The primordial non-Gaussian parameter fNL has been shown to be scale-dependent in several models of inflation with a variable speed of sound. Starting from a simple ansatz for a scale-dependent amplitude of the primordial curvature bispectrum for two common phenomenological models of primordial non-Gaussianity, we perform a Fisher matrix analysis of the bispectra of the temperature and polarization of the Cosmic Microwave Background (CMB) radiation and derive the expected constraints on the parameter nNG that quantifies the running of fNL(k) for current and future CMB missions such as WMAP, Planck and CMBPol. We find that CMB information alone, in the event of a significant detection of the non-Gaussian component, corresponding to fNL = 50 for the local model and fNL = 100 for the equilateral model of non-Gaussianity, is able to determine nNG with a 1-sigma uncertainty of Delta nNG = 0.1 and Delta nNG = 0.3, respectively, for the Planck mission. In addition, we consider a Fisher matrix analysis of the galaxy power spectrum to determine the expected constraints on the running parameter nNG for the local model and of the galaxy bispectrum for the equilateral model from future photometric and spectroscopic surveys. We find that, in both cases, large-scale structure observations should achieve results comparable to or even better than those from the CMB, while showing some complementarity due to the different distribution of the non-Gaussian signal over the relevant range of scales. Finally, we compare our findings to the predictions on the amplitude and running of non-Gaussianity of DBI inflation, showing how the constraints on a scale-dependent fNL(k) translate into constraints on the parameter space of the theory.
We forecast combined future constraints from the cosmic microwave background and large-scale structure on the models of primordial non-Gaussianity. We study the generalized local model of non-Gaussianity, where the parameter f_NL is promoted to a function of scale, and present the principal component analysis applicable to an arbitrary form of f_NL(k). We emphasize the complementarity between the CMB and LSS by using Planck, DES and BigBOSS surveys as examples, forecast constraints on the power-law f_NL(k) model, and introduce the figure of merit for measurements of scale-dependent non-Gaussia…
We develop a complete set of tools for CMB forecasting, simulation and estimation of primordial running bispectra, arising from a variety of curvaton and single-field (DBI) models of Inflation. We validate our pipeline using mock CMB running non-Gaussianity realizations and test it on real data by obtaining experimental constraints on the $f_{\rm NL}$ running spectral index, $n_{\rm NG}$, using WMAP 9-year data. Our final bounds (68\% C.L.) read $-0.6< n_{\rm NG}<1.4$, $-0.3< n_{\rm NG}<1.2$, $-1.1<n_{\rm NG}<0.7$ for the single-field curvaton, two-field curvaton and DBI scenarios, respectivel…
Next-generation galaxy surveys will be able to measure perturbations on scales beyond the equality scale. On these ultra-large scales, primordial non-Gaussianity leaves signatures that can shed light on the mechanism by which perturbations in the early Universe are generated. We perform a forecast analysis for constraining local type non-Gaussianity and its two-parameter extension with a simple scale-dependence. We combine different clustering measurements from future galaxy surveys -- a 21cm intensity mapping survey and two photometric galaxy surveys -- via the multi-tracer approach. Furtherm…
We forecast future constraints on local-type primordial non-Gaussianity parameter $f_{\rm NL}$ with a photometric galaxy survey by Euclid, a continuum galaxy survey by Square Kilometre Array (SKA), and their combination. We derive a general expression for the covariance matrix of the power spectrum estimates of multiple tracers to show how the so-called multitracer technique improves constraints on $f_{\rm NL}$. In particular we clarify the role of the overlap fraction of multiple tracers and the division method of the tracers. Our Fisher matrix analysis indicates that stringent constraints of…
We use data from the WMAP temperature maps to constrain a scale-dependent generalization of the popular 'local' model for primordial non-Gaussianity. In the model where the parameter fNL is allowed to run with scale k, fNL(k) = fNL* (k/k_piv)^n, we constrain the running to be n = 0.30(+1.9)(-1.2) at 95% confidence, marginalized over the amplitude fNL*. The constraints depend somewhat on the prior probabilities assigned to the two parameters. In the near future, constraints from a combination of Planck and large-scale structure surveys are expected to improve this limit by about an order of mag…
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 …
In this letter we present constraints on the scale-dependent "local" type primordial non-Gaussianity, which is described by non-Gaussianity's spectral index $n_{\rm NG}$, from the NRAO VLA Sky Survey and the quasar catalog of the Sloan Digital Sky Survey (SDSS) Data Release 6, together with the SDSS Data Release 12 photo-z sample. Here, we use the auto-correlation analyses of these three probes and their cross-correlation analyses with the cosmic microwave background (CMB) temperature map, and obtain the tight constraint on the spectral index: $n_{\rm NG}=0.2 ^{+0.7}_{-1.0}$ ($1\,σ$ C.L.), whi…
We study the constraining power on primordial non-Gaussianity of future surveys of the large-scale structure of the Universe for both near-term surveys (such as the Dark Energy Survey - DES) as well as longer term projects such as Euclid and WFIRST. Specifically we perform a Fisher matrix analysis forecast for such surveys, using DES-like and Euclid-like configurations as examples, and take account of any expected photometric and spectroscopic data. We focus on two-point statistics and we consider three observables: the 3D galaxy power spectrum in redshift space, the angular galaxy power spect…
We forecast constraints on primordial non-Gaussianity (PNG) and bias parameters from measurements of galaxy power spectrum and bispectrum in future radio continuum and optical surveys. In the galaxy bispectrum, we consider a comprehensive list of effects, including the bias expansion for non-Gaussian initial conditions up to second order, redshift space distortions, redshift uncertainties and theoretical errors. These effects are all combined in a single PNG forecast for the first time. Moreover, we improve the bispectrum modelling over previous forecasts, by accounting for trispectrum contrib…
We consider whether the non-Gaussian scale-dependent halo bias can be used not only to constrain the local form of non-Gaussianity but also to distinguish among different shapes. In particular, we ask whether it can constrain the behavior of the primordial three-point function in the squeezed limit where one of the momenta is much smaller than the other two. This is potentially interesting since the observation of a three-point function with a squeezed limit that does not go like the local nor equilateral templates would be a signal of non-trivial dynamics during inflation. To this end we use …
We use cosmological N-body simulations to investigate whether measurements of the moments of large-scale structure can yield constraints on primordial non-Gaussianity. We measure the variance, skewness, and kurtosis of the evolved density field from simulations with Gaussian and three different non-Gaussian initial conditions: a local model with f_NL=100, an equilateral model with f_NL=-400, and an orthogonal model with f_NL=-400. We show that the moments of the dark matter density field differ significantly between Gaussian and non-Gaussian models. We also make the measurements on mock galaxy…
We present an analysis of the constraints on the amplitude of primordial non-Gaussianity of local type described by the dimensionless parameter $f_{\rm NL}$. These constraints are set by the auto-correlation functions (ACFs) of two large scale structure probes, the radio sources from NRAO VLA Sky Survey (NVSS) and the quasar catalogue of Sloan Digital Sky Survey Release Six (SDSS DR6 QSOs), as well as by their cross-correlation functions (CCFs) with the cosmic microwave background (CMB) temperature map (Integrated Sachs-Wolfe effect). Several systematic effects that may affect the observationa…
We study the cosmic variance limit on constraining primordial non-Gaussianity for a variety of theory-motivated shapes. We consider general arguments for 2D and 3D surveys, with a particular emphasis on the CMB. A scale-invariant $N$-point correlator can be measured with a signal-to-noise that naively scales with the square root of the number of observed modes. This intuition generally fails for two reasons. First, the signal-to-noise scaling is reduced due to the blurring of the last scattering surface at short distances. This blurring is caused by the combination of projection and damping, b…
We examine the cosmological constraining power of future large-scale weak lensing surveys on the model of \emph{Euclid}, with particular reference to primordial non-Gaussianity. Our analysis considers several different estimators of the projected matter power spectrum, based on both shear and flexion, for which we review the covariances and Fisher matrices. The bounds provided by cosmic shear alone for the local bispectrum shape, marginalized over $σ_8$, are at the level of $Δf_\mathrm{NL} \sim 100$. We consider three additional bispectrum shapes, for which the cosmic shear constraints range f…
The primordial non-Gaussianity parameters fNL and tauNL may be scale-dependent. We investigate the capability of future measurements of the CMB mu-distortion, which is very sensitive to small scales, and of the large-scale halo bias to test the running of local non-Gaussianity. We show that, for an experiment such as PIXIE, a measurement of the mu-temperature correlation can pin down the spectral indices n_fNL and n_tauNL to values of the order of 0.3 if fNL = 20 and tauNL = 5000. A similar value can be achieved with an all-sky survey extending to redshift z ~ 1. In the particular case in whic…
Galaxy bispectrum is a promising probe of inflationary physics in the early universe as a measure of primordial non-Gaussianity (PNG), whereas its signal-to-noise ratio is significantly affected by the mode coupling due to non-linear gravitational growth. In this paper, we examine the standard reconstruction method of linear cosmic mass density fields from non-linear galaxy density fields to de-correlate the covariance in redshift-space galaxy bispectra. In particular, we evaluate the covariance of the bispectrum for massive-galaxy-sized dark matter halos with reconstruction by using 4000 inde…
Constraining primordial non-Gaussianity and parity-violation through Scalar-Induced Gravitational Waves with next-generation ground-based interferometers
Università di Pisa（比萨大学）；Istituto Nazionale di Fisica Nucleare (INFN)（意大利国家核物理研究所）；Università degli Studi di Padova（帕多瓦大学）；Istituto Nazionale di Astrofisica (INAF)（意大利国家天体物理研究所）
In this thesis, the effect of non-Gaussianity upon the abundance of primordial black holes (PBHs), and the implications of such an effect are considered. It is shown that even small non-Gaussianity parameters can have a large effect on the constraints that can be placed on the primordial curvature perturbation power spectrum - which can become stronger or weaker by an order of magnitude. The effects of super-horizon curvature perturbation modes at the time of PBH formation are considered, and it is shown that these have little effect on the formation of a PBH, but can have an indirect effect o…
Primordial Black Holes (PBH's) can form in the early Universe from the collapse of large density fluctuations. Tight observational limits on their abundance constrain the amplitude of the primordial fluctuations on very small scales which can not otherwise be constrained, with PBH's only forming from the extremely rare large fluctuations. The number of PBH's formed is therefore sensitive to small changes in the shape of the tail of the fluctuation distribution, which itself depends on the amount of non-Gaussianity present. We study, for the first time, how quadratic and cubic local non-Gaussia…
We compute in detail how deviations from Einstein gravity at the inflation energy scale could appear as non-Gaussian features in the sky. To illustrate this we use multi-field $α-$attractor models in the framework of supergravity to realise inflation. We find no obvious obstacle for having choices of model's parameters that generate non-Gaussian features of the equilateral and local type at the $\cal O$(1) level in the $f_{\rm NL}$ non-Gaussianity parameter, thus being potentially detectable in future cosmological surveys. This non-Gaussianity has its origin in either the non-canonical kinetic…
We investigate the effect of primordial non-Gaussianity on the cross-correlation between the CMB anisotropies and the 21 cm fluctuations from the epoch of reionization. We assume an analytic reionization model and an ionization fraction with $f_{\rm NL}$ induced scale dependent bias. We estimate the angular power spectrum of the cross-correlation of the CMB and 21 cm. In order to evaluate the detectability, the signal-to-noise (S/N) ratio for only a single redshift slice is also calculated for current and future observations, such as CMB observations by Planck satellite and 21 cm observations …
Tensor non-Gaussianities are a key ingredient to test the symmetries and the presence of higher spin fields during the inflationary epoch. Indeed, the shape of the three point correlator of the graviton is totally fixed by the symmetries of the de Sitter stage and, in the case of parity conservation, gets contributions only from the ordinary gravity action plus a higher derivative term called the (Weyl)$^3$ action. We discuss current and future bounds on the three point tensor contribution from the (Weyl)$^3$ term using cosmic microwave background (CMB) bispectra. Our results indicate that for…
It is possible that the primordial non-Gaussianity is dominated by the higher order terms, such as that set by $g_{NL}$, not $f_{NL}$. In this paper we derive the spectral index and running of $g_{NL}$ from a single isocurvature scalar field. The scale dependences of non-Gaussianity parameters are detectable if the mass of isocurvature field is not too small compared to the Hubble parameter during inflation. In addition, we also apply our results to investigate the curvaton model with near quadratic potential in detail.
We use cosmic microwave background (CMB) data from the 9-year WMAP release to derive constraints on monodromy inflation, which is characterized by a linear inflaton potential with a periodic modulation. We identify two possible periodic modulations that significantly improve the fit, but it is unclear whether this improvement is associated with a "signal" or with the scatter in the measured angular power spectrum. The unmodulated potential is mildly favored by standard model selection criteria. A modulated inflationary potential can generate substantial primordial non-Gaussianity, of a specifi…
Inflationary cosmology is the leading explanation of the very early universe. Many different models of inflation have been constructed which fit current observational data. In this work theoretical and numerical methods for constraining the parameter space of a wide class of such models are described. First, string-theoretic models with large non-Gaussian signatures are investigated. An upper bound is placed on the amplitude of primordial gravitational waves produced by ultra-violet Dirac-Born-Infeld inflation. In all but the most finely tuned cases, this bound is incompatible with a lower bou…
Primordial non-Gaussianity induces a scale-dependent bias in large scale structure (LSS) data, proportional to $f_{\rm NL}/k^2$ for the exact local ansatz. Recent work has shown that models of inflation that predict a large squeezed limit bispectrum, such as multi-field models and single field inflation with a modified initial state, typically give rise to a generalized local ansatz, with the scale-dependent bias now proportional to ${\cal A}_{\rm NL}/k^α$. We use photometric measurements of the angular power spectrum of luminous red galaxies and quasars in the Sloan Digital Sky Survey Data Re…
We show a primordial non-linear "f_NL" term may produce unphysically large CMB anisotropy for a red-tilted primordial power spectrum (n<1), because of coupling to primordial fluctuation on the largest scale. We consider a primordial power spectrum models of a running spectral index, and a transition at very low wavenumbers. We find that only negative running spectral index models are allowed, provided that there is no transition at a low wavenumbers (i.e. k<<1). For models of a constant spectral index, we find log(k_c/k_0)> -184, at 1 sigma level, on the transition scale of sharp cut-off model…
We investigate the statistical power of higher-order statistics and cross-correlation statistics to constrain the primordial non-Gaussianity from the imaging surveys. In particular, we consider the local-type primordial non- Gaussianity and discuss how well one can tightly constrain the higher-order non-Gaussian parameters ($g_{\rm NL}$ and $τ_{\rm NL}$) as well as the leading order parameter $f_{\rm NL}$ from the halo/galaxy clustering and weak gravitational lensing measurements. Making use of a strong scale-dependent behavior in the galaxy/halo clustering, Fisher matrix analysis reveals that…
We derive the spectral indices and their runnings of local form $f_{NL}$ and $g_{NL}$ from a DBI isocurvature field and we find that the indices are suppressed by the sound speed $c_s$. This effect can be interpreted by the Lorentz boost from the viewpoint in the frame where brane is moving.
Constraining primordial non-Gaussianity and energy injection with the thermal Sunyaev-Zeldovich effect and integrated Sachs-Wolfe effect cross-correlation
Guangdong Technion - Israel Institute of Technology（广东以色列理工学院）；North-West University（西北大学）；Adekunle Ajasin University（阿德库恩莱·阿贾辛大学）；Stellenbosch University（斯泰伦博斯大学）；National Institute for Theoretical and Computational Sciences (NITheCS)（南非国家理论与计算科学研究所）
The presence of additional particles during inflation leads to non-Gaussianity in late-time correlators of primordial curvature perturbations. The shape and amplitude of this signal depend on the mass and spin of the extra particles. Constraints on this distinct form of primordial non-Gaussianity, therefore, provide a wealth of information on the particle content during inflation. We investigate the potential of upcoming galaxy surveys in constraining such a signature through its impact on the observed galaxy power spectrum. Primordial non-Gaussianity of various shapes induces a scale-dependen…
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…
Primordial non-Gaussianity of local type is predicted to lead to enhanced halo clustering on very large scales. Photometric quasars, which can be seen from cosmological redshifts z>2 even in wide-shallow optical surveys, are promising tracers for constraining non-Gaussianity using this effect. However, large-scale systematics can also mimic this signature of non-Gaussianity. In order to assess the contribution of systematic effects, we cross-correlate overdensity maps of photometric quasars from the Sloan Digital Sky Survey (SDSS) Data Release 6 (DR6) in different redshift ranges. We find that…
We calculate the three-point correlation function of the comoving curvature perturbation generated during an inflationary epoch driven by false vacuum energy. We get a novel false vacuum shape bispectrum, which peaks in the equilateral limit. Using this result, we propose a scenario which we call "old curvaton". The shape of the resulting bispectrum lies between the local and the false vacuum shapes. In addition we have a large running of the spectral index.
In the pursuit of primordial non-Gaussianities, we hope to access smaller scales across larger comoving volumes. At low redshift, the search for primordial non-Gaussianities is hindered by gravitational collapse, to which we often associate a scale $k_{\rm NL}$. Beyond these scales, it will be hard to reconstruct the modes sensitive to the primordial distribution. When forecasting future constraints on the amplitude of primordial non-Gaussianity, $f_{\rm NL}$, off-diagonal components are usually neglected in the covariance because these are small compared to the diagonal. We show that the indu…
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 r…
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 show how the peak-background split can be generalized to predict the effect of non-local primordial non-Gaussianity on the clustering of halos. Our approach is applicable to arbitrary primordial bispectra. We show that the scale-dependence of halo clustering predicted in the peak-background split (PBS) agrees with that of the local-biasing model on large scales. On smaller scales, k >~ 0.01 h/Mpc, the predictions diverge, a consequence of the assumption of separation of scales in the peak-background split. Even on large scales, PBS and local biasing do not generally agree on the amplitude o…
We discuss how primordial non-Gaussianity of the curvature perturbation helps to constrain models of the early universe. Observations are consistent with Gaussian initial conditions, compatible with the predictions of the simplest models of inflation. Deviations are constrained to be at the sub percent level, constraining alternative models such as those with multiple fields, non-canonical kinetic terms or breaking the slow-roll conditions. We introduce some of the most important models of inflation which generate non-Gaussian perturbations and provide practical tools on how to calculate the t…
We analyze multi-field inflationary systems which yield strongly scale dependent non-Gaussianity with a shape that is very close to the local shape. As in usual multi-field models, the non-Gaussianity arises from the non-linear transfer of scalar field fluctuations to curvature perturbations. Here we consider models in which higher order terms (loops) dominate over the lowest order source of non-linearity. The magnitude of non-Gaussianity depends on an infrared cutoff which is determined by our observational probes measuring non-Gaussianity. In our models, the running is positive and large (n_…
The cosmic microwave background radiation is supposed to be Gaussian and this hypothesis is in good agreement with the recent very accurate measurements. Nonetheless a tiny amount of non-Gaussianity is predicted by the standard inflation scenario, while more exotic models suggest a higher degree of non-Gaussianity. Tightly constraining the level of Gaussianity in the CMB data represents then a fundamental handle to understand the physics and the origin of our universe. By means of needlets, a novel rendition of wavelets, characterised by excellent properties of localisations both in harmonic a…
Primordial non-Gaussianity is a sensitive probe of the inflationary era, with a number of important theoretical targets living an order of magnitude beyond the reach of current CMB constraints. Maps of the large-scale structure of the universe, in principle, have the raw statistical power to reach these targets, but the complications of nonlinear evolution are thought to present serious, if not insurmountable, obstacles to reaching these goals. In this paper, we will argue that the challenge presented by nonlinear structure formation has been overstated. The information encoded in primordial n…
We investigate the possibility of constraining primordial non-Gaussianity using the 3D bispectrum of Ly-alpha forest. The strength of the quadratic non-Gaussian correction to an otherwise Gaussian primordial gravitational field is assumed to be dictated by a single parameter fnl. We present the first prediction for bounds on fnl using Ly-alpha flux spectra along multiple lines of sight. The 3D Ly-$α$ transmitted flux field is modeled as a biased tracer of the underlying matter distribution sampled along 1D skewers corresponding to quasars sight lines. The precision to which fnl can be constrai…
When applied to the non-linear matter distribution of the universe, neural networks have been shown to be very statistically sensitive probes of cosmological parameters, such as the linear perturbation amplitude $σ_8$. However, when used as a "black box", neural networks are not robust to baryonic uncertainty. We propose a robust architecture for constraining primordial non-Gaussianity $f_{NL}$, by training a neural network to locally estimate $σ_8$, and correlating these local estimates with the large-scale density field. We apply our method to N-body simulations, and show that $σ(f_{NL})$ is…
We introduce the numbers of hot and cold spots, $n_h$ and $n_c$, of excursion sets of the CMB temperature anisotropy maps as statistical observables that can discriminate different non-Gaussian models. We numerically compute them from simulations of non-Gaussian CMB temperature fluctuation maps. The first kind of non-Gaussian model we study is the local type primordial non-Gaussianity. The second kind of models have some specific form of the probability distribution function from which the temperature fluctuation value at each pixel is drawn, obtained using HEALPIX. We find the characteristic …
We investigate tomography of 21-cm brightness temperature fluctuations during the Dark Ages as a probe for constraining primordial non-Gaussianity. We expand the 21- cm brightness temperature up to cubic order in perturbation theory and improve previous models of the signal by including the effect of the free electron fraction. Using modified standard perturbation theory methods that include baryonic pressure effects we derive an improved secondary bispectrum and for the first time derive the secondary trispectrum of 21-cm brightness temperature fluctuations. We then forecast the amount of inf…
