Enormous information about interactions is contained in the non-Gaussianities of the primordial curvature perturbations, which are essential to break the degeneracy of inflationary models. We study the primordial bispectra for G-inflation models predicting both sharp and broad peaks in the primordial scalar power spectrum. We calculate the non-Gaussianity parameter $f_{\mathrm{NL}}$ in the equilateral limit and squeezed limit numerically, and confirm that the consistency relation holds in these models. Even though $f_{\mathrm{NL}}$ becomes large at the scales before the power spectrum reaches the peak and the scales where there are wiggles in the power spectrum, it remains to be small at the peak scales. Therefore, the contributions of non-Gaussianity to the scalar induced secondary gravitational waves and primordial black hole abundance are expected to be negligible.
Here we review the present status of modelling of and searching for primordial non-Gaussianity of cosmological perturbations. After introducing the models for non-Gaussianity generation during inflation, we discuss the search for non-Gaussian signatures in the Cosmic Microwave Background and in the Large-Scale Structure of the Universe.
Several bright and massive galaxy candidates at high redshifts have been recently observed by the James Webb Space Telescope. Such early massive galaxies seem difficult to reconcile with standard $Λ$ Cold Dark Matter model predictions. We discuss under which circumstances such observed massive galaxy candidates can be explained by introducing primordial non-Gaussianity in the initial conditions of the cosmological perturbations.
A significant abundance of primordial black hole (PBH) dark matter can be produced by curvature perturbations with power spectrum $Δ_ζ^2(k_{\mathrm{peak}})\sim \mathcal{O}(10^{-2})$ at small scales, associated with the generation of observable scalar induced gravitational waves (SIGWs). However, the primordial non-Gaussianity may play a non-negligible role, which is not usually considered. We propose two inflation models that predict double peaks of order $\mathcal{O}(10^{-2})$ in the power spectrum and study the effects of primordial non-Gaussianity on PBHs and SIGWs. This model is driven by …
Primordial non-Gaussianity is a potentially powerful discriminant of the physical mechanisms that generated the cosmological fluctuations observed today. Any detection of non-Gaussianity would have profound implications for our understanding of cosmic structure formation. In this paper, we review past and current efforts in the search for primordial non-Gaussianity in the large scale structure of the Universe.
The bispectrum of scalar mode density perturbations is analysed for the strong regime of warm inflationary models. This analysis generalises previous results by allowing damping terms in the inflaton equation of motion that are dependent on temperature. A significant amount of non-gaussianity emerges with constant (or local) non-linearity parameter $f_{NL}\sim 20$, in addition to the terms with non-constant $f_{NL}$ which are characteristic of warm inflation.
The general kind noncanonical warm inflation is introduced and its total non-Gaussianity of perturbation on uniform energy density hypersurfaces is studied. The total non-Gaussianity contains two complementary parts: the three- and the four-point correlations. The three-point correlation part denoted by $f^{int}_{NL}$, comes from the three-point correlation of inflaton field, while the four-point correlation part, denoted by $f_{NL}^{δN}$, is the contribution due to the four-point correlation function of the inflaton field. The aforementioned two parts of non-Gaussianity in general noncanonica…
We study the scale dependent bias of the halo power spectrum arising from primordial non-Gaussianity. We present an analytic result of the halo bias including up to the trispectrum contributions. We find the scale dependent bias opens a new possibility of probing the relation between the non-linearity parameters $\fnl$ and $\tnl$.
Non-Gaussianities of dynamical origin are disentangled from primordial ones using the formalism of large deviation statistics with spherical collapse dynamics. This is achieved by relying on accurate analytical predictions for the one-point probability distribution function (PDF) and the two-point clustering of spherically-averaged cosmic densities (sphere bias). Sphere bias extends the idea of halo bias to intermediate density environments and voids as underdense regions. In the presence of primordial non-Gaussianity, sphere bias displays a strong scale dependence relevant for both high and l…
We discuss quantum gravitational loop effects to observable quantities such as curvature power spectrum and primordial non-Gaussianity of cosmic microwave background (CMB) radiation. We first review the previously shown case where one gets a time dependence for zeta-zeta correlator due to loop corrections. Then we investigate the effect of loop corrections to primordial non-Gaussianity of CMB. We conclude that, even with a single scalar inflaton, one might get a huge value for non-Gaussianity which would exceed the observed value by at least 30 orders of magnitude. Finally we discuss the conse…
We study nonlinear cosmological perturbations and their possible non-Gaussian character in an extended non-minimal inflation where gravity is coupled non-minimally to both the scalar field and its derivatives. By expansion of the action up to the third order, we focus on the non-linearity and non-Gaussianity of perturbations in comparison with recent observational data. By adopting an inflation potential of the form V(phi) = (1/n)(lambda)(phi)^n, we show that for n = 4, for instance, this extended model is consistent with observation if 0.013 <lambda< 0.095 in appropriate units. By restricting…
We address the dual challenge of estimating deviations from Gaussianity arising in models of the Early Universe, whilst retaining information necessary to assess whether a detection of non-Gaussianity is primordial. We do this by constructing a new statistic, the bispectrum-related power spectrum, which is constructed from a map of the Cosmic Microwave Background. The estimator is optimised for primordial non-Gaussianity detection, but can also be useful in distinguishing primordial non-Gaussianity from secondary non-Gaussianity, such as may arise from unsubtracted point sources, or residuals …
We explore the possibility of detecting primordial non-Gaussianity of the local type using weak lensing peak counts. We measure the peak abundance in sets of simulated weak lensing maps corresponding to three models f_NL={0, +100, -100}. Using survey specifications similar to those of Euclid and without assuming any knowledge of the lens and source redshifts, we find the peak functions of the non-Gaussian models with f_NL=+-100 to differ by up to 15% from the Gaussian peak function at the high-mass end. For the assumed survey parameters, the probability of fitting an f_NL=0 peak function to th…
Primordial magnetic fields (PMFs) create a large squeezed-type non-Gaussianity in tensor perturbation, which generates non-Gaussian temperature fluctuations in the cosmic microwave background (CMB). We for the first time derive an observational constraint on such a tensor non-Gaussianity from observed CMB maps. Analyzing temperature maps of the WMAP 7-year data, we find that such a tensor non-Gaussianity is consistent with zero. This gives an upper bound on PMF strength smoothed on $1 ~ {\rm Mpc}$ as $B_{1 ~ \rm Mpc} < 3.1 ~{\rm nG}$ at $95%$ C.L.
We present N-body cosmological numerical simulations including a primordial non-Gaussianity in the density fluctuation field quantified by the non-linear parameter $f_{NL}$. We have used MPGRAFIC code to produce initial conditions and the Adaptive Mesh Refinement (AMR) code RAMSES to evolve the large scale structure formation. We estimated the higher order momenta of the initial distribution of density fluctuations, investigated the redshift evolution of the non-linear power spectrum and estimated the discrepancy introduced by the primordial non-Gaussianity in the non-linear power spectrum.
We present a systematic study of galaxy bias in the presence of primordial non-Gaussianity in General Relativity (GR) at second order in perturbation theory. The non-linearity of the Poisson equation in GR and primordial non-Gaussianity are consistently included. We show that the inclusion of non-local primordial non-Gaussianity in addition to local non-Gaussianity is important to show the absence of the modulation of small scale clustering by the long-wavelength mode in the single field slow-roll inflation. We study the bispectrum of the relativistic galaxy density in several gauges and ident…
A $δN$ formalism is used to study the non-Gaussianity of the primordial curvature perturbation on an uniform density hypersurfaces generated by the warm inflation for the first time. After introducing the framework of the warm inflation and the $δN$ formalism, we obtain an analytic expression for the nonlinear parameter $f_{NL}$ that describes the non-Gaussianity in slow roll approximation, and find that the $δN$ formalism gives a very good result. We analyse the magnitude of $f_{NL}$ and compare our result with those of the standard inflation. Then we discuss two concrete examples: the quarti…
Primordial non-Gaussianity generated in an inflationary model where inflation is preceded by a radiation era is discussed. It is shown that both bispectrum and trispectrum non-Gaussianities are enhanced due to the presence of pre-inflationary radiation era. One distinguishing feature of such a scenario is that the trispectrum non-Gaussianity is larger than the bispectrum one.
The merger rate of primordial black holes depends on their initial clustering. In the absence of primordial non-Gaussianity correlating short and large-scales, primordial black holes are distributed à la Poisson at the time of their formation. However, primordial non-Gaussianity of the local-type may correlate primordial black holes on large-scales. We show that future experiments looking for CMB $μ$-distortion would test the hypothesis of initial primordial black hole clustering induced by local non-Gaussianity, while existing limits already show that significant non-Gaussianity is necessary …
We derive a formula for the halo/galaxy bispectrum on the basis of the integrated Perturbation Theory (iPT). In addition to the gravity-induced non-Gaussianity, we consider the non-Gaussianity of the primordial curvature perturbations, and investigate in detail the effect of such primordial non-Gaussianity on the large-scale halo/galaxy bispectrum. In iPT, the effects of primordial non-Gaussianity are wholly encapsulated in the linear (primordial) polyspectra, and we systematically calculate the contributions to the large-scale behaviors arising from the three types of primordial bispectrum (l…
We study the halo mass function in the presence of the kurtosis type of primordial non-Gaussianity. The kurtosis corresponds to the trispectrum as defined in Fourier space. The primordial trispectrum is commonly characterized by two parameters, $τ_{\rm NL}$ and $g_{\rm NL}$. As applications of the derived non-Gaussian mass function, we consider the effect on the abundance of void structure, the effect on early star formation and on formation of the most massive object at high redshift. We show that by comparing the effects of primordial non-Gaussianity on cluster abundance with that on void ab…
We show that the ability to probe primordial non-Gaussianity with cluster counts is drastically improved by adding the excess variance of counts which contains information on the clustering. The conflicting dependences of changing the mass threshold and including primordial non-Gaussianity on the mass function and biasing indicate that the self-calibrated cluster counts well break the degeneracy between primordial non-Gaussianity and the observable-mass relation. Based on the Fisher matrix analysis, we show that the count variance improves constraints on f_NL by more than an order of magnitude…
We investigate the halo bias in the case where the primordial curvature fluctuations, $Φ$, are sourced from both a Gaussian random field and a Gaussian-squared field, as $Φ({\bf x}) = ϕ({\bf x}) + ψ({\bf x})^2 - <ψ({\bf x})^2>$, so-called "ungaussiton model". We employ the peak-background split formula and find a new scale-dependence in the halo bias induced from the Gaussian-squared field.
Implications of Pulsar Timing Array Data for Scalar-Induced Gravitational Waves and Primordial Black Holes: Primordial Non-Gaussianity $f_{\mathrm{NL}}$ Considered
Evolution and abundance of the large-scale structures we observe today, such as clusters of galaxies, is sensitive to the statistical properties of dark matter primordial density fluctuations, which is assumed to follow a Gaussian probability distribution function. Within this assumption, a significant disagreement have been found between clusters counts made by Planck and their prediction when calibrated by CMB angular power spectrum. The purpose of this work is to relax the Gaussianty assumption and test if Non-Gaussianity in dark matter primordial density fluctuations, could alleviate the t…
Primordial non-Gaussianity is a potentially powerful discriminant of the physical mechanisms that generated the cosmological fluctuations observed today. Any detection of significant non-Gaussianity would thus have profound implications for our understanding of cosmic structure formation. The large scale mass distribution in the Universe is a sensitive probe of the nature of initial conditions. Recent theoretical progress together with rapid developments in observational techniques will enable us to critically confront predictions of inflationary scenarios and set constraints as competitive as…
We present a new probe of primordial non-Gaussianity via the 21cm radiation from minihalos at high redshifts. We calculate the fluctuations in the brightness temperature (measured against the cosmic microwave background) of the 21cm background from minihalos containing HI at redshift \sim 6-20, and find a significant enhancement due to small non-Gaussianity with amplitude f_NL \leq 1. This enhancement can be attributed to the nonlinear bias which is strongly increased in the presence of non-Gaussianity. We show that our results are robust against changes in the assumed mass function and some p…
We study the impact of primordial non-Gaussianity on the density profile of dark matter halos by using the semi-analytical model introduced recently by Dalal {\it et al.} which relates the peaks of the initial linear density field to the final density profile of dark matter halos. Models with primordial non-Gaussianity typically produce an initial density field that differs from that produced in Gaussian models. We use the path-integral formulation of excursion set theory to calculate the non-Gaussian corrections to the peak profile and derive the statistics of the peaks of non-Gaussian densit…
If dark energy and dark matter interact via exchange of energy and momentum, then this may affect the galaxy power spectrum on large scales. When this happens, it may be degenerate with the signal from primordial non-Gaussianity via scale-dependent bias. We consider a class of interacting dark energy models and show that the matter overdensity is scale-dependent on large scales. We estimate the effective non-Gaussianity arising from the large-scale effects of interaction in the dark sector. The signal of dark sector interaction can be disentangled from a primordial non-Gaussian signal by measu…
The large-scale clustering of galaxies can serve as a probe of primordial non-Gaussianity in the Universe competitive with the anisotropies of the CMB. Here, we present improved theoretical predictions which include an important, previously overlooked correction to the bias. We demonstrate that the new predictions are able to reproduce the results of N-body simulations, explaining the significant departures seen from previous theoretical results. These refined predictions open the way to accurate constraints on primordial physics with large-scale structure surveys.
We study the signature of primordial non-Gaussianity imprinted on the power spectrum of the 21-cm line differential brightness temperature during dark ages. Employing the perturbative treatment of gravitational clustering, we quantitatively estimate the effects of the non-Gaussian and one-loop corrections on the 21-cm power spectrum. The potential impact of the use of the 21-cm power spectrum for the constraint on local-type primordial non-Gaussianity is investigated based on the Fisher matrix analysis. Our results show that the 21-cm power spectrum for an array with a baseline of several tens…
We clarify the role of gauge invariance for the computation of quantum non-Gaussian correlators in inflation. A gauge invariant generating functional for n-point functions is given and the special status of the spatially flat gauge is pointed out. We also comment on the relation between gauge transformations, field redefinitions, the choice of $t={\rm const}$ hypersurfaces and the use of boundary terms in computations of non-Gaussianity.
In this note we examine the derivation of scale-dependent bias due to primordial non-Gaussianity of the local type in the context of general relativity. We justify the use of the Poisson equation in general relativistic perturbation theory and thus the derivation of scale-dependent bias as a test of primordial non-Gaussianity, using the spherical collapse model. The corollary is that the form of scale-dependent bias does not receive general relativistic corrections on scales larger than the Hubble radius. This leads to a formally divergent correlation function for biased tracers of the mass di…
Primordial non-Gaussianity is a crucial test of inflationary cosmology. We consider the impact of non-Gaussianity on the ionization power spectrum from 21 cm emission during the epoch of reionization. We focus on the power spectrum on large scales at redshifts of 7 to 8 and explore the expected constraint on the local non-Gaussianity parameter f_NL for current and next-generation 21 cm experiments. We show that experiments such as SKA and MWA could measure f_NL values of order 10. This can be improved by an order of magnitude with a fast-Fourier transform telescope like Omniscope.
In this review, 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 non-linear dynamics on super-horizon scales.
Study of primordial non-Gaussianity $f_{\mathrm{NL}}$ and $g_{\mathrm{NL}}$ with the cross-correlations between the scalar-induced gravitational waves and the cosmic microwave background
We consider primordial fluctuations in thermal inflation scenario. Since the thermal inflation drives about 10 $e$-folds after the standard inflation, the time of horizon-exit during inflation corresponding to the present observational scale shifts toward the end of inflation. It generally makes the primordial power spectrum more deviated from a scale-invariant one and hence renders some models inconsistent with observations. We present a mechanism of generating the primordial curvature perturbation at the end of thermal inflation utilizing a fluctuating coupling of a flaton field with the fie…
Primordial black holes may owe their origin to the small-scale enhancement of the comoving curvature perturbation generated during inflation. Their mass fraction at formation is markedly sensitive to possible non-Gaussianities in such large, but rare fluctuations. We discuss a path-integral formulation which provides the exact mass fraction of primordial black holes at formation in the presence of non-Gaussianity. Through a couple of classes of models, one based on single-field inflation and the other on spectator fields, we show that restricting to a Gaussian statistics may lead to severe ina…
The theory and methodology is developed to compute the bispectrum in warm inflation, leading to results for the non-linearity parameter and the shape of the bispectrum. Particular attention is paid to the study of the bispectrum in the regime of weak dissipation and how stochastic fluctuations affect the bispectrum. It is shown that, in contrast to the strong dissipative regime, the amplitude of non-Gaussianity is strongly dependent on the parameters governing the microscopic physics in the intermediate and weak dissipation warm inflation regimes. The most important results concern the shape o…
We study primordial fluctuations generated during inflation in a class of models motivated by the DBI Galileons, which are extensions of the DBI action that yield second order field equations. This class of models generalises the DBI Galileons in a similar way with K-inflation. We calculate the primordial non-Gaussianity from the bispectrum of the curvature perturbations at leading order in the slow-varying approximations. We show that the estimator for the equilateral-type non-Gaussianity, $f_{\rm NL} ^{equil}$, can be applied to measure the amplitude of the primordial bispectrum even in the …
We perturbatively study the effect of non-Gaussianities on the mass fraction of primordial black holes (PBHs) at the time of formation by systematically taking its effect into account in the one-point probability distribution function of the primordial curvature perturbation. We focus on the bispectrum and trispectrum and derive formulas that describe their effects on the skewness and kurtosis of the distribution function. Then considering the case of narrowly peaked spectra, we obtain simple formulas that concisely express the effect of the bi- and trispectra. In particular, together with the…
The statistical properties of the primordial perturbations contain clues about the origins of those fluctuations. Although the Planck collaboration has recently obtained tight constraints on primordial non-gaussianity from cosmic microwave background measurements, it is still worthwhile to mine upcoming data sets in effort to place independent or competitive limits. The ionized bubbles that formed at redshift z~6-20 during the Epoch of Reionization are seeded by primordial overdensities, and so the statistics of the ionization field at high redshift are related to the statistics of the primord…
Angular bispectrum and trispectrum of scalar-induced gravitational waves: all contributions from primordial non-Gaussianity $f_\mathrm{NL}$ and $g_\mathrm{NL}$
We describe a general procedure for using number counts of any object to constrain the probability distribution of the primordial fluctuations, allowing for generic weak non-Gaussianity. We apply this procedure to use limits on the abundance of primordial black holes and dark matter ultracompact minihalos (UCMHs) to characterize the allowed statistics of primordial fluctuations on very small scales. We present constraints on the power spectrum and the amplitude of the skewness for two different families of non-Gaussian distributions, distinguished by the relative importance of higher moments. …
We investigate the non-Gaussian signatures of ultra slow-roll inflation. The bispectrum and the trispectrum are calculated with general initial conditions. The trispectrum is of local shape, as in the case of the bispectrum. We show that the prediction of local non-Gaussianity is robust again generalizing the Bunch-Davies vacuum. The Suyama-Yamaguchi relation is saturated in this scenario.
We compute the real space galaxy power spectrum, including the leading order effects of General Relativity and primordial non-Gaussianity from the $f_{\mathrm{NL}}$ and $g_{\mathrm{NL}}$ parameters. Such contributions come from the one-loop matter power spectrum terms dominant at large scales, and from the factors of the non-linear bias parameter $b_{\mathrm{NL}}$ (akin to the Newtonian $b_ϕ$). We assess the detectability of these contributions in Stage-IV surveys. In particular, we note that specific values of the bias parameter may erase the primordial and relativistic contributions to the c…
The primordial non-Gaussianity of local type affects the clustering of dark matter halos, and the planned deep and wide photometric surveys are suitable for examining this class of non-Gaussianity. In our previous paper, we investigated the constraint from the cross correlation between CMB lensing potential and galaxy angular distribution on the primordial non-Gaussianity, without taking into account redshift slicing. To improve our previous analysis, in this paper, we add the galaxy lensing shear into our analysis and take into account redshift slicing to follow the redshift evolution of the …
Galilean Genesis is generically plagued with a strong coupling problem, but this can be avoided depending on the hierarchy between a classical energy scale of genesis and a strong coupling scale. In this paper, we investigate whether or not the models of Galilean Genesis without the strong coupling problem can explain the statistical properties of the observed CMB fluctuations based on two unified frameworks of Galilean Genesis. By focusing on the class in which the propagation speeds of the scalar and tensor perturbations are constant, we show that the models avoiding strong coupling and allo…
The standard nonlinear perturbation theory of the gravitational instability is extended to incorporate the nonlocal bias, redshift-space distortions, and primordial non-Gaussianity. We show that local Eulerian bias is not generally compatible to local Lagrangian bias in nonlinear regime. The Eulerian and Lagrangian biases are nonlocally related order by order in the general perturbation theory. The relation between Eulerian and Lagrangian kernels of density perturbations with biasing are derived. The effects of primordial non-Gaussianity and redshift-space distortions are also incorporated in …
Single field inflationary models predict nearly Gaussian initial conditions and hence a detection of non-Gaussianity would be a signature of the more complex inflationary scenarios. In this paper we study the effect on the cosmic microwave background and on large scale structure from primordial non-Gaussianity in a two-field inflationary model in which both the inflaton and curvaton contribute to the density perturbations. We show that in addition to the previously described enhancement of the galaxy bias on large scales, this setup results in large-scale stochasticity. We provide joint constr…
We calculate tensor bispectrum in a theory of massive tensor gravitons which predicts blue-tilted and largely amplified primordial gravitational waves. We find that a new 3-point interaction can produce a larger tensor bispectrum than the conventional one from general relativity. The bispectrum peaks at the squeezed configuration and its slope towards the squeezed limit is determined by the graviton mass. This squeezed tensor bispectrum may be observed as the quadrupolar modulation of the tensor power spectrum by interferometers.
Primordial black holes (PBHs) are black holes which may have formed very early on during the radiation dominated era in the early universe. We present here a method by which the large scale perturbations in the density of primordial black holes may be used to place tight constraints on non-gaussianity if PBHs account for dark matter (DM). The presence of local-type non-gaussianity is known to have a significant effect on the abundance of primordial black holes, and modal coupling from the observed CMB scale modes can significantly alter the number density of PBHs that form within different reg…
We study the non-Gaussian features in single-field slow-roll inflationary scenario where inflation is preceded by a radiation era. In such a scenario both bispectrum and trispectrum non-Gaussianities are enhanced. Interestingly, the trispectrum in this scenario does not depend up on the slow-roll parameters and thus $τ_{NL}$ is larger than $f_{NL}$ which can be a signature of such a pre-inflationary radiation era.
We present a systematic study of galaxy biasing in the presence of primordial non-Gaussianity. For a large class of non-Gaussian initial conditions, we define a general bias expansion and prove that it is closed under renormalization, thereby showing that the basis of operators in the expansion is complete. We then study the effects of primordial non-Gaussianity on the statistics of galaxies. We show that the equivalence principle enforces a relation between the scale-dependent bias in the galaxy power spectrum and that in the dipolar part of the bispectrum. This provides a powerful consistenc…
We discuss generation of non-Gaussianity in density perturbation through the super-horizon evolution during inflation by using the so-called $δN$ formalism. We first provide a general formula for the non-linearity parameter generated during inflation. We find that it is proportional to the slow-roll parameters, multiplied by the model dependent factors that may enhance the non-gaussianity to the observable ranges. Then we discuss three typical examples to illustrate how difficult to generate sizable non-Gaussianity through the super-horizon evolution. First example is the double inflation mode…
The general expression for the second order large scale curvature perturbation in the form of a functional over a background solution is derived. The explicit expressions was obtained for two special forms of the inflationary potential. In the considered cases, it is shown that a significant level of non-Gaussianity can be generated during the super-Hubble evolution only if nonadiabatic perturbations are non-negligible at the end of inflation.
