitrary. We find that under reasonable assumptions, the non-Gaussianity iscompletely determined by five parameters. In special limits of the parameter space, onefinds distinctive ‘shapes’ of the non-Gaussianity. In models with a small soundspeed, several of these shapes would become potentially observable in the nearfuture. Different limits of our formulae recover various previously known results.

Enhancement of superhorizon scale inflationary curvature perturbations

We show that there exists a simple mechanism which can enhance the amplitude of curvature perturbations on superhorizon scales, relative to their amplitude at horizon crossing, even in some single-field inflation models. We give a criterion for this enhancement in general single-field inflation models; the condition for a significant effect is that the quantity $a\stackrel{\ifmmode \dot{}\else \.{}\fi{}}{\ensuremath{\varphi}}/H$ become sufficiently small, as compared to its value at horizon crossing, for some time interval during inflation.