Primordial non-Gaussianity Signal Research Articles

Relativistic second-order initial conditions for simulations of large-scale structure

Relativistic corrections to the evolution of structure can be used to test general relativity on cosmological scales. They are also a well-known systematic contamination in the search for a primordial non-Gaussian signal. We present a numerical framework to generate RELativistic second-order Initial Conditions (RELIC) based on a generic (not necessarily separable) second-order kernel for the density perturbations. In order to keep the time complexity manageable we introduce a scale cut that separates long and short scales, and neglect the “short-short” coupling that will eventually be swamped by uncontrollable higher-order effects. To test our approach, we use the second-order Einstein-Boltzmann code SONG to provide the numerical second-order kernel in a ΛCDM model, and we demonstrate that the realisations generated by RELIC reproduce the bispectra well whenever at least one of the scales is a “long” mode. We then present a generic algorithm that takes a perturbed density field as an input and provides particle initial data that matches this input to arbitrary order in perturbations for a given particle-mesh scheme. We implement this algorithm in the relativistic N-body code gevolution to demonstrate how our framework can be used to set precise initial conditions for cosmological simulations of large-scale structure.

Local primordial non-Gaussianity in the relativistic galaxy bispectrum

Next-generation galaxy and 21cm intensity mapping surveys will rely on a combination of the power spectrum and bispectrum for high-precision measurements of primordial non-Gaussianity. In turn, these measurements will allow us to distinguish between various models of inflation. However, precision observations require theoretical precision at least at the same level. We extend the theoretical understanding of the galaxy bispectrum by incorporating a consistent general relativistic model of galaxy bias at second order, in the presence of local primordial non-Gaussianity. The influence of primordial non-Gaussianity on the bispectrum extends beyond the galaxy bias and the dark matter density, due to redshift-space effects. The standard redshift-space distortions at first and second order produce a well-known primordial non-Gaussian imprint on the bispectrum. Relativistic corrections to redshift-space distortionsgenerate new contributions to this primordial non-Gaussian signal, arising from: (1) a coupling of first-order scale-dependent bias with first-order relativistic observational effects, and (2) linearly evolved non-Gaussianity in the second-order velocity and metric potentials which appear in relativistic observational effects.Our analysis allows for a consistent separation of the relativistic `contamination' from the primordial signal, in order to avoid biasing the measurements by using an incorrect theoretical model. We show that the bias from using a Newtonian analysis of the squeezed bispectrum could be Δ fNL∼ 5 for a Stage IV Hα survey.

Matter trispectrum: theoretical modelling and comparison to N-body simulations

The power spectrum has long been the workhorse summary statistics for large-scale structure cosmological analyses. However, gravitational non-linear evolution moves precious cosmological information from the two-point statistics (such as the power spectrum) to higher-order correlations. Moreover, information about the primordial non-Gaussian signal lies also in higher-order correlations. Without tapping into these, that information remains hidden. While the three-point function (or the bispectrum), even if not extensively, has been studied and applied to data, there has been only limited discussion about the four point/trispectrum. This is because the high-dimensionality of the statistics (in real space a skew-quadrilateral has 6 degrees of freedom), and the high number of skew-quadrilaterals, make the trispectrum numerically and algorithmically very challenging. Here we address this challenge by studying the i-trispectrum, an integrated trispectrum that only depends on four k-modes moduli. We model and measure the matter i-trispectrum from a set of 5000 QUIJOTE N-body simulations both in real and redshift space, finding good agreement between simulations outputs and model up to mildly non-linear scales. Using the power spectrum, bispectrum and i-trispectrum joint data-vector covariance matrix estimated from the simulations, we begin to quantify the added-value provided by the i-trispectrum. In particular, we forecast the i-trispectrum improvements on constraints on the local primordial non-Gaussianity amplitude parameters fnl and gnl. For example, using the full joint data-vector, we forecast fnl constraints up to two times (∼32%) smaller in real (redshift) space than those obtained without i-trispectrum.

From matter to galaxies: general relativistic bias for the one-loop bispectrum

We write down the Lagrangian bias expansion in general relativity up to 4th order in terms of operators describing the curvature of an early-time hypersurface for comoving observers. They can be easily expanded in synchronous or comoving gauges. This is necessary for the computation of the one-loop halo bispectrum, where relativistic effects can be degenerate with a primordial non-Gaussian signal. Since the bispectrum couples scales, an accurate prediction of the squeezed limit behavior needs to be both non-linear and relativistic. We then evolve the Lagrangian bias operators in time in comoving gauge, obtaining non-local operators analogous to what is known in the Newtonian limit. Finally, we show how to renormalize the bias expansion at an arbitrary time and find that this is crucial in order to cancel unphysical 1/k2 divergences in the large-scale power spectrum and bispectrum that could be mistaken for a contamination to the non-Gaussian signal.

Relativistic cosmological large scale structures at one-loop

The large scale structure bispectrum in the squeezed limit couples large with small scales. Since relativity is important at large scales and non-linear loop corrections are important at small scales, the proper calculation of the observed bispectrum in this limit requires a non-linear relativistic calculation. We compute the matter bispectrum in general relativity in the weak field approximation. The calculation is as involved as existing second-order results. We find several differences with the Newtonian calculation such as the non-cancellation of IR divergences, the need to renormalize the background, and the fact that initial conditions must be set at second order in perturbation theory. For the bispectrum, we find relativistic corrections to be as large as the newtonian result in the squeezed limit. In that limit relativistic one-loop contributions, which we compute for the first time, can be as large as tree level results and have the same 1/k2 dependence as a primordial local non-Gaussianity signal where k is the momentum approaching zero. Moreover, we find the time dependence of the relativistic corrections to the bispectrum to be the same as that of a primordial non-Gaussianity signal.

The observed galaxy bispectrum from single-field inflation in the squeezed limit

Using the consistency relation in Fourier space, we derive the observed galaxy bispectrum from single-field inflation in the squeezed limit, in which one of the three modes has a wavelength much longer than the other two. This provides a non-trivial check of the full computation of the bispectrum based on second-order cosmological perturbation theory in this limit. We show that gauge modes need to be carefully removed in the second-order cosmological perturbations in order to calculate the observed galaxy bispectrum in the squeezed limit. We then give an estimate of the effective non-Gaussianity due to general-relativistic lightcone effects that could mimic a primordial non-Gaussian signal.

Non-Gaussianities due to relativistic corrections to the observed galaxy bispectrum

High-precision constraints on primordial non-Gaussianity (PNG) will significantly improve our understanding of the physics of the early universe. Among all the subtleties in using large scale structure observables to constrain PNG, accounting for relativistic corrections to the clustering statistics is particularly important for the upcoming galaxy surveys covering progressively larger fraction of the sky. We focus on relativistic projection effects due to the fact that we observe the galaxies through the light that reaches the telescope on perturbed geodesics. These projection effects can give rise to an effective fNL that can be misinterpreted as the primordial non-Gaussianity signal and hence is a systematic to be carefully computed and accounted for in modelling of the bispectrum. We develop the technique to properly account for relativistic effects in terms of purely observable quantities, namely angles and redshifts. We give some examples by applying this approach to a subset of the contributions to the tree-level bispectrum of the observed galaxy number counts calculated within perturbation theory and estimate the corresponding non-Gaussianity parameter, fNL, for the local, equilateral and orthogonal shapes. For the local shape, we also compute the local non-Gaussianity resulting from terms obtained using the consistency relation for observed number counts. Our goal here is not to give a precise estimate of fNL for each shape but rather we aim to provide a scheme to compute the non-Gaussian contamination due to relativistic projection effects. For the terms considered in this work, we obtain contamination of fNLloc ∼ \U0001d4aa(1).

Degeneracy between primordial non-Gaussianity and interaction in the dark sector

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 measuring the power at two redshifts.

Optimal bispectrum estimator and simulations of the CMB lensing-integrated Sachs Wolfe non-Gaussian signal

In this paper we present the tools to optimally extract the Lensing-Integrated Sachs Wolfe (L-ISW) bispectrum signal from future CMB data. We implement two different methods to simulate the non-Gaussian CMB maps with the L-ISW signal: a non-perturbative method based on the FLINTS lensing code and the separable mode expansion method. We implement the Komatsu, Spergel and Wandelt (KSW) optimal estimator analysis for the Lensing-ISW bispectrum and we test it on the non-Gaussian simulations in the case of a realistic CMB experimental settings with an inhomogeneous sky coverage. We show that the estimator approaches the Cramer-Rao bound and that Wiener filtering the L-ISW simulations gives a slight improvement on the estimate of $f_{NL}^{L-ISW}$ of $\leq 10%$. For a realistic CMB experimental setting accounting for anisotropic noise and masked sky, we show that the linear term of the estimator is highly correlated to the cubic term and it is necessary to recover the signal and the optimal error bars. We also show that the L-ISW bispectrum, if not correctly accounted for, yields an underestimation of the $f_{NL}^{local}$ error bars of $\simeq 4%$. A joint analysis of the non-Gaussian shapes and/or L-ISW template subtraction is needed in order to recover unbiased results of the primordial non-Gaussian signal from ongoing and future CMB experiments.

Statistics of the excursion sets in models with local primordial non-Gaussianity

We use the statistics of regions above or below a temperature threshold (excursion sets) to study the cosmic microwave background (CMB) anisotropy in models with primordial non-Gaussianity of the local type. By computing the full-sky spatial distribution and clustering of pixels above/below threshold from a large set of simulated maps with different levels of non-Gaussianity, we find that a positive value of the dimensionless non-linearity parameter f_NL enhances the number density of the cold CMB excursion sets along with their clustering strength, and reduces that of the hot ones. We quantify the robustness of this effect, which may be important to discriminate between the simpler Gaussian hypothesis and non-Gaussian scenarios, arising either from non-standard inflation or alternative early-universe models. The clustering of hot and cold pixels exhibits distinct non-Gaussian signatures, particularly at angular scales of about 75 arcmin (i.e. around the Doppler peak), which increase linearly with f_NL. Moreover, the clustering changes strongly as a function of the smoothing angle. We propose several statistical tests to maximize the detection of a local primordial non-Gaussian signal, and provide some theoretical insights within this framework, including an optimal selection of the threshold level. We also describe a procedure which aims at minimizing the cosmic variance effect, the main limit within this statistical framework.

THE MASS FUNCTION OF VOID GROUPS AS A PROBE OF PRIMORDIAL NON-GAUSSIANITY

The primordial non-Gaussianity signal, if measured accurately, will allow us to distinguish between different candidate models for cosmic inflation. Since the galaxy groups located in void regions are rare events, their abundance may be a sensitive probe of primordial non-Gaussianity. We construct an analytic model for the mass function of void groups in the framework of the extended Press-Schechter theory with non-Gaussian initial conditions and investigate how it depends on the primordial non-Gaussianity parameter. A feasibility study is conducted by fitting the analytic mass function of void groups to the observational results from the galaxy group catalog of the Sloan Digital Sky Survey Data Release 4 by adjusting the primordial non-Gaussianity parameter.

The integrated bispectrum as a test of cosmic microwave background non-Gaussianity: detection power and limits on fNL with WMAP data

We propose a fast and efficient bispectrum statistic for cosmic microwave background (CMB) temperature anisotropies to constrain the amplitude of the primordial non-Gaussian signal measured in terms of the non-linear coupling parameter f$_{NL$. We show how the method can achieve a remarkable computational advantage by focusing on subsets of the multipole configurations, where the non-Gaussian signal is more concentrated. The detection power of the test increases roughly linearly with the maximum multipole, as shown in the ideal case of an experiment without noise and gaps. The CPU-time scales as l$^3$$_max$ instead of l$^5$$_max$ for the full bispectrum, which for Planck resolution l$_max$ \~{} 3000 means an improvement in speed of a factor of 10$^7$ compared with the full bispectrum analysis with minor loss in precision. This approach is complementary to the fast method introduced by Komatsu, Spergel \amp Wandelt using a reconstruction of the primordial fluctuation field. We find that the introduction of a galactic cut partially destroys the optimality of the configuration, which will then need to be dealt with in the future. We find for an ideal experiment with l$_max$ = 2000 that upper limits of f$_NL$ \lt 8 can be obtained at 1$\sigma$. For the case of the WMAP experiment, we would be able to put limits of |f$_NL$| \lt 40 if no galactic cut were present. Using the real data with a galactic cut, we obtain an estimate of -80 \lt f$_NL$ \lt 80 and -160 \lt f$_NL$ \lt 160 at 1 and 2$\sigma$, respectively. }