Dark matter and halo bispectrum in redshift space: theory and applications

We present a phenomenological modification of the standard perturbation theory prediction for the bispectrum in redshift space that allows us to extend the model to mildly non-linear scales over a wide range of redshifts, $z\leq1.5$. We find that we can describe the bispectrum of dark matter particles with $\sim5$ accuracy for $k_i\lesssim0.10\,h/{\rm Mpc}$ at $z=0$, for $k_i\lesssim0.15\,h/{\rm Mpc}$ at $z=0.5$, for $k_i\lesssim0.17\,h/{\rm Mpc}$ at $z=1.0$ and for $k_i\lesssim0.20\,h/{\rm Mpc}$ at $z=1.5$. We also test that the fitting formula is able to describe with similar accuracy the bispectrum of cosmologies with different $\Omega_m$, in the range $0.2\lesssim \Omega_m \lesssim 0.4$, and consequently with different values of the logarithmic grow rate $f$ at $z=0$, $0.4\lesssim f(z=0) \lesssim 0.6$. We apply this new formula to recover the bias parameters, $f$ and $\sigma_8$, by combining the redshift space power spectrum monopole and quadrupole with the bispectrum monopole for both dark matter particles and haloes. We find that the combination of these three statistics can break the degeneracy between $b_1$, $f$ and $\sigma_8$. For dark matter particles the new model can be used to recover $f$ and $\sigma_8$ with $\sim1$ accuracy. For dark matter haloes we find that $f$ and $\sigma_8$ present larger systematic shifts, $\sim10$. The systematic offsets arise because of limitations in the modelling of the interplay between bias and redshift space distortions, and represent a limitation as the statistical errors of forthcoming surveys reach this level. Conveniently, we find that these residual systematics are mitigated for combinations of parameters. The improvement on the modelling of the bispectrum presented in this paper will be useful for extracting information from current and future galaxy surveys. [abridged]Comment: 37 pages, 17 figures, 8 tables. Published in JCA

A tale of many H0H_0

The Hubble parameter $H_0$, is not a univocally-defined quantity: it relates redshifts to distances in the near Universe, but is also a key parameter of the $\Lambda$CDM standard cosmological model. As such, $H_0$ affects several physical processes at different cosmic epochs, and multiple observables. We have counted more than a dozen $H_0$'s which are expected to agree if a) there are no significant systematics in the data and their interpretation and b) the adopted cosmological model is correct. With few exceptions (proverbially confirming the rule) these determinations do not agree at high statistical significance; their values cluster around two camps: the low (68 km/s/Mpc) and high (73 km/s/Mpc) camp. It appears to be a matter of anchors: the shape of the Universe expansion history agrees with the model, it is the normalizations that disagree. Beyond systematics in the data/analysis, if the model is incorrect there are only two viable ways to "fix" it: by changing the early time ($z\gtrsim 1100$) physics and thus the early time normalization, or by a global modification, possibly touching the model's fundamental assumptions (e.g., homogeneity, isotropy, gravity). None of these three options has the consensus of the community. The research community has been actively looking for deviations from $\Lambda$CDM for two decades; the one we might have found makes us wish we could put the genie back in the bottle.Comment: To appear in Annual Reviews of Astronomy and Astrophysic

A tale of two (or more) hh's

We use the large-scale structure galaxy data (LSS) from the BOSS and eBOSS surveys, in combination with abundances information from Big Bang Nucleosynthesis (BBN) to measure two values of the Hubble expansion rate, $H_0=100h\,[{\rm km}\, {\rm s}^{-1}\,{\rm Mpc}^{-1}]$, each of them based on very different physical processes. One is a (traditional) late-time-background measurement based on determining the BAO scale and using BBN abundances on baryons for calibrating its absolute size (BAO+BBN). This method anchors $H_0$ to the (standard) physics of the sound horizon scale at pre-recombination times. The other is a newer early-time based measurement associated with the broadband shape of the power spectrum. This second method anchors $H_0$ to the physics of the matter-radiation equality scale, which also needs BBN information for determining the suppression of baryons in the power spectrum shape (shape+BBN). Within the $\Lambda$CDM model, we find very good consistency among these two $H_0$'s: BAO+BBN (+growth) delivers $H_0=67.42_{-0.94}^{+0.88}$ $(67.37_{-0.95}^{+0.86})$ km s$^{-1}$Mpc$^{-1}$ , whereas the shape+BBN (+growth) delivers $H_0 = 70.1_{-2.1}^{+2.1}$ $(70.1_{-2.1}^{+1.9})$ km s$^{-1}$ Mpc$^{-1}$, where "growth" stands for information from the late-time-perturbations captured by the growth of structure parameter. These are the tightest sound-horizon free $H_0$ constraints from LSS data to date. As a consequence to be viable, any $\Lambda$CDM extension proposed to address the so-called "Hubble tension" needs to modify consistently not only the sound horizon scale physics, but also the matter-radiation equality scale, in such a way that both late- and early-based $H_0$'s return results mutually consistent and consistent with the high $H_0$ value recovered by the standard cosmic distance ladder (distance-redshift relation) determinations.Comment: 42 pages, 12 figures, 3 tables, to be submitted to JCAP. Comments welcom

Optimal Redshift Weighting For Redshift Space Distortions

The low statistical errors on cosmological parameters promised by future galaxy surveys will only be realised with the development of new, fast, analysis methods that reduce potential systematic problems to low levels. We present an efficient method for measuring the evolution of the growth of structure using Redshift Space Distortions (RSD), that removes the need to make measurements in redshift shells. We provide sets of galaxy-weights that cover a wide range in redshift, but are optimised to provide differential information about cosmological evolution. These are derived to optimally measure the coefficients of a parameterisation of the redshift-dependent matter density, which provides a framework to measure deviations from the concordance $\Lambda$CDM cosmology, allowing for deviations in both geometric and/or growth. We test the robustness of the weights by comparing with alternative schemes and investigate the impact of galaxy bias. We extend the results to measure the combined anisotropic Baryon Acoustic Oscillation (BAO) and RSD signals.Comment: 10 pages, 5 figures, submitted to MNRA

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 introducing 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 \textsc{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 $f_\mathrm{nl}$ and $g_\mathrm{nl}$. For example, using the full joint data-vector, we forecast $f_\mathrm{nl}$ constraints up to two times ($\sim32\%$) smaller in real (redshift) space than those obtained without i-trispectrum.Comment: accepted: 6th of November 2020, published: 11th of January 2021 , 64 pages (35 pages for the main text), 15 figure

Blind Observers of the Sky

The concept of blind analysis, a key procedure to remove the human-based systematic error called confirmation bias, has long been an integral part of data analysis in many research areas. In cosmology, blind analysis is recently making its entrance, as the field progresses into a fully fledged high-precision science. The credibility, reliability and robustness of results from future sky-surveys will dramatically increase if the effect of confirmation bias is kept under control by using an appropriate blinding procedure. Here, we present a catalog-level blinding scheme for galaxy clustering data apt to be used in future spectroscopic galaxy surveys. We shift the individual galaxy positions along the line of sight based on 1) a geometric shift mimicking the Alcock-Paczynski effect and 2) a perturbative shift akin to redshift-space distortions. This procedure has several advantages. After combining the two steps above, it is almost impossible to accidentally unblind. The procedure induces a shift in cosmological parameters without changing the galaxies' angular positions, hence without interfering with the effects of angular systematics. Since the method is applied at catalog level, there is no need to adopt several blinding schemes tuned to different summary statistics, likelihood choices or types of analyses. By testing the method on mock catalogs and the BOSS DR12 catalog we demonstrate its performance in blinding galaxy clustering data for relevant cosmological parameters sensitive to the background expansion rate and the growth rate of structures.Comment: 45 pages, 18 figures, 6 table

GEO-FPT: a model of the galaxy bispectrum at mildly non-linear scales

We present GEO-FPT (Geometric Fitted Perturbation Theory), a new model for the galaxy bispectrum anisotropic signal in redshift space, with functional form rooted in perturbation theory. It also models the dependence of the bispectrum with the geometric properties of the triangles in Fourier space, and has a broader regime of validity than state-of-the-art theoretical models based on perturbation theory. We calibrate the free parameters of this model using high-resolution dark matter simulations and perform stringent tests to show that GEO-FPT describes the galaxy bispectrum accurately up to scales of $k\simeq0.12 h{\rm Mpc}^{-1}$ for different cosmological models, as well as for biased tracers of the dark matter field, considering a survey volume of $100$ (Gpc $h^{-1})^3$. In particular, a joint analysis of the power spectrum and bispectrum anisotropic signals, taking into account their full covariance matrix, reveals that the relevant physical quantities -- the BAO peak position (along and across the line-of-sight), and the growth of structure parameters times the amplitude of dark matter fluctuations, $f\sigma_8$-- are recovered in an unbiased way, with an accuracy better than $0.4\%$ and $2\%$ respectively (which is our $2\sigma$ statistical limit of the systematic error estimate). In addition, the bispectrum signal breaks the $f\sigma_8$ degeneracy without detectable bias: $f$ and $\sigma_8$ are recovered with better than $2.7\%$ and $3.8\%$ accuracy respectively (which is our $2\sigma$ statistical limit of the systematic error estimate). GEO-FPT boosts the applicability of the bispectrum signal of galaxy surveys beyond the current limitation of $k\lesssim 0.08\,h$ Mpc$^{-1}$ % and makes the bispectrum a key statistic to unlock the information content from the mildly non-linear regime in the on-going and forthcoming galaxy redshift surveys.Comment: 37 pages, 14 figures. To be submitted to JCAP, comments welcom