Primordial non-Gaussianity Research Articles

Primordial non-Gaussian signatures in CMB polarization

We study the signatures of local type primordial non-Gaussianity, parametrized by fNL, of scalar perturbations in CMB polarization using the probability distribution functions, Minkowski Functionals and Betti numbers. We show that the lowest order non-Gaussian deviation of the PDF of the total polarization intensity is at order (fNLσ)2. We calculate the non-Gaussian deviations of Minkowski Functionals and Betti numbers from simulated polarization maps. If observational issues such as instrumental noise are ignored, we find that E mode polarization provides independent and equally strong constraint on fNL as temperature fluctuations. The constraint is expected to weaken when observational issues are included since the signal-to-noise ratio of polarization data is lower than that of temperature. The non-Gaussian signal in the total polarization intensity, however, is much weaker and has a relatively large cosmic variance and hence may not be useful for detecting local type non-Gaussianity.

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.

FORECASTS ON THE DARK ENERGY AND PRIMORDIAL NON-GAUSSIANITY OBSERVATIONS WITH THE TIANLAI CYLINDER ARRAY

The Tianlai experiment is dedicated to the observation of large scale structures (LSS) by the 21 cm intensity mapping technique. In this paper we make forecasts on its capability at observing or constraining the dark energy parameters and the primordial non-Gaussianity. From the LSS data one can use the baryon acoustic oscillation (BAO) and the growth rate derived from the redshift space distortion (RSD) to measure the dark energy density and equation of state. The primordial non-Gaussianity can be constrained either by looking for scale-dependent bias in the power spectrum, or by using the bispectrum. Here we consider three cases: the Tianlai cylinder array pathfinder which is currently being built, an upgrade of the pathfinder array with more receiver units, and the full-scale Tianlai cylinder array. Using the full-scale Tianlai experiment, we expect $\sigma_{w_0} \sim 0.082$ and $\sigma_{w_a} \sim 0.21$ from the BAO and RSD measurements, $\sigma_{\rm f_{NL}}^{\rm local} \sim 14$ from the power spectrum measurements with scale-dependent bias, and $\sigma_{\rm f_{NL}}^{\rm local} \sim 22$ and $\sigma_{\rm f_{NL}}^{\rm equil} \sim 157$ from the bispectrum measurements.

Effect of primordial non-Gaussianities on the far-UV luminosity function of high-redshift galaxies: implications for cosmic reionization

[Abridged] Understanding how the intergalactic medium (IGM) was reionized at z > 6 is one of the big challenges of current high redshift astronomy. It requires modelling the collapse of the first astrophysical objects (Pop III stars, first galaxies) and their interaction with the IGM, while at the same time pushing current observational facilities to their limits. The observational and theoretical progress of the last few years have led to the emergence of a coherent picture in which the budget of hydrogen-ionizing photons is dominated by low-mass star-forming galaxies, with little contribution from Pop III stars and quasars. The reionization history of the Universe therefore critically depends on the number density of low-mass galaxies at high redshift. In this work, we explore how changes in the statistical properties of initial density fluctuations affect the formation of early galaxies. Following Habouzit et al. (2014), we run 5 N-body simulations with Gaussian and (scale-dependent) non-Gaussian initial conditions, all consistent with Planck constraints. By appealing to a galaxy formation model and to a population synthesis code, we compute the far-UV galaxy luminosity function down to M_UV = -14 at redshift 7 < z < 15. We find that models with strong primordial non-Gaussianities on < Mpc scales show a far-UV luminosity function significantly enhanced in low-mass galaxies. We adopt a reionization model calibrated from state-of-the-art hydrodynamical simulations and show that such non-Gaussianities leave a clear imprint on the Universe reionization history and electron Thomson scattering optical depth tau_E. Although current uncertainties in the physics of reionization and on the determination of tau_E still dominate the signatures of non-Gaussianities, our results suggest that tau_E could ultimately be used to constrain the statistical properties of initial density fluctuations.

Encyclopædia Inflationaris

The current flow of high accuracy astrophysical data, among which are the Cosmic Microwave Background (CMB) measurements by the Planck satellite, offers an unprecedented opportunity to constrain the inflationary theory. This is however a challenging project given the size of the inflationary landscape which contains hundreds of different scenarios. Given that there is currently no observational evidence for primordial non-Gaussianities, isocurvature perturbations or any other non-minimal extension of the inflationary paradigm, a reasonable approach is to consider the simplest models first, namely the slow-roll single field models with minimal kinetic terms. This still leaves us with a very populated landscape, the exploration of which requires new and efficient strategies. It has been customary to tackle this problem by means of approximate model independent methods while a more ambitious alternative is to study the inflationary scenarios one by one. We have developed the new publicly available runtime library ASPIC1 to implement this last approach. The ASPIC code provides all routines needed to quickly derive reheating consistent observable predictions within this class of scenarios. ASPIC has been designed as an evolutive code which presently supports 74 different models, a number that may be compared with three or four representing the present state of the art. In this paper, for each of the ASPIC models, we present and collect new results in a systematic manner, thereby constituting the first Encyclopædia Inflationaris. Finally, we discuss how this procedure and ASPIC could be used to determine the best model of inflation by means of Bayesian inference.

Constraints on Primordial Non-Gaussianity from 800 000 Photometric Quasars.

We derive robust constraints on primordial non-Gaussianity (PNG) using the clustering of 800 000 photometric quasars from the Sloan Digital Sky Survey in the redshift range 0.5<z<3.5. These measurements rely on the novel technique of extended mode projection to control the impact of spatially varying systematics in a robust fashion, making use of blind analysis techniques. This allows the accurate measurement of quasar halo bias at the largest scales, while discarding as little as possible of the data. The standard local-type PNG parameters f_{NL} and g_{NL} both imprint a k^{-2} scale-dependent effect in the bias. Constraining these individually, we obtain -49<f_{NL}<31 and -2.7×10^{5}<g_{NL}<1.9×10^{5}, while their joint constraints lead to -105<f_{NL}<72 and -4.0×10^{5}<g_{NL}<4.9×10^{5} (all at 95%C.L.). Introducing a running parameter n_{f_{NL}} to constrain b(k)∝k^{-2+n_{f_{NL}}} and a generalized PNG amplitude f[over ˜]_{NL}, we obtain -45.5 exp(3.7n_{f_{NL}})<f[over ˜]_{NL}<34.4 exp(3.3n_{f_{NL}}) at 95%C.L. These results incorporate uncertainties in the cosmological parameters, redshift distributions, shot noise, and the bias prescription used to relate the quasar clustering to the underlying dark matter. These are the strongest constraints obtained to date on PNG using a single population of large-scale structure tracers, and are already at the level of pre-Planck constraints from the cosmic microwave background. A conservative forecast for a Large Synoptic Survey Telescope (LSST)-like survey incorporating mode projection yields σ(f_{NL})∼5-competitive with the Planck result-highlighting the power of upcoming large scale structure surveys to probe the initial conditions of the Universe.

Weighing the giants – IV. Cosmology and neutrino mass

We employ robust weak gravitational lensing measurements to improve cosmological constraints from measurements of the galaxy cluster mass function and its evolution, using X-ray selected clusters detected in the ROSAT All-Sky Survey. Our lensing analysis constrains the absolute mass scale of such clusters at the 8 per cent level, including both statistical and systematic uncertainties. Combining it with the survey data and X-ray follow-up observations, we find a tight constraint on a combination of the mean matter density and late-time normalization of the matter power spectrum, σ8(Ωm/0.3)0.17 = 0.81 ± 0.03, with marginalized, one-dimensional constraints of Ωm = 0.26 ± 0.03 and σ8 = 0.83 ± 0.04. For these two parameters, this represents a factor of 2 improvement in precision with respect to previous work, primarily due to the reduced systematic uncertainty in the absolute mass calibration provided by the lensing analysis. Our new results are in good agreement with constraints from cosmic microwave background (CMB) data, both Wilkinson Microwave Anisotropy Probe (WMAP) and Planck (plus WMAP polarization), under the assumption of a flat ΛCDM cosmology with minimal neutrino mass. Consequently, we find no evidence for non-minimal neutrino mass from the combination of cluster data with CMB, supernova and baryon acoustic oscillation measurements, regardless of which all-sky CMB data set is used (and independent of the recent claimed detection of B modes on degree scales). We also present improved constraints on models of dark energy (both constant and evolving), modifications of gravity, and primordial non-Gaussianity. Assuming flatness, the constraints for a constant dark energy equation of state from the cluster data alone are at the 15 per cent level, improving to ∼6 per cent when the cluster data are combined with other leading probes.

Impact of polarization on the intrinsic cosmic microwave background bispectrum

We compute the bispectrum induced in the cosmic microwave background (CMB) temperature and polarisation by the evolution of the primordial density perturbations using the second-order Boltzmann code SONG. We show that adding polarisation increases the signal-to-noise ratio by a factor four with respect to temperature alone and we estimate the observability of this intrinsic bispectrum and the bias it induces on measurements of primordial non-Gaussianity. When including all physical effects except the late-time non-linear evolution, we find for the intrinsic bispectrum a signal-to-noise of $S/N=3.8,\,2.9,\,1.6$ and $0.5$ for, respectively, an ideal experiment with an angular resolution of $\ell_\text{max}=3000$, the proposed CMB surveys PRISM and COrE, and Planck's polarised data; the bulk of this signal comes from the $E$-polarisation and from squeezed configurations. We discuss how CMB lensing is expected to reduce these estimates as it suppresses the bispectrum for squeezed configurations and contributes to the noise in the estimator. We find that the presence of the intrinsic bispectrum will bias a measurement of primordial non-Gaussianity of local type by $f_{NL}^\text{bias}=0.66$ for an ideal experiment with $\ell_\text{max}=3000$. Finally, we verify the robustness of our results by reproducing the analytical approximation for the squeezed-limit bispectrum in the general polarised case.

General relativistic corrections and non-Gaussianity in large-scale structure

General relativistic cosmology cannot be reduced to linear relativistic perturbations superposed on an isotropic and homogeneous (Friedmann–Robertson–Walker) background, even though such a simple scheme has been successfully applied to analyse a large variety of phenomena (such as cosmic microwave background primary anisotropies, matter clustering on large scales, weak gravitational lensing, etc). The general idea of going beyond this simple paradigm is what characterizes most of the efforts made in recent years: the study of second and higher-order cosmological perturbations including all general relativistic contributions—also in connection with primordial non-Gaussianities—the idea of defining large-scale structure observables directly from a general relativistic perspective, the various attempts to go beyond the Newtonian approximation in the study of nonlinear gravitational dynamics, by using e.g., post-Newtonian treatments, are all examples of this general trend. Here we summarize some of these directions of investigation, with the aim of emphasizing future prospects in this area of cosmology, both from a theoretical and observational point of view.

The inflationary origin of the Cold Spot anomaly

Single-field inflation, arguably the simplest and most compelling paradigm for the origin of our Universe, is strongly supported by the recent results of the Planck satellite and the BICEP2 experiment. The results from Planck, however, also confirm the presence of a number of anomalies in the Cosmic Microwave Background (CMB), whose origin becomes problematic in single-field inflation. Among the most prominent and well-tested of these anomalies is the Cold Spot, which constitutes the only significant deviation from Gaussianity in the CMB. Planck's non-detection of primordial non-Gaussianity on smaller scales thus suggests the existence of a physical mechanism whereby significant non-Gaussianity is generated on large angular scales only. In this Letter, we address this question by developing a localized version of the inhomogeneous reheating scenario, which postulates the existence of a scalar field able to modify the decay of the inflaton on localized spatial regions only. We demonstrate that if the Cold Spot is due to an overdensity in the last scattering surface, the localization mechanism offers a feasible explanation for it, thus providing a physical mechanism for the generation of localized non-Gaussianity in the CMB. If, on the contrary, the Cold Spot is caused by a newly discovered supervoid (as recently claimed), we argue that the localization mechanism, while managing to enhance underdensities, may well shed light on the rarity of the discovered supervoid.

Planck2013 results. XXIV. Constraints on primordial non-Gaussianity

The Planck nominal mission cosmic microwave background (CMB) maps yield unprecedented constraints on primordial non-Gaussianity (NG). Using three optimal bispectrum estimators, separable template-fitting (KSW), binned, and modal, we obtain consistent values for the primordial local, equilateral, and orthogonal bispectrum amplitudes, quoting as our final result fNL^local= 2.7+/-5.8, fNL^equil= -42+/-75, and fNL^ortho= -25+\-39 (68% CL statistical). NG is detected in the data; using skew-C_l statistics we find a nonzero bispectrum from residual point sources, and the ISW-lensing bispectrum at a level expected in the LambdaCDM scenario. The results are based on comprehensive cross-validation of these estimators on Gaussian and non-Gaussian simulations, are stable across component separation techniques, pass an extensive suite of tests, and are confirmed by skew-C_l, wavelet bispectrum and Minkowski functional estimators. Beyond estimates of individual shape amplitudes, we present model-independent, 3-dimensional reconstructions of the Planck CMB bispectrum and thus derive constraints on early-Universe scenarios that generate primordial NG, including general single-field models of inflation, excited initial states (non-Bunch-Davies vacua), and directionally-dependent vector models. We provide an initial survey of scale-dependent feature and resonance models. These results bound both general single-field and multi-field model parameter ranges, such as the speed of sound, c_s \geq 0.02 (95% CL), in an effective field theory parametrization, and the curvaton decay fraction r_D \geq 0.15 (95% CL). The Planck data significantly limit the viable parameter space of the ekpyrotic/cyclic scenarios. The amplitude of the 4-point function in the local model tauNL < 2800 (95% CL). These constraints represent the highest precision tests to date of physical mechanisms for the origin of cosmic structure.

Primordial non-Gaussianities in single field inflationary models with non-trivial initial states

We compute the non-Gaussianities that arise in single field, slow roll inflationary models arising from arbitrary homogeneous initial states, as well as subleading contributions to the power spectrum. Non Bunch-Davies vacuum initial states can arise if the transition to the single field, slow roll inflation phase occurs only shortly before observable modes left the horizon. They can also arise from new physics at high energies that has been integrated out. Our general result for the bispectrum exhibits several features that were previously seen in special cases.

Computation of the halo mass function using physical collapse parameters: application to non-standard cosmologies

In this article we compare the halo mass function predicted by the excursion set theory with a drifting diffusive barrier against the results of N-body simulations for several cosmological models. This includes the standard ΛCDM case for a large range of halo masses, models with different types of primordial non-Gaussianity, and the Ratra-Peebles quintessence model of Dark Energy. We show that in all those cosmological scenarios, the abundance of dark matter halos can be described by a drifting diffusive barrier, where the two parameters describing the barrier have physical content. In the case of the Gaussian ΛCDM, the statistics are precise enough to actually predict those parameters at different redshifts from the initial conditions. Furthermore, we found that the stochasticity in the barrier is non-negligible making the simple deterministic spherical collapse model a bad approximation even at very high halo masses. We also show that using the standard excursion set approach with a barrier inspired by peak patches leads to inconsistent predictions of the halo mass function.

Integrated perturbation theory and one-loop power spectra of biased tracers

General and explicit predictions from the integrated perturbation theory (iPT) for power spectra and correlation functions of biased tracers are derived and presented in the one-loop approximation. The iPT is a general framework of the nonlinear perturbation theory of cosmological density fields in presence of nonlocal bias, redshift-space distortions, and primordial non-Gaussianity. Analytic formulas of auto and cross power spectra of nonlocally biased tracers in both real and redshift spaces are derived and the results are comprehensively summarized. The main difference from previous formulas derived by the present author is to include effects of generally nonlocal Lagrangian bias and primordial non-Gaussianity, and the derivation method of the new formula is fundamentally different from the previous one. Relations to recent work on improved methods of nonlinear perturbation theory in literature are clarified and discussed.

THE EXTENDED ZEL'DOVICH MASS FUNCTIONS OF CLUSTERS AND ISOLATED CLUSTERS IN THE PRESENCE OF PRIMORDIAL NON-GAUSSIANITY

We present new formulae for the mass functions of the clusters and the isolated clusters with non Gaussian initial conditions. For this study, we adopt the Extended Zel'dovich (EZL) model as a basic framework, focusing on the case of primordial non-Gaussianity of the local type whose degree is quantified by a single parameter $f_{nl}$. By making a quantitative comparison with the N-body results, we first demonstrate that the EZL formula with the constant values of three fitting parameters still works remarkably well for the local $f_{nl}$ case. We also modify the EZL formula to find an analytic expression for the mass function of isolated clusters which turns out to have only one fitting parameter other than the overall normalization factor and showed that the modified EZL formula with a constant value of the fitting parameter matches excellently the N-body results with various values of $f_{nl}$ at various redshifts. Given the simplicity of the generalized EZL formulae and their good agreements with the numerical results, we finally conclude that the EZL mass functions of the massive clusters and isolated clusters should be useful as an analytic guideline to constrain the scale dependence of the primordial non-Gaussianity of the local type.

Non-Gaussianity after BICEP2.

We analyze primordial non-Gaussianity in single-field inflationary models when the tensor-to-scalar ratio is large. Our results show that detectable levels of non-Gaussianity f(NL) ∼ 50 are still possible in the simplest class of models described by the effective theory of inflation. However, the shape is very tightly constrained, making a sharp prediction that could be confirmed or falsified by a future detection of non-Gaussianity.

Second order density perturbations for dust cosmologies

We present simple expressions for the relativistic first and second order fractional density perturbations for Friedmann-Lema\^{\i}tre cosmologies with dust, in four different gauges: the Poisson, uniform curvature, total matter and synchronous-comoving gauges. We include a cosmological constant and arbitrary spatial curvature in the background. A distinctive feature of our approach is our description of the spatial dependence of the perturbations using a canonical set of quadratic differential expressions involving an arbitrary spatial function that arises as a conserved quantity. This enables us to unify, simplify and extend previous seemingly disparate results. We use the primordial matter and metric perturbations that emerge at the end of the inflationary epoch to determine the additional arbitrary spatial function that arises when integrating the second order perturbation equations. This introduces a non-Gaussianity parameter into the expressions for the second order density perturbation. In the special case of zero spatial curvature we show that the time evolution simplifies significantly, and requires the use of only two nonelementary functions, the so-called growth suppression factor at the linear level, and one new function at the second order level. We expect that the results will be useful in applications, for example, studying the effects of primordial non-Gaussianity on the large scale structure of the Universe.

Constraining primordial non-Gaussianity with moments of the large-scale density field

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 fNL = 100, an equilateral model with fNL = −400, and an orthogonal model with fNL = −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 catalogues that contain galaxies with clustering properties similar to those of luminous red galaxies. We find that, in the case of skewness and kurtosis, galaxy bias reduces the detectability of non-Gaussianity. However, in the case of the variance, galaxy bias greatly amplifies the detectability of non-Gaussianity. In all cases, we find that redshift distortions do not significantly affect the detectability. When we restrict our measurements to volumes equivalent to the Sloan Digital Sky Survey II or Baryon Oscillation Spectroscopic Survey samples, the probability of detecting a departure from the Gaussian model is high by using measurements of the variance, but very low by using only skewness and kurtosis. We estimate that in order to detect an amount of non-Gaussianity that is consistent with recent cosmic microwave background constraints using skewness or kurtosis, we would need a galaxy survey that is much larger than any planned future survey. However, future surveys should be large enough to place meaningful constraints using galaxy variance measurements.

Reionization and CMB non-Gaussianity

We show how cross-correlating a high-redshift external tracer field, such as the 21-cm neutral hydrogen distribution and product maps involving cosmic microwave background (CMB) temperature and polarization fields, that probe mixed bispectrum involving these fields, can help to determine the reionization history of the Universe, beyond what can be achieved from cross-spectrum analysis. Taking clues from recent studies for the detection of primordial non-Gaussianity, we develop a set of estimators that can study reionization using a power spectrum associated with the bispectrum (or skew-spectrum). We use the matched filtering inherent in this method to investigate different reionization histories. We check to what extent they can be used to rule out various models of reionization and study cross-contamination from different sources such as the lensing of the CMB. The estimators can be fine-tuned to optimize study of a specific reionization history. We consider three different types of tracers in our study, namely: proto-galaxies; 21-cm maps of neutral hydrogen; and quasars. We also consider four alternative models of reionization. We find that the cumulative signal-to-noise ratio (S/N) for detection at ℓmax = 2000 can reach |$\mathcal {O}(70)$| for cosmic variance limited all-sky experiments. Combining 100 GHz, 143 GHz and 217 GHz channels of the Planck experiment, we find that the S/N lies in the range |$\mathcal {O}(5)$|–|$\mathcal {O}(35)$|⁠. The S/N depends on the specific choice of a tracer field, and multiple tracers can be effectively used to map out the entire reionization history with reasonable S/N. Contamination from weak lensing is investigated and found to be negligible, and the effects of Thomson scattering from patchy reionization are also considered.

Angular-averaged consistency relations of large-scale structures

The cosmological dynamics of gravitational clustering satisfies an approximate invariance with respect to the cosmological parameters that is often used to simplify analytical computations. We describe how this approximate symmetry gives rise to angular-averaged consistency relations for the matter density correlations. This allows one to write the ($\ensuremath{\ell}+n$) density correlation, with $\ensuremath{\ell}$ large-scale linear wave numbers that are integrated over angles, and $n$ fixed small-scale nonlinear wave numbers, in terms of the small-scale $n$-point density correlation and $\ensuremath{\ell}$ prefactors that involve the linear power spectra at the large-scale wave numbers. These relations, which do not vanish for equal-time statistics, go beyond the already known kinematic consistency relations. They could be used to detect primordial non-Gaussianities, modifications of gravity, limitations of galaxy biasing schemes, or to help design analytical models of gravitational clustering.