Challenges and prospects of probing galaxy clustering with three-point statistics

In this work we explore three-point statistics applied to the large-scale structure in our Universe. Three-point statistics, such as the bispectrum, encode information not accessible via the standard analysis method—the power spectrum—and thus provide the potential for greatly improving current constraints on cosmological parameters. They also present us with additional challenges, and we focus on two of these arising from a measurement as well as modelling point of view. The first challenge we address is the covariance matrix of the bispectrum, as its precise estimate is required when performing likelihood analyses. Covariance matrices are usually estimated from a set of independent simulations, whose minimum number scales with the dimension of the covariance matrix. Because there are many more possibilities of finding triplets of galaxies than pairs, compared to the power spectrum this approach becomes rather prohibitive. With this motivation in mind, we explore a novel alternative to the bispectrum: the line correlation function (LCF). It specifically targets information in the phases of density modes that are invisible to the power spectrum, making it a potentially more efficient probe than the bispectrum, which measures a combination of amplitudes and phases. We derive the covariance properties and the impact of shot noise for the LCF and compare these theoretical predictions with measurements from N-body simulations. Based on a Fisher analysis we assess the LCF’s sensitivity on cosmological parameters, finding that it is particularly suited for constraining galaxy bias parameters and the amplitude of fluctuations. As a next step we contrast the Fisher information of the LCF with the full bispectrum and two other recently proposed alternatives. We show that the LCF is unlikely to achieve a lossless compression of the bispectrum information, whereas a modal decomposition of the bispectrumcan reduce the size of the covariancematrix by at least an order of magnitude. The second challenge we consider in this work concerns the relation between the dark matter field and luminous tracers, such as galaxies. Accurate knowledge of this galaxy bias relation is required in order to reliably interpret the data gathered by galaxy surveys. On the largest scales the dark matter and galaxy densities are linearly related, but a variety of additional terms need to be taken into account when studying clustering on smaller scales. These have been fully included in recent power spectrumanalyses, whereas the bispectrummodel relied on simple prescriptions that were likely extended beyond their realm of validity. In addition, treating power spectrumand bispectrum on different footings means that the two models become inconsistent on small scales. We introduce a new formalism that allows us to elegantly compute the lacking bispectrum contributions from galaxy bias, without running into the renormalization problem. Furthermore, we fit our new model to simulated data by implementing these contributions into a likelihood code. We show that they are crucial in order to obtain results consistent with those fromthe power spectrum, and that the bispectrum retains its capability of significantly reducing uncertainties in measured parameters when combined with the power spectrum

Towards optimal cosmological parameter recovery from compressed bispectrum statistics

Over the next decade, improvements in cosmological parameter constraints will be driven by surveys of large-scale structure in the Universe. The information they contain can be measured by suitably-chosen correlation functions, and the non-linearity of structure formation implies that significant information will be carried by the three-point function or higher correlators. Extracting this information is extremely challenging, requiring accurate modelling and significant computational resources to estimate the covariance matrix describing correlation between different Fourier configurations. We investigate whether it is possible to reduce this matrix without significant loss of information by using a proxy that aggregates the bispectrum over a subset of configurations. Specifically, we study constraints on ΛCDM parameters from a future galaxy survey combining the power spectrum with (a) the integrated bispectrum, (b) the line correlation function and (c) the modal decomposition of the bispectrum. We include a simple estimate for the degradation of the bispectrum with shot noise. Our results demonstrate that the modal bispectrum has comparable performance to the Fourier bispectrum, even using considerably fewer modes than Fourier configurations. The line correlation function has good performance, but is less effective. The integrated bispectrum is comparatively insensitive to the background cosmology. Addition of bispectrum data can improve constraints on bias parameters and σ8 by a factor between 3 and 5 compared to power spectrum measurements alone. For other parameters, improvements of up to ∼ 20% are possible. Finally, we use a range of theoretical models to explore the sophistication required to produce realistic predictions for each proxy

Testing one-loop galaxy bias: Cosmological constraints from the power spectrum

We investigate the impact of different assumptions in the modeling of one-loop galaxy bias on the recovery of cosmological parameters, as a follow-up of the analysis done in the first paper of the series at fixed cosmology. To carry out these tests we focus on the real-space galaxy-power spectrum from a set of three different synthetic galaxy samples whose clustering properties are meant to match the ones of the CMASS and LOWZ catalogs of BOSS and the SDSS Main Galaxy Sample. We investigate the relevance of allowing for either short range nonlocality or scale-dependent stochasticity by fitting the real-space galaxy autopower spectrum or the combination of galaxy-galaxy and galaxy-matter power spectrum. From a comparison among the goodness of fit (χ2), unbiasedness of cosmological parameters (FoB), and figure of merit (FoM) of the model, we find that a simple four-parameter model (linear, quadratic, cubic nonlocal bias, and constant shot noise) with fixed quadratic tidal bias provides a robust modeling choice for the autopower spectrum of the three galaxy samples, up to kmax ¼ 0.3h Mpc−1 and for an effective volume of 6h−3 Gpc3. Instead, a joint analysis of the two observables fails at larger scales, and a model extension with either higher derivatives or scale-dependent shot noise is necessary to reach a similar kmax, with the latter providing the most accurate and stable results. Throughout the majority of the paper, we fix the description of the nonlinear matter evolution using a hybrid perturbative-N-body approach, RESPRESSO, that was found in the first paper to be the closest performing to the measured matter spectrum. We also test the impact of different modeling assumptions based on perturbative approaches, such as galilean-invariant Renormalised Perturbation Theory (gRPT) and effective field theory (EFT). In all cases, we find the inclusion of scale-dependent shot noise to increase the range of validity of the model in terms of FoB and χ2. Interestingly, these model extensions with additional free parameters do not necessarily lead to an increase in the maximally achievable FoM for the cosmological parameters ðh; Ωch2; AsÞ, which are generally consistent with those of the simpler model at smaller kmax

COMET: Clustering Observables Modelled by Emulated perturbation Theory

In this paper we present COMET, a Gaussian process emulator of the galaxy power spectrum multipoles in redshift-space. The model predictions are based on one-loop perturbation theory and we consider two alternative descriptions of redshift-space distortions: one that performs a full expansion of the real- to redshift-space mapping, as in recent effective field theory models, and another that preserves the non-perturbative impact of small-scale velocities by means of an effective damping function. The outputs of COMET can be obtained at arbitrary redshifts (up to $z \sim 3$), for arbitrary fiducial background cosmologies, and for a large parameter space that covers the shape parameters $\omega_c$, $\omega_b$, and $n_s$, as well as the evolution parameters $h$, $A_s$, $\Omega_K$, $w_0$, and $w_a$. This flexibility does not impair COMET's accuracy, since we exploit an exact degeneracy between the evolution parameters that allows us to train the emulator on a significantly reduced parameter space. While the predictions are sped up by at least two orders of magnitude, validation tests reveal an accuracy of $0.1\,\%$ for the monopole and quadrupole ($0.3\,\%$ for the hexadecapole), or alternatively, better than $0.25\,\sigma$ for all three multipoles in comparison to statistical uncertainties expected for the Euclid survey with a tenfold increase in volume. We show that these differences translate into shifts in mean posterior values that are at most of the same size, meaning that COMET can be used with the same confidence as the exact underlying models. COMET is a publicly available Python package that also provides the tree-level bispectrum multipoles in redshift-space and Gaussian covariance matrices.Comment: 18 pages, 10 figures; for the COMET Python package, see https://gitlab.com/aegge/comet-em

Cosmology with phase statistics: parameter forecasts and detectability of BAO

We consider an alternative to conventional three-point statistics such as the bispectrum, which is purely based on the Fourier phases of the density field: the line correlation function. This statistic directly probes the non-linear clustering regime and contains information highly complementary to that contained in the power spectrum. In this work, we determine, for the first time, its potential to constrain cosmological parameters and detect baryon acoustic oscillations (hereafter BAOs). We show how to compute the line correlation function for a discrete sampled set of tracers that follow a local Lagrangian biasing scheme and demonstrate how it breaks the degeneracy between the amplitude of density fluctuations and the bias parameters of the model.We then derive analytic expressions for its covariance and show that it can be written as a sum of a Gaussian piece plus non-Gaussian corrections.We compare our predictions with a large ensemble of N-body simulations and confirm that BAOs do indeed modulate the signal of the line correlation function for scales 50–100 h−1Mpc and that the characteristic S-shape feature would be detectable in upcoming Stage IV surveys at the level of ∼4σ.We then focus on the cosmological information content and compute Fisher forecasts for an idealized Stage III galaxy redshift survey of volume V ∼ 10 h−3 Gpc3 and out to z = 1. We show that combining the line correlation function with the galaxy power spectrum and a Planck-like microwave background survey yields improvements up to a factor of 2 for parameters such as σ8, b1 and b2, compared with using only the two-point information alone

Beyond Λ\LambdaCDM constraints from the full shape clustering measurements from BOSS and eBOSS

We analyse the full shape of anisotropic clustering measurements from the extended Baryon Oscillation Spectroscopic survey (eBOSS) quasar sample together with the combined galaxy sample from the Baryon Oscillation Spectroscopic Survey (BOSS). We obtain constraints on the cosmological parameters independent of the Hubble parameter $h$ for the extensions of the $\Lambda$CDM models, focusing on cosmologies with free dark energy equation of state parameter $w$. We combine the clustering constraints with those from the latest CMB data from Planck to obtain joint constraints for these cosmologies for $w$ and the additional extension parameters - its time evolution $w_{\rm{a}}$, the physical curvature density $\omega_{K}$ and the neutrino mass sum $\sum m_{\nu}$. Our joint constraints are consistent with flat $\Lambda$CDM cosmological model within 68\% confidence limits. We demonstrate that the Planck data are able to place tight constraints on the clustering amplitude today, $\sigma_{12}$, in cosmologies with varying $w$ and present the first constraints for the clustering amplitude for such cosmologies, which is found to be slightly higher than the $\Lambda$CDM value. Additionally, we show that when we vary $w$ and allow for non-flat cosmologies and the physical curvature density is used, Planck prefers a curved universe at $4\sigma$ significance, which is $\sim2\sigma$ higher than when using the relative curvature density $\Omega_{\rm{K}}$. Finally, when $w$ is varied freely, clustering provides only a modest improvement (of 0.021 eV) on the upper limit of $\sum m_{\nu}$.Comment: 12 pages, 6 figures, submitted to MNRA

Inflation and Dark Energy from spectroscopy at z > 2

The expansion of the Universe is understood to have accelerated during two epochs: in its very first moments during a period of Inflation and much more recently, at z < 1, when Dark Energy is hypothesized to drive cosmic acceleration. The undiscovered mechanisms behind these two epochs represent some of the most important open problems in fundamental physics. The large cosmological volume at 2 < z < 5, together with the ability to efficiently target high-$z$ galaxies with known techniques, enables large gains in the study of Inflation and Dark Energy. A future spectroscopic survey can test the Gaussianity of the initial conditions up to a factor of ~50 better than our current bounds, crossing the crucial theoretical threshold of $\sigma(f_{NL}^{\rm local})$ of order unity that separates single field and multi-field models. Simultaneously, it can measure the fraction of Dark Energy at the percent level up to $z = 5$, thus serving as an unprecedented test of the standard model and opening up a tremendous discovery space