Large non-Gaussianity Research Articles

Primordial non-Gaussianity from ultra slow-roll Galileon inflation

We present a detailed study of the generation of large primordial non-Gaussianities during the slow-roll (SR) to ultra-slow roll (USR) transitions in the framework of Galileon inflation. We found out that due to having sharp transitions in the USR phase, which persist with a duration of Δ𝒩USR ∼ 2 e-folds, we are able to generate the non-Gaussianity amplitude of the order: |f NL| ∼ 𝒪(10-2) in the SRI, -5 < f NL < 5 in the USR, and -2 < f NL < 2 in the SRII phases. As a result, we are able to achieve a cumulative average value of |f NL| ∼ 𝒪(1). This implies that our results strictly satisfy Maldacena's no-go theorem in the squeezed limit only for SRI, while they strictly violate the same condition in both the USR and SRII phases.The non-renormalization theorem in the Galileon theory helps to support our results regarding the generation of large mass primordial black holes along with large non-Gaussianities, which we show to be dependent on the specific positions of the transition wave numbers fixed at low scales.

Savior curvatons and large non-Gaussianity

Curvatons are light (compared to the Hubble scale during inflation) spectator fields during inflation that potentially contribute to adiabatic curvature perturbations post-inflation. They can alter CMB observables such as the spectral index ns, the tensor-to-scalar ratio r, and the local non-Gaussianity fNLloc\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {f}_{\ extrm{NL}}^{\\left(\ extrm{loc}\\right)} $$\\end{document}. We systematically explore the observable space of a curvaton with a quadratic potential. We find that when the underlying inflation model does not satisfy the ns and r observational constraints but can be made viable with a significant contribution from what we call a savior curvaton, a large fNLloc\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\left|{f}_{\ extrm{NL}}^{\\left(\ extrm{loc}\\right)}\\right| $$\\end{document}> 0.05, such that the model is distinguishable from single-field inflation, is inevitable. On the other hand, when the underlying inflation model already satisfies the ns and r observational constraints, so significant curvaton contribution is forbidden, a large fNLloc\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\left|{f}_{\ extrm{NL}}^{\\left(\ extrm{loc}\\right)}\\right| $$\\end{document}> 0.05 is possible in the exceptional case when the isocurvature fluctuation in the curvaton fluid is much greater than the global curvature fluctuation.

Ruling Out Initially Clustered Primordial Black Holes as Dark Matter.

Combining constraints from microlensing and Lyman-α forest, we provide a simple argument to show that large spatial clustering of stellar-mass primordial black holes at the time of formation, such as the one induced by the presence of large non-Gaussianities, is ruled out. Therefore, it is not possible to evade existing constraints preventing stellar-mass primordial black holes from being a dominant constituent of the dark matter by boosting their initial clustering.

Non-Gaussianity in DHOST inflation

DHOST inflation models where deviations from a pure de Sitter background are induced by an axion-like potential can lead to large non-Gaussianities. We investigate the nature of non-Gaussianities in these models and compare to the results given by the Planck experiment. The overlap between the DHOST non-Gaussianities and the equilateral, orthogonal and local templates can be rendered arbitrarily small. On the other hand, this does not preclude DHOST models from showing large non-Gaussianities as exemplified by their reduced bispectrum. As a result, they could be probed by future experiments and also by a more thorough analysis of the existing Planck data.

Origin of ultra-light fields during inflation and their suppressed non-Gaussianity

We study the structure of multi-field inflation models where the primordial curvature perturbation is able to vigorously interact with an ultra-light isocurvature field — a massless fluctuation orthogonal to the background inflationary trajectory in field space. We identify a class of inflationary models where ultra-light fields can emerge as a consequence of an underlying “scaling transformation” that rescales the entire system's action and keeps the classical equations of motion invariant. This scaling invariance ensures the existence of an ultra-light fluctuation that freezes after horizon crossing. If the inflationary trajectory is misaligned with respect to the scaling symmetry direction, then the isocurvature field is proportional to this ultra-light field, and becomes massless. In addition, we find that even if the isocurvature field interacts strongly with the curvature perturbation — transferring its own statistics to the curvature perturbation — it is unable to induce large non-Gaussianity. The reason is simply that the same mechanism ensuring a suppressed mass for the isocurvature field is also responsible for suppressing its self-interactions. As a result, in models with light isocurvature fields the bispectrum is generally expected to be slow-roll suppressed, but with a squeezed limit that differs from Maldacena's consistency relation.

Minimizing gravitational lensing contributions to the primordial bispectrum covariance

The next generation of ground-based CMB experiments aim to measure temperature and polarization fluctuations up to $\ell_{\rm max} \approx 5000$ over half of the sky. Combined with Planck data on large scales, this will provide improved constraints on primordial non-Gaussianity. However, the impressive resolution of these experiments will come at a price. Besides signal confusion from galactic foregrounds, extra-galactic foregrounds and late-time gravitational effects, gravitational lensing will introduce large non-Gaussianity that can become the leading contribution to the bispectrum covariance through the connected 4-point function. Here, we compute this effect analytically for the first time on the full sky for both temperature and polarization. We compare our analytical results with those obtained directly from map-based simulations of the CMB sky for several levels of instrumental noise. Of the standard shapes considered in the literature, the local shape is most affected, resulting in a 35\% increase of the estimator standard deviation for an experiment like the Simons Observatory (SO) and a 110\% increase for a cosmic-variance limited experiment, including both temperature and polarization modes up to $\ell_{\rm max} = 3800$. Because of the nature of the lensing 4-point function, the impact on other shapes is reduced while still non negligible for the orthogonal shape. Two possible avenues to reduce the non-Gaussian contribution to the covariance are proposed. First by marginalizing over lensing contributions, such as the ISW-lensing 3pt function in temperature, and second by delensing the CMB. We show the latter method can remove almost all extra covariance, reducing the effect to below $<$5\% for local bispectra. At the same time, delensing would remove signal biases from secondaries induced by lensing, such as ISW-lensing.

Observational Viability of an Inflation Model with E-model Nonminimal Derivative Coupling

Abstract By starting with a two-fields model in which the fields and their derivatives are nonminimally coupled to gravity, and then by using a conformal gauge, we obtain a model in which the derivatives of the canonically normalized field are nonminimally coupled to gravity. By adopting some appropriate functions, we study two cases with constant and E-model nonminimal derivative coupling, while the potential in both cases is chosen to be E-model one. We show that contrary to the single-field α-attractor model, there is an attractor point in the large N and small α limits in our setup, and for both mentioned cases there is an attractor line in these limits that the r−n s trajectories tend to. By studying the linear and nonlinear perturbations in this setup, and by comparing the numerical results with Planck2015 observational data, we obtain some constraints on the free parameter α. We show that by considering the E-model potential and coupling function, the model is observationally viable for all values of M (mass scale of the model). We use the observational constraints on the tensor-to-scalar ratio and the consistency relation to obtain some constraints on the sound speed of the perturbations in this model. As a result, we show that in a nonminimal derivative α-attractor model, it is possible to have small sound speed and therefore large non-Gaussianity.

Primordial fluctuations and non-Gaussianities in sidetracked inflation

Heavy scalar fields can undergo an instability during inflation as a result of their kinetic couplings with the inflaton. This is known as the geometrical destabilization of inflation, as it relies on the effect of the negative curvature of the field-space manifold overcoming the stabilizing force of the potential. This instability can drive the system away from its original path in field space into a new inflationary attractor, a scenario that we dub sidetracked inflation. We study this second phase and its observable consequences in several classes of two-field models. We show that cosmological fluctuations exhibit varied behaviours depending on the potential and the field space geometry, and that they can be captured by single-field effective theories with either a modified dispersion relation, a reduced speed of sound, or an imaginary one—the latter case describing a transient tachyonic growth of the fluctuations. We also numerically calculate the bispectrum with the transport approach, finding large non-Gaussianities of equilateral and orthogonal shapes. In the hyperbolic geometry the potentials of our models present a pole at the boundary of the Poincar'e disk and we discuss their relationships with α-attractors.

Non-Gaussianity in two-field inflation beyond the slow-roll approximation

We use the long-wavelength formalism to investigate the level of bispectral non-Gaussianity produced in two-field inflation models with standard kinetic terms. Even though the Planck satellite has so far not detected any primordial non-Gaussianity, it has tightened the constraints significantly, and it is important to better understand what regions of inflation model space have been ruled out, as well as prepare for the next generation of experiments that might reach the important milestone of Δ fNLlocal=1. We derive an alternative formulation of the previously derived integral expression for fNL, which makes it easier to physically interpret the result and see which types of potentials can produce large non-Gaussianity. We apply this to the case of a sum potential and show that it is very difficult to satisfy simultaneously the conditions for a large fNL and the observational constraints on the spectral index ns. In the case of the sum of two monomial potentials and a constant we explicitly show in which small region of parameter space this is possible, and we show how to construct such a model. Finally, the new general expression for fNL also allows us to prove that for the sum potential the explicit expressions derived within the slow-roll approximation remain valid even when the slow-roll approximation is broken during the turn of the field trajectory (as long as only the ϵ slow-roll parameter remains small).

Some aspects of nonminimal inflation driven by a superpotential

We study a nonminimal inflation which is driven by a superpotential. By adopting the Arnowitt–Deser–Misner formalism, we explore the primordial perturbations and its non-Gaussianity in this framework. By expanding the action up to the second-order in perturbations, we seek the scalar spectral index, its running and the tensor-to-scalar ratio. In this regard, we find the ranges of the nonminimal coupling and superpotential parameters which lead to the observationally viable perturbations parameters. The non-Gaussian feature in both the equilateral and orthogonal configurations in this setup, is studied by exploring the third-order action. We show that in some ranges of the nonminimal and superpotential parameters, the model predicts large non-Gaussianity. By comparing the numerical results with Planck2015 data, we test the viability of the model and find some constraints on the model’s parameters space.

Differentiating G-inflation from string gas cosmology using the effective field theory approach

A characteristic signature of String Gas Cosmology is primordial power spectra for scalar and tensor modes which are almost scale-invariant but with a red tilt for scalar modes but a blue tilt for tensor modes. This feature, however, can also be realized in the so-called G-inflation model, in which Horndeski operators are introduced which leads to a blue tensor tilt by softly breaking the Null Energy Condition. In this article we search for potential observational differences between these two cosmologies by performing detailed perturbation analyses based on the Effective Field Theory approach. Our results show that, although both two models produce blue tilted tensor perturbations, they behave differently in three aspects. Firstly, String Gas Cosmology predicts a specific consistency relation between the index of the scalar modes ns and that of tensor ones nt, which is hard to be reproduced by G-inflation. Secondly, String Gas Cosmology typically predicts non-Gaussianities which are highly suppressed on observable scales, while G-inflation gives rise to observationally large non-Gaussianities because the kinetic terms in the action become important during inflation. However, after finely tuning the model parameters of G-inflation it is possible to obtain a blue tensor spectrum and negligible non-Gaussianities with a degeneracy between the two models. This degeneracy can be broken by a third observable, namely the scale dependence of the nonlinearity parameter, which vanishes for G-inflation but has a blue tilt in the case of String Gas Cosmology. Therefore, we conclude that String Gas Cosmology is in principle observationally distinguishable from the single field inflationary cosmology, even allowing for modifications such as G-inflation.

Holographic non-Gaussianities in general single-field inflation

We use holographic techniques to compute inflationary non-Gaussianities for general single-field inflation, including models with a non-trivial sound speed. In this holographic approach, the inflationary dynamics is captured by a relevant deformation of the dual conformal field theory (CFT) in the UV, while the inflationary correlators are computed by conformal perturbation theory. In this paper, we discuss the effects of higher derivative operators, such as $(\partial_\mu\phi\partial^\mu\phi)^{m}$, which are known to induce a non-trivial sound speed and source potentially large non-Gaussianities. We compute the full inflationary bispectra from the deformed CFT correlators. We also discuss the squeezed limit of the bispectra from the viewpoint of operator product expansions. As is generic in the holographic description of inflation, our power spectrum is blue tilted in the UV region. We extend our bispectrum computation to the IR region by resumming the conformal perturbations to all orders. We provide a self-consistent setup which reproduces a red tilted power spectrum, as well as all possible bispectrum shapes in the slow-roll regime.

Sound Speed of Primordial Fluctuations in Supergravity Inflation.

We study the realization of slow-roll inflation in N=1 supergravities where inflation is the result of the evolution of a single chiral field. When there is only one flat direction in field space, it is possible to derive a single-field effective field theory parametrized by the sound speed c_{s} at which curvature perturbations propagate during inflation. The value of c_{s} is determined by the rate of bend of the inflationary path resulting from the shape of the F-term potential. We show that c_{s} must respect an inequality that involves the curvature tensor of the Kähler manifold underlying supergravity, and the ratio M/H between the mass M of fluctuations ortogonal to the inflationary path, and the Hubble expansion rate H. This inequality provides a powerful link between observational constraints on primordial non-Gaussianity and information about the N=1 supergravity responsible for inflation. In particular, the inequality does not allow for suppressed values of c_{s} (values smaller than c_{s}∼0.4) unless (a)the ratio M/H is of order 1 or smaller, and (b)the fluctuations of mass M affect the propagation of curvature perturbations by inducing on them a nonlinear dispersion relation during horizon crossing. Therefore, if large non-Gaussianity is observed, supergravity models of inflation would be severely constrained.

Odd tensor modes from inflation

The existence of a primordial spectrum of gravitational waves is a generic prediction of inflation. Here, I will discuss under what conditions the coupling of a pseudoscalar inflaton to a U(1) gauge field can induce, in a two-step process, gravitational waves with unusual properties such as: (i) a net chirality, (ii) a blue spectrum, (iii) large non-Gaussianities even if the scalar perturbations are approximately Gaussian and (iv) being detectable in the (relatively) near future by ground-based gravitational interferometers.

Large non-gaussianity in a non-minimally coupled derivative inflationary model with Gauss-Bonnet correction

We study a nonminimal derivative inflationary model in the presence of the Gauss-Bonnet term. To have a complete treatment of the model, we consider a general form of the nonminimal derivative function and also the Gauss-Bonnet coupling term. By following the ADM formalism, expanding the action up to the third order in the perturbations and using the correlation functions, we study the perturbation and its non-Gaussian feature in details. We also study the consistency relation that gets modified in the presence of the Gauss-Bonnet term in the action. We compare the results of our consideration in confrontation with Planck2015 observational data and find some constraints on the model's parameters. Our treatment shows that this model in some ranges of the parameters is consistent with the observational data. Also, in some ranges of model's parameters, the model predicts blue-tilted power spectrum. Finally, we show that nonminimal derivative model in the presence of the GB term has capability to have large non-Gaussianity.

Inflation with an extra light scalar field after Planck

Bayesian inference techniques are used to investigate situations where an additional light scalar field is present during inflation and reheating. This includes (but is not limited to) curvaton-type models. We design a numerical pipeline where ≃ 200 inflaton setups × 10 reheating scenarios = 2000 models are implemented and we present the results for a few prototypical potentials. We find that single-field models are remarkably robust under the introduction of light scalar degrees of freedom. Models that are ruled out at the single-field level are not improved in general, because good values of the spectral index and the tensor-to-scalar ratio can only be obtained for very fine-tuned values of the extra field parameters and/or when large non-Gaussianities are produced. The only exception is quartic large-field inflation, so that the best models after Planck are of two kinds: plateau potentials, regardless of whether an extra field is added or not, and quartic large-field inflation with an extra light scalar field, in some specific reheating scenarios. Using Bayesian complexity, we also find that more parameters are constrained for the models we study than for their single-field versions. This is because the added parameters not only contribute to the reheating kinematics but also to the cosmological perturbations themselves, to which the added field contributes. The interplay between these two effects lead to a suppression of degeneracies that is responsible for having more constrained parameters.

Suppressing the primordial tensor amplitude without changing the scalar sector in quadratic curvature gravity

We address the question of how one can modify the inflationary tensor spectrum without changing at all the successful predictions on the curvature perturbation. We show that this is indeed possible, and determine the two quadratic curvature corrections that are free from instabilities and affect only the tensor sector at the level of linear cosmological perturbations. Both of the two corrections can reduce the tensor amplitude, though one of them generates large non-Gaussianity of the curvature perturbation. It turns out that the other one corresponds to so-called Lorentz-violating Weyl gravity. In this latter case one can obtain as small as 65% of the standard tensor amplitude. Utilizing this effect we demonstrate that even power-law inflation can be within the 2$\sigma$ contour of the Planck results.

Inflation with massive vector fields

We investigate the coupling between the inflaton and massive vector fields. All renormalizable couplings with shift symmetry of the inflaton are considered. The massive vector can be decomposed into a scalar mode and a divergence-free vector mode. We show that the former naturally interacts with the inflaton and the latter decouples at tree level. The model in general predicts fNLequil = O(1), while in some regions of the parameter space large non-Gaussianity can arise.

Generically large nongaussianity in small multifield inflation

If forthcoming measurements of cosmic photon polarization restrict the primordial tensor-to-scalar ratio to r < 0.01, small field inflation will be a principal candidate for the origin of the universe. Here we show that small multifield inflation, without the hybrid mechanism, typically results in large squeezed nongaussianity. Small multifield potentials contain multiple flat field directions, often identified with the gauge invariant field directions in supersymmetric potentials. We find that unless these field directions have equal slopes, large nongaussianity arises. After identifying relevant differences between large and small two-field potentials, we demonstrate that the latter naturally fulfill the Byrnes-Choi-Hall large nongaussianity conditions. Computations of the primordial power spectrum, spectral index, and squeezed bispectrum, reveal that small two-field models which otherwise match observed primordial perturbations, produce excludably large nongaussianity if the inflatons' field directions have unequal slopes.

Probing primordial non-Gaussianity via iSW measurements with SKA continuum surveys

The Planck CMB experiment has delivered the best constraints so far on primordial non-Gaussianity, ruling out early-Universe models of inflation that generate large non-Gaussianity. Although small improvements in the CMB constraints are expected, the next frontier of precision will come from future large-scale surveys of the galaxy distribution. The advantage of such surveys is that they can measure many more modes than the CMB—in particular, forthcoming radio surveys with the Square Kilometre Array will cover huge volumes. Radio continuum surveys deliver the largest volumes, but with the disadvantage of no redshift information. In order to mitigate this, we use two additional observables. First, the integrated Sachs-Wolfe effect—the cross-correlation of the radio number counts with the CMB temperature anisotropies—helps to reduce systematics on the large scales that are sensitive to non-Gaussianity. Second, optical data allows for cross-identification in order to gain some redshift information. We show that, while the single redshift bin case can provide a σ(fNL) ∼ 20, and is therefore not competitive with current and future constraints on non-Gaussianity, a tomographic analysis could improve the constraints by an order of magnitude, even with only two redshift bins. A huge improvement is provided by the addition of high-redshift sources, so having cross-ID for high-z galaxies and an even higher-z radio tail is key to enabling very precise measurements of fNL. We use Fisher matrix forecasts to predict the constraining power in the case of no redshift information and the case where cross-ID allows a tomographic analysis, and we show that the constraints do not improve much with 3 or more bins. Our results show that SKA continuum surveys could provide constraints competitive with CMB and forthcoming optical surveys, potentially allowing a measurement of σ(fNL) ∼ 1 to be made. Moreover, these measurements would act as a useful check of results obtained with other probes at other redshift ranges with other methods.