Primordial non-Gaussianity Parameter Research Articles

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

ABSTRACT We use angular clustering of luminous red galaxies from the Dark Energy Spectroscopic Instrument (DESI) imaging surveys to constrain the local primordial non-Gaussianity parameter fNL. Our sample comprises over 12 million targets, covering 14 000 deg2 of the sky, with redshifts in the range 0.2 < z < 1.35. We identify Galactic extinction, survey depth, and astronomical seeing as the primary sources of systematic error, and employ linear regression and artificial neural networks to alleviate non-cosmological excess clustering on large scales. Our methods are tested against simulations with and without fNL and systematics, showing superior performance of the neural network treatment. The neural network with a set of nine imaging property maps passes our systematic null test criteria, and is chosen as the fiducial treatment. Assuming the universality relation, we find $f_{\rm NL} = 34^{+24(+50)}_{-44(-73)}$ at 68 per cent (95 per cent) confidence. We apply a series of robustness tests (e.g. cuts on imaging, declination, or scales used) that show consistency in the obtained constraints. We study how the regression method biases the measured angular power spectrum and degrades the fNL constraining power. The use of the nine maps more than doubles the uncertainty compared to using only the three primary maps in the regression. Our results thus motivate the development of more efficient methods that avoid overcorrection, protect large-scale clustering information, and preserve constraining power. Additionally, our results encourage further studies of fNL with DESI spectroscopic samples, where the inclusion of 3D clustering modes should help separate imaging systematics and lessen the degradation in the fNL uncertainty.

Constraining primordial non-Gaussianity using neural networks

ABSTRACT We present a novel approach to estimate the value of primordial non-Gaussianity (fNL) parameter directly from the cosmic microwave background (CMB) maps using a convolutional neural network (CNN). While traditional methods rely on complex statistical techniques, this study proposes a simpler approach that employs a neural network to estimate fNL. The neural network model is trained on simulated CMB maps with known fNL in range of [−50, 50], and its performance is evaluated using various metrics. The results indicate that the proposed approach can accurately estimate fNL values from CMB maps with a significant reduction in complexity compared to traditional methods. With 500 validation data, the $f^{\rm output}_{\rm NL}$ against $f^{\rm input}_{\rm NL}$ graph can be fitted as y = ax + b, where $a=0.980^{+0.098}_{-0.102}$ and $b=0.277^{+0.098}_{-0.101}$, indicating the unbiasedness of the primordial non-Gaussianity estimation. The results suggest that the CNN technique can be widely applied to other cosmological parameter estimation directly from CMB images.

Constraining primordial non-Gaussianity from DESI quasar targets and Planck CMB lensing

We detect the cross-correlation between 2.7 million DESI quasar targets across 14,700 deg2 (180 quasars deg-2) and Planck 2018 CMB lensing at ∼30σ. We use the cross-correlation on very large scales to constrain local primordial non-Gaussianity via the scale dependence of quasar bias. The DESI quasar targets lie at an effective redshift of 1.51 and are separated into four imaging regions of varying depth and image quality. We select quasar targets from Legacy Survey DR9 imaging, apply additional flux and photometric redshift cuts to improve the purity and reduce the fraction of unclassified redshifts, and use early DESI spectroscopy of 194,000 quasar targets to determine their redshift distribution and stellar contamination fraction (2.6%). Due to significant excess large-scale power in the quasar autocorrelation, we apply weights to mitigate contamination from imaging systematics such as depth, extinction, and stellar density. We use realistic contaminated mocks to determine the greatest number of systematic modes that we can fit, before we are biased by overfitting and spuriously remove real power. We find that linear regression with one to seven imaging templates removed per region accurately recovers the input cross-power, f NL and linear bias. As in previous analyses, our f NL constraint depends on the linear primordial non-Gaussianity bias parameter, bϕ = 2(b - p)δc assuming universality of the halo mass function. We measure f NL = -26+45 -40 with p = 1.6 (f NL = -18+29 -27 with p = 1.0), and find that this result is robust under several systematics tests. Future spectroscopic quasar cross-correlations with Planck lensing can tighten the f NL constraints by a factor of 2 if they can remove the excess power on large scales in the quasar auto power spectrum.

Quijote-PNG: The Information Content of the Halo Mass Function

We study signatures of primordial non-Gaussianity (PNG) in the redshift-space halo field on nonlinear scales using a combination of three summary statistics, namely, the halo mass function (HMF), power spectrum, and bispectrum. The choice of adding the HMF to our previous joint analysis of the power spectrum and bispectrum is driven by a preliminary field-level analysis, in which we train graph neural networks on halo catalogs to infer the PNG f NL parameter. The covariance matrix and the responses of our summaries to changes in model parameters are extracted from a suite of halo catalogs constructed from the Quijote-png N-body simulations. We consider the three main types of PNG: local, equilateral, and orthogonal. Adding the HMF to our previous joint analysis of the power spectrum and bispectrum produces two main effects. First, it reduces the equilateral f NL predicted errors by roughly a factor of 2 while also producing notable, although smaller, improvements for orthogonal PNG. Second, it helps break the degeneracy between the local PNG amplitude, , and assembly bias, b ϕ , without relying on any external prior assumption. Our final forecasts for the PNG parameters are , , , on a cubic volume of , with a halo number density of , at z = 1, and considering scales up to .

Towards optimal and robust f_nl constraints with multi-tracer analyses

We discuss the potential of the multi-tracer technique to improve observational constraints of the local primordial non-Gaussianity (PNG) parameter f nl from the galaxy power spectrum. For two galaxy samples A and B, the constraining power is ∝ |bB 1 bA ϕ - bA 1 bB ϕ |, where b 1 and bϕ are the linear and PNG galaxy bias parameters. We show this allows for significantly improved constraints compared to the traditional expectation ∝ |bA - bB | based on naive universality-like relations where bϕ ∝ b 1. Using IllustrisTNG galaxy simulation data, we find that different equal galaxy number splits of the full sample lead to different |bB 1 bA ϕ - bA 1 bB ϕ |, and thus have different constraining power. Of all of the strategies explored, splitting by g-r color is the most promising, more than doubling the significance of detecting f nl bϕ ≠ 0. Importantly, since these are constraints on f nl bϕ and not f nl , they do not require priors on the bϕ (b 1) relation. For direct constraints on f nl , we show that multi-tracer constraints can be significantly more robust than single-tracer to bϕ misspecifications and uncertainties; this relaxes the precision and accuracy requirements for bϕ priors. Our results present new opportunities to improve our chances to detect and robustly constrain f nl , and strongly motivate galaxy formation simulation campaigns to calibrate the bϕ (b 1) relation.

Constraints on compensated isocurvature perturbations from BOSS DR12 galaxy data

We use the BOSS DR12 galaxy power spectrum to constrain compensated isocurvature perturbations (CIP), which are opposite-sign primordial baryon and dark matter perturbations that leave the total matter density unchanged. Long-wavelength CIP σ(x) enter the galaxy density contrast as δg (x) ⊃ bσσ(x), with bσ the linear CIP galaxy bias parameter. We parameterize the CIP spectra as Pσσ = A 2 Pℛℛ and Pσℛ = ξ√PσσPℛℛ , where A is the CIP amplitude and ξ is the correlation with the curvature perturbations ℛ. We find a significance of detection of Ab σ ≠ 0 of 1.8σ for correlated CIP (ξ = 1), consistent with no detection. For uncorrelated CIP (ξ = 0), the constraints are instead more significantly shifted away from zero, although this may be due to large-scale data systematics which have a bigger impact on these type of CIP. The constraints on A depend on the assumed priors for the bσ parameter, which we estimate using separate universe simulations. Assuming bσ values representative of all halos we find σA = 145 for correlated CIP and σ |A| = 475 for uncorrelated CIP. Our strongest uncorrelated CIP constraint is for bσ representative of the 33% most concentrated halos, σ |A| = 197, which is better than the current CMB bounds |A| ≲ 360. We also discuss the impact of the local primordial non-Gaussianity parameter f NL in CIP constraints. Our results demonstrate the power of galaxy data to place tight constraints on CIP, and motivate works to understand better the impact of data systematics, as well as to determine theory priors for bσ .

Stellar-reddening-based Extinction Maps for Cosmological Applications

Cosmological surveys must correct their observations for the reddening of extragalactic objects by Galactic dust. Existing dust maps, however, have been found to have spatial correlations with the large-scale structure of the Universe. Errors in extinction maps can propagate systematic biases into samples of dereddened extragalactic objects and into cosmological measurements such as correlation functions between foreground lenses and background objects and the primordial non-Gaussianity parameter f NL. Emission-based maps are contaminated by the cosmic infrared background, while maps inferred from stellar reddenings suffer from imperfect removal of quasars and galaxies from stellar catalogs. Thus, stellar-reddening-based maps using catalogs without extragalactic objects offer a promising path to making dust maps with minimal correlations with large-scale structure. We present two high-latitude integrated extinction maps based on stellar reddenings, with a point-spread functions of FWHMs 6.′1 and 15′. We employ a strict selection of catalog objects to filter out galaxies and quasars and measure the spatial correlation of our extinction maps with extragalactic structure. Our galactic extinction maps have reduced spatial correlation with large-scale structure relative to most existing stellar-reddening-based and emission-based extinction maps.

Quijote-PNG: Quasi-maximum Likelihood Estimation of Primordial Non-Gaussianity in the Nonlinear Halo Density Field

We study primordial non-Gaussian signatures in the redshift-space halo field on nonlinear scales, using a quasi-maximum likelihood estimator based on optimally compressed power spectrum and modal bispectrum statistics. We train and validate the estimator on a suite of halo catalogs constructed from the Quijote-png N-body simulations, which we release to accompany this paper. We verify its unbiasedness and near-optimality for the three main types of primordial non-Gaussianity (PNG): local, equilateral, and orthogonal. We compare the modal bispectrum expansion with a k-binning approach, showing that the former allows for faster convergence of numerical derivatives in the computation of the score function, thus leading to better final constraints. We find, in agreement with previous studies, that the local PNG signal in the halo field is dominated by the scale-dependent bias signature on large scales and saturates at k ∼ 0.2 h Mpc−1, whereas the small-scale bispectrum is the main source of information for equilateral and orthogonal PNG. Combining the power spectrum and bispectrum on nonlinear scales plays an important role in breaking degeneracies between cosmological and PNG parameters; such degeneracies, however, remain strong for equilateral PNG. We forecast that PNG parameters can be constrained with , , and on a cubic volume of at z = 1, considering scales up to .

Constraining primordial non-Gaussianity by combining next-generation galaxy and 21 cm intensity mapping surveys

Surveys of the matter distribution contain ‘fossil’ information on possible non-Gaussianity that is generated in the primordial Universe. This primordial signal survives only on the largest scales where cosmic variance is strongest. By combining different surveys in a multi-tracer approach, we can suppress the cosmic variance and significantly improve the precision on the level of primordial non-Gaussianity. We consider a combination of an optical galaxy survey, like the recently initiated DESI survey, together with a new and very different type of survey, a 21 cm intensity mapping survey, like the upcoming SKAO survey. A Fisher forecast of the precision on the local primordial non-Gaussianity parameter f_{textrm{NL}}, shows that this multi-tracer combination, together with non-overlap single-tracer information, can deliver precision comparable to that from the CMB. Taking account of the largest systematic, i.e. foreground contamination in intensity mapping, we find that sigma (f_{textrm{NL}}) sim 4.

Assembly bias in the local PNG halo bias and its implication for f NL constraints

We use N-body simulations to study halo assembly bias (i.e., the dependence of halo clustering on properties beyond total mass) in the density and primordial non-Gaussianity (PNG) linear bias parameters b 1 and b ϕ, respectively. We consider concentration, spin and sphericity as secondary halo properties, for which we find a clear detection of assembly bias for b 1 and b ϕ. At fixed total mass, halo spin and sphericity impact b 1 and b ϕ in a similar manner, roughly preserving the shape of the linear b ϕ(b 1) relation satisfied by the global halo population. Halo concentration, however, drives b 1 and b ϕ in opposite directions. This induces significant changes to the b ϕ(b 1) relation, with higher concentration halos having higher amplitude of b ϕ(b 1). For z = 0.5 and b 1 ≈ 2 in particular, the population comprising either all halos, those with the 33% lowest or those with the 33% highest concentrations have a PNG bias of b ϕ ≈ 3, b ϕ ≈ -1 and b ϕ ≈ 9, respectively. Varying the halo concentration can make b ϕ very small and even change its sign. These results have important ramifications for galaxy clustering constraints of the local PNG parameter fNL that assume fixed forms for the b ϕ(b 1) relation. We illustrate the significant impact of halo assembly bias in actual data using the BOSS DR12 galaxy power spectrum: assuming that BOSS galaxies are representative of all halos, the 33% lowest or the 33% highest concentration halos yields σ f NL = 44, 165, 19, respectively. Our results suggest taking host halo concentration into account in galaxy selection strategies to maximize the signal-to-noise on f NL. They also motivate more simulation-based efforts to study the b ϕ(b 1) relation of halos and galaxies.

Can we actually constrain fNL using the scale-dependent bias effect? An illustration of the impact of galaxy bias uncertainties using the BOSS DR12 galaxy power spectrum

The scale-dependent bias effect on the galaxy power spectrum is a very promising probe of the local primordial non-Gaussianity (PNG) parameter f NL, but the amplitude of the effect is proportional to f NL bϕ , where bϕ is the linear PNG galaxy bias parameter. Our knowledge of bϕ is currently very limited, yet nearly all existing f NL constraints and forecasts assume precise knowledge for it. Here, we use the BOSS DR12 galaxy power spectrum to illustrate how our uncertain knowledge of bϕ currently prevents us from constraining f NL with a given statistical precision σ fNL. Assuming different fixed choices for the relation between bϕ and the linear density bias b 1, we find that σ fNL can vary by as much as an order of magnitude. Our strongest bound is f NL = 16 ± 16 (1σ), while the loosest is f NL = 230 ± 226 (1σ) for the same BOSS data. The impact of bϕ can be especially pronounced because it can be close to zero. We also show how marginalizing over bϕ with wide priors is not conservative, and leads in fact to biased constraints through parameter space projection effects. Independently of galaxy bias assumptions, the scale-dependent bias effect can only be used to detect f NL ≠ 0 by constraining the product f NL bϕ , but the error bar σ fNL remains undetermined and the results cannot be compared with the CMB; we find f NL bϕ ≠ 0 with 1.6σ significance. We also comment on why these issues are important for analyses with the galaxy bispectrum. Our results strongly motivate simulation-based research programs aimed at robust theoretical priors for the bϕ parameter, without which we may never be able to competitively constrain f NL using galaxy data.

Primordial non-Gaussianity from the completed SDSS-IV extended Baryon Oscillation Spectroscopic Survey II: measurements in Fourier space with optimal weights

ABSTRACTWe present measurements of the local primordial non-Gaussianity parameter $f_{\mathrm{NL}}^\mathrm{local} $from the clustering of 343 708 quasars with redshifts 0.8 < z < 2.2 distributed over 4808 deg2 from the final data release (DR16) of the extended Baryon Acoustic Oscillation Spectroscopic Survey (eBOSS), the largest volume spectroscopic survey up to date. Our analysis is performed in Fourier space, using the power spectrum monopole at very large scales to constrain the scale-dependent halo bias. We demonstrate the robustness of our analysis pipeline with EZ-mock catalogues that simulate the eBOSS DR16 target selection. We carefully assess the impact of systematics on our measurement, exploiting a novel neural network scheme for cleaning the DR16 sample as well as test multiple contamination removal methods. We estimate the bias due to the overcorrection of the systematic removal to be sub-dominant compared to the statistical uncertainty. We find fNL = −12 ± 21 (68 per cent confidence) for the main clustering sample including quasars with redshifts between 0.8 and 2.2, after applying redshift weighting techniques, designed for non-Gaussianity measurement from large scales structure, to optimize our analysis, which improve our results by 37 per cent.

Predictions for local PNG bias in the galaxy power spectrum and bispectrum and the consequences for f NL constraints

We use hydrodynamical separate universe simulations with the IllustrisTNG model to predict the local primordial non-Gaussianity (PNG) bias parameters b ϕ and b ϕδ, which enter at leading order in the galaxy power spectrum and bispectrum. This is the first time that b ϕδ is measured from either gravity-only or galaxy formation simulations. For dark matter halos, the popular assumption of universality overpredicts the b ϕδ(b 1) relation in the range 1 ≲ b 1 ≲ 3 by up to Δ b ϕδ ∼ 3 (b 1 is the linear density bias). The adequacy of the universality relation is worse for the simulated galaxies, with the relations b ϕ(b 1) and b ϕδ(b 1) being generically redshift-dependent and very sensitive to how galaxies are selected (we test total, stellar and black hole mass, black hole mass accretion rate and color). The uncertainties on b ϕ and b ϕδ have a direct, often overlooked impact on the constraints of the local PNG parameter f NL, which we study and discuss. For a survey with V = 100 Gpc3/h3 at z=1, uncertainties Δ b ϕ ≲ 1 and Δ b ϕδ ≲ 5 around values close to the fiducial can yield relatively unbiased constraints on f NL using power spectrum and bispectrum data. We also show why priors on galaxy bias are useful even in analyses that fit for products f NL b ϕ and f NL b ϕδ. The strategies we discuss to deal with galaxy bias uncertainties can be straightforwardly implemented in existing f NL constraint analyses (we provide fits for some of the bias relations). Our results motivate more works with galaxy formation simulations to refine our understanding of b ϕ and b ϕδ towards improved constraints on f NL.

Joint analyses of 2D CMB lensing and 3D galaxy clustering in the spherical Fourier-Bessel basis

Cross-correlating cosmic microwave background (CMB) lensing and galaxy clustering has been shown to greatly improve the constraints on the local primordial non-Gaussianity (PNG) parameter $f_{\rm NL}$ by reducing sample variance and also parameter degeneracies. To model the full use of the 3D information of galaxy clustering, we forecast $f_{\rm NL}$ measurements using the decomposition in the spherical Fourier-Bessel (SFB) basis, which can be naturally cross-correlated with 2D CMB lensing in spherical harmonics. In the meantime, such a decomposition would also enable us to constrain the growth rate of structure, a probe of gravity, through the redshift-space distortion (RSD). As a comparison, we also consider the tomographic spherical harmonic (TSH) analysis of galaxy samples with different bin sizes. Assuming galaxy samples that mimic a few future surveys, we perform Fisher forecasts using linear modes for $f_{\rm NL}$ and the growth rate exponent $\gamma$, marginalized over standard $\Lambda$ cold dark matter ($\Lambda$CDM) cosmological parameters and two nuisance parameters that account for clustering bias and magnification bias. Compared to TSH analysis using only one bin, SFB analysis could improve $\sigma(f_{\rm NL})$ by factors 3 to 12 thanks to large radial modes. With future wide-field and high-redshift photometric surveys like the LSST, the constraint $\sigma(f_{\rm NL}) < 1$ could be achieved using linear angular multipoles up to $\ell_{\rm min}\simeq 20$. Compared to using galaxy auto-power spectra only, joint analyses with CMB lensing could improve $\sigma(\gamma)$ by factors 2 to 5 by reducing degeneracies with other parameters, especially the clustering bias. For future spectroscopic surveys like the DESI or $\textit{Euclid}$, using linear scales, $\gamma$ could be constrained to $3\,\%$ precision assuming the GR fiducial value.

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.

Non-Gaussianity constraints using future radio continuum surveys and the multitracer technique

ABSTRACT Tighter constraints on measurements of primordial non-Gaussianity (PNG) will allow the differentiation of inflationary scenarios. The cosmic microwave background bispectrum – the standard method of measuring the local non-Gaussianity – is limited by cosmic variance. Therefore, it is sensible to investigate measurements of non-Gaussianity using the large-scale structure. This can be done by investigating the effects of non-Gaussianity on the power spectrum on large scales. In this study, we forecast the constraints on the local PNG parameter fNL that can be obtained with future radio surveys. We utilize the multitracer method that reduces the effect of cosmic variance and takes advantage of the multiple radio galaxy populations that are differently biased tracers of the same underlying dark matter distribution. Improvements on previous work include the use of observational bias and halo mass estimates, updated simulations, and realistic photometric redshift expectations, thus producing more realistic forecasts. Combinations of Square Kilometre Array simulations and radio observations were used as well as different redshift ranges and redshift bin sizes. It was found that in the most realistic case the 1σ error on fNL falls within the range 4.07–6.58, rivalling the tightest constraints currently available.

CMB-S4 forecast on the primordial non-Gaussianity parameter of feature models

We present forecasts on the primordial non-Gaussianity parameter $f_\text{NL}$ of feature models for the future Cosmic Microwave Background Stage-4 (CMB-S4) experiments. The Fisher matrix of the bispectrum estimator was computed using noise covariances expected for preliminary CMB-S4 specifications including ones for the Simons Observatory. We introduce a novel method that improves the computation by orthonormalising the covariance matrix. The most sensitive CMB-S4 experiment with 1' beam and 1$\mu K$-arcmin noise would yield a factor of 1.7-2.2 times more stringent constraints compared to Planck. Under the Simons Observatory baseline conditions the improvement would be about 1.3-1.6 times to Planck. We also thoroughly studied the effects of various model and experimental parameters on the forecast. Detailed analysis on the constraints coming from temperature and E-mode polarisation, in particular, provided some insight into detecting oscillatory features in the CMB bispectrum.

Galaxy bispectrum from massive spinning particles

Massive spinning particles, if present during inflation, lead to a distinctive bispectrum of primordial perturbations, the shape and amplitude of which depend on the masses and spins of the extra particles. This signal, in turn, leaves an imprint in the statistical distribution of galaxies; in particular, as a non-vanishing galaxy bispectrum, which can be used to probe the masses and spins of these particles. In this paper, we present for the first time a new theoretical template for the bispectrum generated by massive spinning particles, valid for a general triangle configuration. We then proceed to perform a Fisher-matrix forecast to assess the potential of two next-generation spectroscopic galaxy surveys, EUCLID and DESI, to constrain the primordial non-Gaussianity sourced by these extra particles. We model the galaxy bispectrum using tree-level perturbation theory, accounting for redshift-space distortions and the Alcock-Paczynski effect, and forecast constraints on the primordial non-Gaussianity parameters marginalizing over all relevant biases and cosmological parameters. Our results suggest that these surveys would potentially be sensitive to any primordial non-Gaussianity with an amplitude larger than fNL≈ 1, for massive particles with spins 2, 3, and 4. Interestingly, if non-Gaussianities are present at that level, these surveys will be able to infer the masses of these spinning particles to within tens of percent. If detected, this would provide a very clear window into the particle content of our Universe during inflation.

Extracting foreground-obscured μ-distortion anisotropies to constrain primordial non-Gaussianity

Correlations between cosmic microwave background (CMB) temperature, polarization and spectral distortion anisotropies can be used as a probe of primordial non-Gaussianity. Here, we perform a reconstruction of $\mu$-distortion anisotropies in the presence of Galactic and extragalactic foregrounds, applying the so-called Constrained ILC component separation method to simulations of proposed CMB space missions (PIXIE, LiteBIRD, CORE, PICO). Our sky simulations include Galactic dust, Galactic synchrotron, Galactic free-free, thermal Sunyaev-Zeldovich effect, as well as primary CMB temperature and $\mu$-distortion anisotropies, the latter being added as correlated field. The Constrained ILC method allows us to null the CMB temperature anisotropies in the reconstructed $\mu$-map (and vice versa), in addition to mitigating the contaminations from astrophysical foregrounds and instrumental noise. We compute the cross-power spectrum between the reconstructed (CMB-free) $\mu$-distortion map and the ($\mu$-free) CMB temperature map, after foreground removal and component separation. Since the cross-power spectrum is proportional to the primordial non-Gaussianity parameter, $f_{\rm NL}$, on scales $k\simeq 740$ Mpc$^{-1}$, this allows us to derive $f_{\rm NL}$-detection limits for the aforementioned future CMB experiments. Our analysis shows that foregrounds degrade the theoretical detection limits (based mostly on instrumental noise) by more than one order of magnitude, with PICO standing the best chance at placing upper limits on scale-dependent non-Gaussianity. We also discuss the dependence of the constraints on the channel sensitivities and chosen bands. Like for $B$-mode polarization measurements, extended coverage at frequencies $\nu\lesssim 40\,{\rm GHz}$ and $\nu\gtrsim 400\,{\rm GHz}$ provides more leverage than increased channel sensitivity.

Constraining primordial non-Gaussianity with bispectrum and power spectrum from upcoming optical and radio surveys

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 contributions. All effects have an impact on final predicted bounds, which varies with the type of survey. We find that the bispectrum can lead to improvements up to a factor $\sim 5$ over bounds based on the power spectrum alone, leading to significantly better constraints for local-type PNG, with respect to current limits from \textit{Planck}. Future radio and photometric surveys could obtain a measurement error of $\sigma(f_{\mathrm{NL}}^{\mathrm{loc}}) \approx 0.2$. In the case of equilateral PNG, galaxy bispectrum can improve upon present bounds only if significant improvements in the redshift determinations of future, large volume, photometric or radio surveys could be achieved. For orthogonal non-Gaussianity, expected constraints are generally comparable to current ones.