non-Gaussianity Parameter fNL Research Articles

Local primordial non-Gaussianity from the large-scale clustering of photometric DESI luminous red galaxies

Abstract We use angular clustering of luminous red galaxies from the Dark Energy Spectroscopic Instrument (DESI) imaging surveys to constrain the local primordial non-Gaussianity parameter fNL. Our sample comprises over 12 million targets, covering 14,000 square degrees of the sky, with redshifts in the range 0.2 < z < 1.35. We identify Galactic extinction, survey depth, and astronomical seeing as the primary sources of systematic error, and employ linear regression and artificial neural networks to alleviate non-cosmological excess clustering on large scales. Our methods are tested against simulations with and without fNL and systematics, showing superior performance of the neural network treatment. The neural network with a set of nine imaging property maps passes our systematic null test criteria, and is chosen as the fiducial treatment. Assuming the universality relation, we find $f_{\rm NL} = 34^{+24(+50)}_{-44(-73)}$ at 68 per cent(95 per cent) confidence. We apply a series of robustness tests (e.g. cuts on imaging, declination, or scales used) that show consistency in the obtained constraints. We study how the regression method biases the measured angular power-spectrum and degrades the fNL constraining power. The use of the nine maps more than doubles the uncertainty compared to using only the three primary maps in the regression. Our results thus motivate the development of more efficient methods that avoid over-correction, protect large-scale clustering information, and preserve constraining power. Additionally, our results encourage further studies of fNL with DESI spectroscopic samples, where the inclusion of 3D clustering modes should help separate imaging systematics and lessen the degradation in the fNL uncertainty.

Induced gravitational waves from non-attractor inflation and NANOGrav data

In this paper, we investigate the scalar-induced gravitational waves in single-field non-attractor inflation for the Pulsar Timing Arrays data. Our model comprises three phases of inflation: the first and third phases are slow-roll inflation, while the second phase is a period of non-attractor inflation. We analyze the model's predictions for various values of the sound speed cs and examine the sharp transitions to the final attractor phase. Furthermore, we study the model's predictions for NANOGrav observations and future gravitational wave observations. We also calculate the non-Gaussianity parameter fNL for the non-attractor setup with a general sound speed and the sharpness parameter.

Primordial non-Gaussianity as a probe of seesaw and leptogenesis

We present the possibility that the seesaw mechanism and nonthermal leptogenesis can be investigated via primordial non-Gaussianities in the context of a majoron curvaton model. Originating as a massless Nambu-Goldstone boson from the spontaneous breaking of the global baryon (B) minus lepton (L) number symmetry at a scale vB−L, majoron becomes massive when it couples to a new confining sector through anomaly. Acting as a curvaton, majoron produces the observed red-tilted curvature power spectrum without relying on any inflaton contribution, and its decay in the post-inflationary era gives rise to a nonthermal population of right-handed neutrinos that participate in leptogenesis. A distinctive feature of the mechanism is the generation of observable non-Gaussianity, in the parameter space where the red-tilted power spectrum and sufficient baryon asymmetry are produced. We find that the non-Gaussianity parameter fNL ≳ O\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{O} $$\\end{document}(0.1) is produced for high-scale seesaw (vB−L at O\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{O} $$\\end{document}(1014−17) GeV) and leptogenesis (M1 ≳ O\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{O} $$\\end{document}(106) GeV) where the latter represents the lightest right-handed neutrino mass. While the current bounds on local non-Gaussianity excludes some part of parameter space, the rest can be fully probed by future experiments like CMB-S4, LSST, and 21 cm tomography.

First constraints on small-scale non-Gaussianity from UV galaxy luminosity functions

UV luminosity functions provide a wealth of information on the physics of galaxy formation in the early Universe. Given that this probe indirectly tracks the evolution of the mass function of dark matter halos, it has the potential to constrain alternative theories of structure formation. One of such scenarios is the existence of primordial non-Gaussianity at scales beyond those probed by observations of the Cosmic Microwave Background. Through its impact on the halo mass function, such small-scale non-Gaussianity would alter the abundance of galaxies at high redshifts. In this work we present an application of UV luminosity functions as measured by the Hubble Space Telescope to constrain the non-Gaussianity parameter fNL for wavenumbers above a cut-off scale kcut. After marginalizing over the unknown astrophysical parameters and accounting for potential systematic errors, we arrive at a 2σ bound of fNL=71+426−237 for a cut-off scale kcut=0.1 Mpc−1 in the bispectrum of the primordial gravitational potential. Moreover, we perform forecasts for the James Webb Space Telescope and the Nancy Grace Roman Space Telescope, finding an expected improvement of a factor 3–4 upon the current bound.

PBH in single field inflation: the effect of shape dispersion and non-Gaussianities

Primordial black holes (PBHs) may result from high peaks in a random field of cosmological perturbations. In single field inflationary models, such perturbations can be seeded as the inflaton overshoots a small barrier on its way down the potential. PBHs are then produced through two distinct mechanisms, during the radiation era. The first one is the familiar collapse of large adiabatic overdensities. The second one is the collapse induced by relic bubbles where the inflaton field is trapped in a false vacuum. The latter are due to rare backward fluctuations of the inflaton which prevented it from overshooting the barrier in horizon sized regions. We consider (numerically and analytically) the effect of non-Gaussianities on the threshold for overdensities to collapse into a PBH. Since typical high peaks have some dispersion in their shape or profile, we also consider the effect of such dispersion on the corresponding threshold for collapse. With these results we estimate the most likely channel for PBH production as a function of the non-Gaussianity parameter fNL. We also compare the threshold for collapse coming from the perturbative versus the non perturbative template for the non-Gaussianity arising in this model. We show that i) for fNL ≳ 3.5, the population of PBH coming from false vacuum regions dominates over that which comes from the collapse of large adiabatic overdensities, ii) the non-perturbative template of the non-Gaussianities is important to get accurate results. iii) the effect of the dispersion is small in determining the threshold for the compaction function, although it can be appreciable in determining the threshold amplitude for the curvature perturbation at low fNL. We also confirm that the volume averaged compaction function provides a very accurate universal estimator for the threshold.

Estimates for the impact of ultraviolet background fluctuations on galaxy clustering measurements

ABSTRACT Spatial fluctuations in ultraviolet backgrounds can subtly modulate the distribution of extragalactic sources, a potential signal and systematic for large-scale structure surveys. While this modulation has been shown to be significant for 3D Ly α forest surveys, its relevance for other large-scale structure probes has been hardly explored, despite being the only astrophysical process that likely can affect clustering measurements on the scales of ≳Mpc. We estimate that the background fluctuations, modulating the amount of H i, have a fractional effect of (0.03–0.3) × (k/[10−2 Mpc−1])−1 on the power spectrum of 21 cm intensity maps at z = 1–3. We find a smaller effect for H α and Ly α intensity mapping surveys of (0.001–0.1) × (k/[10−2 Mpc−1])−1 and even smaller effect for more traditional surveys that correlate the positions of individual H α or Ly α emitters. We also estimate the effect of backgrounds on low-redshift galaxy surveys in general based on a simple model in which background fluctuations modulate the rate halo gas cools, modulating star formation: We estimate a maximum fractional effect on the power of ∼0.01 (k/[10−2 Mpc−1])−1 at z = 1. We compare sizes of these imprints to cosmological parameter benchmarks for the next generation of redshift surveys: We find that ionizing backgrounds could result in a bias on the squeezed triangle non-Gaussianity parameter fNL that can be larger than unity for power spectrum measurements with a SPHEREx-like galaxy survey, and typical values of intensity bias. Marginalizing over a shape of the form k−1PL, where PL is the linear matter power spectrum, removes much of this bias at the cost of ${\approx } 40{{\ \rm per\ cent}}$ larger statistical errors.

Slow-roll corrections in multi-field inflation: a separate universes approach

In view of cosmological parameters being measured to ever higher precision, theoretical predictions must also be computed to an equally high level of precision. In this work we investigate the impact on such predictions of relaxing some of the simplifying assumptions often used in these computations. In particular, we investigate the importance of slow-roll corrections in the computation of multi-field inflation observables, such as the amplitude of the scalar spectrum Pζ, its spectral tilt ns, the tensor-to-scalar ratio r and the non-Gaussianity parameter fNL. To this end we use the separate universes approach and δ N formalism, which allows us to consider slow-roll corrections to the non-Gaussianity of the primordial curvature perturbation as well as corrections to its two-point statistics. In the context of the δ N expansion, we divide slow-roll corrections into two categories: those associated with calculating the correlation functions of the field perturbations on the initial flat hypersurface and those associated with determining the derivatives of the e-folding number with respect to the field values on the initial flat hypersurface. Using the results of Nakamura & Stewart '96, corrections of the first kind can be written in a compact form. Corrections of the second kind arise from using different levels of slow-roll approximation in solving for the super-horizon evolution, which in turn corresponds to using different levels of slow-roll approximation in the background equations of motion. We consider four different levels of approximation and apply the results to a few example models. The various approximations are also compared to exact numerical solutions.

Frame covariant nonminimal multifield inflation

We introduce a frame-covariant formalism for inflation of scalar-curvature theories by adopting a differential geometric approach which treats the scalar fields as coordinates living on a field-space manifold. This ensures that our description of inflation is both conformally and reparameterization covariant. Our formulation gives rise to extensions of the usual Hubble and potential slow-roll parameters to generalized fully frame-covariant forms, which allow us to provide manifestly frame-invariant predictions for cosmological observables, such as the tensor-to-scalar ratio r, the spectral indices nR and nT, their runnings αR and αT, the non-Gaussianity parameter fNL, and the isocurvature fraction βiso. We examine the role of the field space curvature in the generation and transfer of isocurvature modes, and we investigate the effect of boundary conditions for the scalar fields at the end of inflation on the observable inflationary quantities. We explore the stability of the trajectories with respect to the boundary conditions by using a suitable sensitivity parameter. To illustrate our approach, we first analyze a simple minimal two-field scenario before studying a more realistic nonminimal model inspired by Higgs inflation. We find that isocurvature effects are greatly enhanced in the latter scenario and must be taken into account for certain values in the parameter space such that the model is properly normalized to the observed scalar power spectrum PR. Finally, we outline how our frame-covariant approach may be extended beyond the tree-level approximation through the Vilkovisky–De Witt formalism, which we generalize to take into account conformal transformations, thereby leading to a fully frame-invariant effective action at the one-loop level.

Erratum: [Probing primordial non-Gaussianity with SKA galaxy redshift surveys: a fully relativistic analysis

The Square Kilometre Array (SKA) will produce spectroscopic surveys of tens to hundreds of millions of HI galaxies, eventually covering 30,000 sq. deg. and reaching out to redshift z~2. The huge volumes probed by the SKA will allow for some of the best constraints on primordial non-Gaussianity, based on measurements of the large-scale power spectrum. We investigate various observational set-ups for HI galaxy redshift surveys, compatible with the SKA Phase 1 and Phase 2 (full SKA) configurations. We use the corresponding number counts and bias for each survey from realistic simulations and derive the magnification bias and the evolution of source counts directly from these. For the first time, we produce forecasts that fully include the general relativistic effects on the galaxy number counts. These corrections to the standard analysis become important on very large scales, where the signal of primordial non-Gaussianity grows strongest. Our results show that, for the full survey, the non-Gaussianity parameter fNL can be constrained down to an accuracy of 1.54. This improves the current limit set by the Planck satellite by a factor of five, using a completely different approach.

Moment transport equations and their application to the perturbed universe

There are many inflationary models that allow the formation of the large-scale structure of the observable universe. The non-gaussianity parameter fNL is a useful tool to discriminate among these cosmological models when comparing the theoretical predictions with the satellite survey results like those from WMAP and Planck. The goal of this proceeding contribution is to review the moment transport equations methodology and the subsequent calculation of the fNL parameter.

Optimization of spectroscopic surveys for testing non-Gaussianity

We investigate optimization strategies to measure primordial non-Gaussianity with future spectroscopic surveys. We forecast measurements coming from the 3D galaxy power spectrum and compute constraints on primordial non-Gaussianity parameters fNL and nNG. After studying the dependence on those parameters upon survey specifications such as redshift range, area, number density, we assume a reference mock survey and investigate the trade-off between number density and area surveyed. We then define the observational requirements to reach the detection of fNL of order 1. Our results show that power spectrum constraints on non-Gaussianity from future spectroscopic surveys can improve on current CMB limits, but the multi-tracer technique and higher order correlations will be needed in order to reach an even better precision in the measurements of the non-Gaussianity parameter fNL.

Probing primordial non-Gaussianity with SKA galaxy redshift surveys: a fully relativistic analysis

The Square Kilometre Array (SKA) will produce spectroscopic surveys of tens to hundreds of millions of neutral hydrogen (H I) galaxies, eventually covering 30 000 deg2 and reaching out to redshift z≳2. The huge volumes probed by the SKA will allow for some of the best constraints on primordial non-Gaussianity, based on measurements of the large-scale power spectrum.We investigate various observational set-ups for HI galaxy redshift surveys, compatible with the SKA Phase 1 and Phase 2 (full SKA) configurations.We use the corresponding number counts and bias for each survey from realistic simulations and derive the magnification bias and the evolution of source counts directly from these. For the first time, we produce forecasts that fully include the general relativistic effects on the galaxy number counts. These corrections to the standard analysis become important on very large scales, where the signal of primordial non-Gaussianity grows strongest. Our results showthat, for the full survey, the non-Gaussianity parameter fNL can be constrained down to σ(fNL) = 1.54. This improves the current limit set by the Planck satellite by a factor of 5, using a completely different approach.

On the scalar consistency relation away from slow roll

As is well known, the non-Gaussianity parameter fNL, which is often used to characterize the amplitude of the scalar bi-spectrum, can be expressed completely in terms of the scalar spectral index ns in the squeezed limit, a relation that is referred to as the consistency condition. This relation, while it is largely discussed in the context of slow roll inflation, is actually expected to hold in any single field model of inflation, irrespective of the dynamics of the underlying model, provided inflation occurs on the attractor at late times. In this work, we explicitly examine the validity of the consistency relation, analytically as well as numerically, away from slow roll. Analytically, we first arrive at the relation in the simple case of power law inflation. We also consider the non-trivial example of the Starobinsky model involving a linear potential with a sudden change in its slope (which leads to a brief period of fast roll), and establish the condition completely analytically. We then numerically examine the validity of the consistency relation in three inflationary models that lead to the following features in the scalar power spectrum due to departures from slow roll: (i) a sharp cut off at large scales, (ii) a burst of oscillations over an intermediate range of scales, and (iii) small, but repeated, modulations extending over a wide range of scales. It is important to note that it is exactly such spectra that have been found to lead to an improved fit to the CMB data, when compared to the more standard power law primordial spectra, by the Planck team. We evaluate the scalar bi-spectrum for an arbitrary triangular configuration of the wavenumbers in these inflationary models and explicitly illustrate that, in the squeezed limit, the consistency condition is indeed satisfied even in situations consisting of strong deviations from slow roll. We conclude with a brief discussion of the results.

Examining the consistency relations describing the three-pointfunctions involving tensors

It is well known that the non-Gaussianity parameter fNL characterizing the scalar bi-spectrum can be expressed in terms of the scalar spectral index in the squeezed limit, a property that is referred to as the consistency relation. In contrast to the scalar bi-spectrum, the three-point cross-correlations involving scalars and tensors and the tensor bi-spectrum have not received adequate attention, which can be largely attributed to the fact that the tensors had remained undetected at the level of the power spectrum until very recently. The detection of the imprints of the primordial tensor perturbations by BICEP2 and its indication of a rather high tensor-to-scalar ratio, if confirmed, can open up a new window for understanding the tensor perturbations, not only at the level of the power spectrum, but also in the realm of non-Gaussianities. In this work, we consider the consistency relations associated with the three-point cross-correlations involving scalars and tensors as well as the tensor bi-spectrum in inflationary models driven by a single, canonical, scalar field. Characterizing the cross-correlations in terms of the dimensionless non-Gaussianity parameters CNLℛ and CNLγ that we had introduced earlier, we express the consistency relations governing the cross-correlations as relations between these non-Gaussianity parameters and the scalar or tensor spectral indices, in a fashion similar to that of the purely scalar case. We also discuss the corresponding relation for the non-Gaussianity parameter hNL used to describe the tensor bi-spectrum. We analytically establish these consistency relations explicitly in the following two situations: a simple example involving a specific case of power law inflation and a non-trivial scenario in the so-called Starobinsky model that is governed by a linear potential with a sharp change in its slope. We also numerically verify the consistency relations in three types of inflationary models that permit deviations from slow roll and lead to scalar power spectra with features which typically result in an improved fit to the data than the more conventional, nearly scale invariant, spectra. We close with a summary of the results we have obtained.

Reanalyzing the upper limit on the tensor-to-scalar perturbation ratio [formula omitted] in a quartic potential inflationary model

We study the polynomial chaotic inflation model with a single scalar field in a double well quartic potential which has recently been shown to be consistent with Planck data. In particular, we study the effects of lifting the degeneracy between the two vacua on the inflationary observables, i.e., spectral index ns and tensor-to-scalar perturbation ratio rT. We find that removing the degeneracy allows the model to satisfy the upper limit constraints on rT from Planck data, provided the field starts near the local maximum. We also calculate the scalar power spectrum and non-Gaussianity parameter fNL for the primordial scalar perturbations in this model.

More on loops in reheating: non-gaussianities and tensor power spectrum

We consider the single field chaotic m2ϕ2 inflationary model with a period of preheating, where the inflaton decays to another scalar field χ in the parametric resonance regime. In a recent work, one of us has shown that the χ modes circulating in the loops during preheating notably modify the ⟨ζζ⟩ correlation function. We first rederive this result using a different gauge condition hence reconfirm that superhorizon ζ modes are affected by the loops in preheating. Further, we examine how χ loops give rise to non-gaussianity and affect the tensor perturbations. For that, all cubic and some higher order interactions involving two χ fields are determined and their contribution to the non-gaussianity parameter fNL and the tensor power spectrum are calculated at one loop. Our estimates for these corrections show that while a large amount of non-gaussianity can be produced during reheating, the tensor power spectrum receive moderate corrections. We observe that the loop quantum effects increase with more χ fields circulating in the loops indicating that the perturbation theory might be broken down. These findings demonstrate that the loop corrections during reheating are significant and they must be taken into account for precision inflationary cosmology.

Remarks on non-Gaussian fluctuations of the inflaton and constancy of ζ outside the horizon

We have pointed out that the non-Gaussianity arising from cubic self interactions of the inflaton field is proportional to ξNe. For scales of interest Ne = 60, and for models such as new inflation, natural inflation, and running mass inflation ξ is large compared to the slow roll parameter. Therefore, the contribution from self interactions should not be outrightly ignored while retaining other terms in the non-Gaussianity parameter fNL. But the Ne dependent term seems to imply the growth of non-Gaussianities outside the horizon. Therefore, we have briefly discussed the issue of the constancy of correlations of the curvature perturbation ζ outside the horizon. We have then presented our results on the 3-point function of ζk, and found that the Ne dependent contribution to fNL from self interactions of the inflaton field is cancelled by contributions from other terms associated with non-linearities in cosmological perturbation theory.

Fluid inflation

In this work we present an inflationary mechanism based on fluid dynamics. Starting with the action for a single barotropic perfect fluid, we outline the procedure to calculate the power spectrum and the bispectrum of the curvature perturbation. It is shown that a perfect barotropic fluid naturally gives rise to a non-attractor inflationary universe in which the curvature perturbation is not frozen on super-horizon scales. We show that a scale-invariant power spectrum can be obtained with the local non-Gaussianity parameter fNL = 5/2.

BINGO: a code for the efficient computation of the scalar bi-spectrum

We present a new and accurate Fortran code, the BI-spectra and Non-Gaussianity Operator (BINGO), for the efficient numerical computation of the scalar bi-spectrum and the non-Gaussianity parameter fNL in single field inflationary models involving the canonical scalar field. The code can calculate all the different contributions to the bi-spectrum and the parameter fNL for an arbitrary triangular configuration of the wavevectors. Focusing firstly on the equilateral limit, we illustrate the accuracy of BINGO by comparing the results from the code with the spectral dependence of the bi-spectrum expected in power law inflation. Then, considering an arbitrary triangular configuration, we contrast the numerical results with the analytical expression available in the slow roll limit, for, say, the case of the conventional quadratic potential. Considering a non-trivial scenario involving deviations from slow roll, we compare the results from the code with the analytical results that have recently been obtained in the case of the Starobinsky model in the equilateral limit. As an immediate application, we utilize BINGO to examine of the power of the non-Gaussianity parameter fNL to discriminate between various inflationary models that admit departures from slow roll and lead to similar features in the scalar power spectrum. We close with a summary and discussion on the implications of the results we obtain.

Mixed non-Gaussianity in multiple-DBI inflation

We study a model of multiple-field DBI inflation leading to mixed form of primordial non-Gaussianity, including equilateral and local bispectrum shapes. We present a general formalism based on the Hamilton-Jacobi approach, allowing us to go beyond slow-roll, combining the three-point function for the fields at Hubble-exit with the non-linear evolution of super-Hubble scales. We are able to obtain analytic results by taking a separable Ansatz for the Hubble rate. We find general expressions for both the equilateral and local type non-Gaussianity parameter fNL. The equilateral non-Gaussianity includes the usual enhancement for small sound speeds, but multiplied by an analytic factor which can lead to a suppression. We illustrate our results with two scenarios. In the first model, previously found to have detectable local non-Gaussianity, we find that the equilateral signal is not sufficiently suppressed to evade current observational bounds. In our second scenario we construct a model which exhibits both a detectable equilateral fNL and a negative local fNL.