arXiv subjects

Roman Scoccimarro

Publications and source records attributed to Roman Scoccimarro.

At least 19 recordsLinked to original sources

arXiv2025

Vlasov Perturbation Theory applied to $\Lambda$CDM

We apply the framework of Vlasov Perturbation Theory (VPT) to the two-loop matter power spectrum within $\Lambda$CDM cosmologies. The main difference to Standard Perturbation Theory (SPT) arises from taking the velocity dispersion tensor into account, and the resulting screening of the backreaction of UV modes renders loop integrals cutoff-independent. VPT is informed about non-perturbative small scale dynamics via the average value of the dispersion generated by shell-crossing, which impacts the evolution of perturbations on weakly non-linear scales. When using an average dispersion from halo models, the VPT power spectrum agrees with the one from the simulation, up to differences from missing three-loop contributions. Alternatively, treating the average dispersion as free parameter we find a remarkably stable prediction of the matter power spectrum from collisionless dynamics at percent level for a wide range of the dispersion scale. We quantify the impact of truncating the Vlasov hierarchy for the cumulants of the phase-space distribution function, finding that the two-loop matter power spectrum is robust to neglecting third and higher cumulants. Finally, we introduce and validate a simplified fast scheme fVPT that can be easily incorporated into existing codes and is as numerically efficient as SPT.

astro-ph.CO↗

arXiv2025

Vlasov Perturbation Theory and the role of higher cumulants

We develop a new approach to Vlasov Perturbation Theory (VPT) that solves for the hierarchy of cumulants of the phase-space distribution function to arbitrarily high truncation order in the context of cosmological structure formation driven by collisionless dark matter. We investigate the impact of higher cumulants on density and velocity power spectra as well as the bispectrum, and compare to scale-free $N$-body simulations. While there is a strong difference between truncation at the first cumulant, i.e. standard perturbation theory (SPT), and truncation at the second (i.e. including the velocity dispersion tensor), the third cumulant has a small quantitative impact and fourth and higher cumulants only have a minor effect on these summary statistics at weakly non-linear scales. We show that spurious exponential growth is absent in vector and tensor modes if scalar-mode constraints on the non-Gaussianity of the background distribution function that results from shell-crossing are satisfied, guaranteeing the screening of UV modes for all fluctuations of any type, as expected physically. We also show analytically that loop corrections to the power spectrum are finite within VPT for any initial power spectra consistent with hierarchical clustering, unlike SPT. Finally, we discuss the relation to and contrast our predictions with effective field theory (EFT), and discuss how the advantages of VPT and EFT approaches could be combined.

astro-ph.CO↗

arXiv2023

Wide-angle and relativistic effects in Fourier-space clustering statistics

Galaxy power spectrum and bispectrum signals are distorted by peculiar velocities and other relativistic effects arising from a perturbed spacetime background. In addition, study of correlation functions of tracers in Fourier space is often done in the plane-parallel approximation under which it is assumed that line-of-sight (LOS) vectors are parallel. In this work we show that a simple perturbative procedure can be employed for a fast evaluation of beyond plane-parallel (wide-angle) corrections to the power spectrum and bispectrum. We also show that evolution of linear matter density fluctuations in a relativistic context can be found from a simple method. For the power spectrum at linear level, we compare leading order wide-angle contributions to multipoles of the galaxy power spectrum with those from non-integrated and integrated relativistic corrections and estimate their possible contamination on local fNL measurements to be of order a few. We also compute wide-angle corrections in the presence of nonlinear terms at one-loop order. For the bispectrum, we show that wide-angle effects alone, even with fully symmetric choices of LOS, give rise to imaginary, odd-parity multipoles of the galaxy bispectrum (dipole, octupole, etc.) which are in many cases larger than previously known ones of relativistic origin. We calculate these contributions and provide an estimator for measuring the leading order bispectrum dipole from data, using a symmetric LOS definition. Finally, we calculate the leading order corrections to multipoles of real plane-parallel bispectrum multipoles and estimate the apparent local fNL induced to be of order unity.

astro-ph.CO↗

arXiv2023

Squeezing $f_{\rm NL}$ out of the matter bispectrum with consistency relations

We show how consistency relations can be used to robustly extract the amplitude of local primordial non-Gaussianity ($f_{\rm NL}$) from the squeezed limit of the matter bispectrum, well into the non-linear regime. First, we derive a non-perturbative relation between primordial non-Gaussianity and the leading term in the squeezed bispectrum, revising some results present in the literature. This relation is then used to successfully measure $f_{\rm NL}$ from $N$-body simulations. We discuss the dependence of our results on different scale cuts and redshifts. Specifically, the analysis is strongly dependent on the choice of the smallest soft momentum, $q_{\rm min}$, which is the most sensitive to primordial bispectrum contributions, but is largely independent of the choice of the largest hard momentum, $k_{\rm max}$, due to the non-Gaussian nature of the covariance. We also show how the constraints on $f_{\rm NL}$ improve at higher redshift, due to a reduced off-diagonal covariance. In particular, for a simulation with $f_{\rm NL} = 100$ and a volume of $(2.4 \text{ Gpc}/h)^3$, we measure $f_{\rm NL} = 98 \pm 12$ at redshift $z=0$ and $f_{\rm NL} = 97 \pm 8$ at $z=0.97$. Finally, we compare our results with a Fisher forecast, showing that the current version of the analysis is satisfactorily close to the Fisher error. We regard this as a first step towards the realistic application of consistency relations to constrain primordial non-Gaussianity using observations.

astro-ph.CO↗

arXiv2022

Perturbation theory with dispersion and higher cumulants: framework and linear theory

The standard perturbation theory (SPT) approach to gravitational clustering is based on a fluid approximation of the underlying Vlasov-Poisson dynamics, taking only the zeroth and first cumulant of the phase-space distribution function into account (density and velocity fields). This assumption breaks down when dark matter particle orbits cross and leads to well-known problems, e.g. an anomalously large backreaction of small-scale modes onto larger scales that compromises predictivity. We extend SPT by incorporating second and higher cumulants generated by orbit crossing. For collisionless matter, their equations of motion are completely fixed by the Vlasov-Poisson system, and thus we refer to this approach as Vlasov Perturbation Theory (VPT). Even cumulants develop a background value, and they enter the hierarchy of coupled equations for the fluctuations. The background values are in turn sourced by power spectra of the fluctuations. The latter can be brought into a form that is formally analogous to SPT, but with an extended set of variables and linear as well as non-linear terms, that we derive explicitly. In this paper, we focus on linear solutions, which are far richer than in SPT, showing that modes that cross the dispersion scale set by the second cumulant are highly suppressed. We derive stability conditions on the background values of even cumulants from the requirement that exponential instabilities be absent. We also compute the expected magnitude of averaged higher cumulants for various halo models and show that they satisfy the stability conditions. Finally, we derive self-consistent solutions of perturbations and background values for a scaling universe and study the convergence of the cumulant expansion. The VPT framework provides a conceptually straightforward and deterministic extension of SPT that accounts for the decoupling of small-scale modes.

astro-ph.CO↗

arXiv2022

Perturbation theory with dispersion and higher cumulants: non-linear regime

We present non-linear solutions of Vlasov Perturbation Theory (VPT), describing gravitational clustering of collisionless dark matter with dispersion and higher cumulants induced by orbit crossing. We show that VPT can be cast into a form that is formally analogous to standard perturbation theory (SPT), but including additional perturbation variables, non-linear interactions, and a more complex propagation. VPT non-linear kernels have a crucial decoupling property: for fixed total momentum, the kernels becomes strongly suppressed when any of the individual momenta cross the dispersion scale into the non-linear regime. This screening of UV modes allows us to compute non-linear corrections to power spectra even for cosmologies with very blue power-law input spectra, for which SPT diverges. We compare predictions for the density and velocity divergence power spectra as well as the bispectrum at one-loop order to N-body results in a scaling universe with spectral indices $-1\leq n_s\leq +2$. We find a good agreement up to the non-linear scale for all cases, with a reach that increases with the spectral index $n_s$. We discuss the generation of vorticity as well as vector and tensor modes of the velocity dispersion, showing that neglecting vorticity when including dispersion would lead to a violation of momentum conservation. We verify momentum conservation when including vorticity, and compute the vorticity power spectrum at two-loop order, necessary to recover the correct large-scale limit with slope $n_w=2$. Comparing to our N-body measurements confirms the cross-over from $k^4$ to $k^2$ scaling on large scales. Our results provide a proof-of-principle that perturbative techniques for dark matter clustering can be systematically improved based on the known underlying collisionless dynamics.

astro-ph.CO↗

arXiv2022

Cosmological implications of the full shape of anisotropic clustering measurements in BOSS and eBOSS

We present the analysis of the full shape of anisotropic clustering measurement from the extended Baryon Oscillation Spectroscopic Survey (eBOSS) quasar sample together with the combined galaxy sample from the Baryon Oscillation Spectroscopic Survey (BOSS), re-analysed using an updated recipe for the non-linear matter power spectrum and the non-local bias parameters. We obtain constraints for flat $Λ$CDM cosmologies, focusing on the cosmological parameters that are independent of the Hubble parameter $h$. Our recovered value for the RMS linear perturbation theory variance as measured on the scale of $12\,{\rm Mpc}$ is $σ_{12}=0.805\pm 0.049$, while using the traditional reference scale of $8\,h^{-1}{\rm Mpc}$ gives $σ_{8}=0.815\pm 0.044$. We quantify the agreement between our measurements and the latest CMB data from Planck using the suspiciousness metric, and find them to be consistent within $0.64 \pm 0.03σ$. Combining our clustering constraints with the $3\times2$pt data sample from the Dark Energy Survey (DES) Year 1 release slightly degrades this agreement to the level of $1.54 \pm 0.08σ$, while still showing an overall consistency with Planck. We furthermore study the effect of imposing a Planck - like prior on the parameters that define the shape of the linear matter power spectrum, and find significantly tighter constraints on the parameters that control the evolution of density fluctuations. In particular, the combination of low-redshift data sets prefers a value of the physical dark energy density $ω_{\rm DE}=0.335 \pm 0.011$, which is 1.7$σ$ higher than the one preferred by Planck.

astro-ph.CO↗

arXiv2021

The Quijote simulations

The Quijote simulations are a set of 44,100 full N-body simulations spanning more than 7,000 cosmological models in the $\{Ω_{\rm m}, Ω_{\rm b}, h, n_s, σ_8, M_ν, w \}$ hyperplane. At a single redshift the simulations contain more than 8.5 trillions of particles over a combined volume of 44,100 $(h^{-1}{\rm Gpc})^3$; each simulation follow the evolution of $256^3$, $512^3$ or $1024^3$ particles in a box of $1~h^{-1}{\rm Gpc}$ length. Billions of dark matter halos and cosmic voids have been identified in the simulations, whose runs required more than 35 million core hours. The Quijote simulations have been designed for two main purposes: 1) to quantify the information content on cosmological observables, and 2) to provide enough data to train machine learning algorithms. In this paper we describe the simulations and show a few of their applications. We also release the Petabyte of data generated, comprising hundreds of thousands of simulation snapshots at multiple redshifts, halo and void catalogs, together with millions of summary statistics such as power spectra, bispectra, correlation functions, marked power spectra, and estimated probability density functions.

astro-ph.CO↗

arXiv2020

Cosmological constraints from BOSS with analytic covariance matrices

We use analytic covariance matrices to carry out a full-shape analysis of the galaxy power spectrum multipoles from the Baryon Oscillation Spectroscopic Survey (BOSS). We obtain parameter estimates that agree well with those based on the sample covariance from two thousand galaxy mock catalogs, thus validating the analytic approach and providing substantial reduction in computational cost. We also highlight a number of additional advantages of analytic covariances. First, the analysis does not suffer from sampling noise, which biases the constraints and typically requires inflating parameter error bars. Second, it allows us to study convergence of the cosmological constraints when recomputing the analytic covariances to match the best-fit power spectrum, which can be done at a negligible computational cost, unlike when using mock catalogs. These effects reduce the systematic error budget of cosmological constraints, which suggests that the analytic approach may be an important tool for upcoming high-precision galaxy redshift surveys such as DESI and Euclid. Finally, we study the impact of various ingredients in the power spectrum covariance matrix and show that the non-Gaussian part, which includes the regular trispectrum and super-sample covariance, has a marginal effect ($\lesssim 10 \%$) on the cosmological parameter error bars. We also suggest improvements to analytic covariances that are commonly used in Fisher forecasts.

astro-ph.CO↗

arXiv2020

Galaxy Power Spectrum Multipoles Covariance in Perturbation Theory

We compute the covariance of the galaxy power spectrum multipoles in perturbation theory, including the effects of nonlinear evolution, nonlinear and nonlocal bias, radial redshift-space distortions, arbitrary survey window and shot noise. We rewrite the power spectrum FKP estimator in terms of the usual windowed galaxy fluctuations and the fluctuations in the number of galaxies inside the survey volume. We show that this leads to a stronger super-sample covariance than assumed in the literature and causes a substantial leakage of Gaussian information. We decompose the covariance matrix into several contributions that provide an insight into its behavior for different biased tracers. We show that for realistic surveys, the covariance of power spectrum multipoles is already dominated by shot noise and super survey mode coupling in the weakly non-linear regime. Both these effects can be accurately modeled analytically, making a perturbative treatment of the covariance very compelling. Our method allows for the covariance to be varied as a function of cosmology and bias parameters very efficiently, with survey geometry entering as fixed kernels that can be computed separately using fast fourier transforms (FFTs). We find excellent agreement between our analytic covariance and that estimated from BOSS DR12 Patchy mock catalogs in the whole range we tested, up to $k=0.6$ h/Mpc. This bodes well for application to future surveys such as DESI and Euclid. The CovaPT code that accompanies this paper is available at https://github.com/JayWadekar/CovaPT

astro-ph.CO↗

arXiv2020

Constraining $M_ν$ with the Bispectrum I: Breaking Parameter Degeneracies

Massive neutrinos suppress the growth of structure below their free-streaming scale and leave an imprint on large-scale structure. Measuring this imprint allows us to constrain the sum of neutrino masses, $M_ν$, a key parameter in particle physics beyond the Standard Model. However, degeneracies among cosmological parameters, especially between $M_ν$ and $σ_8$, limit the constraining power of standard two-point clustering statistics. In this work, we investigate whether we can break these degeneracies and constrain $\smnu$ with the next higher-order correlation function --- the bispectrum. We first examine the redshift-space halo bispectrum of $800$ $N$-body simulations from the HADES suite and demonstrate that the bispectrum helps break the $M_ν$--$σ_8$ degeneracy. Then using 22,000 $N$-body simulations of the Quijote suite, we quantify for the first time the full information content of the redshift-space halo bispectrum down to nonlinear scales using a Fisher matrix forecast of $\{Ω_m$, $Ω_b$, $h$, $n_s$, $σ_8$, $M_ν\}$. For $k_{\rm max}{=}0.5~h/{\rm Mpc}$, the bispectrum provides $Ω_m$, $Ω_b$, $h$, $n_s$, and $σ_8$ constraints 1.9, 2.6, 3.1, 3.6, and 2.6 times tighter than the power spectrum. For $M_ν$, the bispectrum improves the 1$σ$ constraint from 0.2968 to 0.0572 eV --- over 5 times tighter than the power spectrum. Even with priors from {\em Planck}, the bispectrum improves $M_ν$ constraints by a factor of 1.8. Although we reserve marginalizing over a more complete set of bias parameters to the next paper of the series, these constraints are derived for a $(1~h^{-1}{\rm Gpc})^3$ box, a substantially smaller volume than upcoming surveys. Thus, our results demonstrate that the bispectrum offers significant improvements over the power spectrum, especially for constraining $M_ν$.

astro-ph.CO↗

arXiv2019

A non-perturbative test of consistency relations and their violation

In this paper, we verify the large scale structure consistency relations using N-body simulations, including modes in the highly non-linear regime. These relations (pointed out by Kehagias & Riotto and Peloso & Pietroni) follow from the symmetry of the dynamics under a shift of the Newtonian potential by a constant and a linear gradient, and predict the absence of certain poles in the ratio between the (equal time) squeezed bispectrum and power spectrum. The consistency relations, as symmetry statements, are exact, but have not been previously checked beyond the perturbative regime. Our test using N-body simulations not only offers a non-perturbative check, but also serves as a warm-up exercise for applications to observational data. A number of subtleties arise when taking the squeezed limit of the bispectrum--we show how to circumvent or address them. An interesting by-product of our investigation is an explicit demonstration that the linear-gradient symmetry is unaffected by the periodic boundary condition of the simulations. Lastly, we verify using simulations that the consistency relations are violated when the initial conditions are non-gaussian (of the local fNL type). The methodology developed here paves the way for constraining primordial non-gaussianity using large scale structure data, including (numerous) highly non-linear modes that are otherwise hard to interpret and utilize.

astro-ph.CO↗

arXiv2019

Bias Loop Corrections to the Galaxy Bispectrum

Combination of the power spectrum and bispectrum is a powerful way of breaking degeneracies between galaxy bias and cosmological parameters, enabling us to maximize the constraining power from galaxy surveys. Recent cosmological constraints treat the power spectrum and bispectrum on an uneven footing: they include one-loop bias corrections for the power spectrum but not the bispectrum. To bridge this gap, we develop the galaxy bias description up to fourth order in perturbation theory, conveniently expressed through a basis of Galilean invariants that clearly split contributions that are local and nonlocal in the second derivatives of the linear gravitational potential. In addition, we consider relevant contributions from short-range nonlocality (higher-derivative terms), stress-tensor corrections and stochasticity. To sidestep the usual renormalization of bias parameters that complicates predictions beyond leading order, we recast the bias expansion in terms of multipoint propagators, which take a simple form in our split-basis with loop corrections depending only on bias parameters corresponding to nonlocal operators. We show how to take advantage of Galilean invariance to compute the time evolution of bias and present results for the fourth-order parameters for the first time. We also discuss the possibilities of reducing the bias parameter space by using the evolution of bias and exploiting degeneracies between various bias contributions in the large-scale limit. Our baseline model allows to verify these simplifications for any application to large-scale structure data sets.

astro-ph.CO↗

arXiv2018

Towards Accurate Modelling of Galaxy Clustering on Small Scales: Testing the Standard $Λ\mathrm{CDM}$ + Halo Model

Interpreting the small-scale clustering of galaxies with halo models can elucidate the connection between galaxies and dark matter halos. Unfortunately, the modelling is typically not sufficiently accurate for ruling out models statistically. It is thus difficult to use the information encoded in small scales to test cosmological models or probe subtle features of the galaxy-halo connection. In this paper, we attempt to push halo modelling into the "accurate" regime with a fully numerical mock-based methodology and careful treatment of statistical and systematic errors. With our forward-modelling approach, we can incorporate clustering statistics beyond the traditional two-point statistics. We use this modelling methodology to test the standard $Λ\mathrm{CDM}$ + halo model against the clustering of SDSS DR7 galaxies. Specifically, we use the projected correlation function, group multiplicity function and galaxy number density as constraints. We find that while the model fits each statistic separately, it struggles to fit them simultaneously. Adding group statistics leads to a more stringent test of the model and significantly tighter constraints on model parameters. We explore the impact of varying the adopted halo definition and cosmological model and find that changing the cosmology makes a significant difference. The most successful model we tried (Planck cosmology with Mvir halos) matches the clustering of low luminosity galaxies, but exhibits a 2.3$σ$ tension with the clustering of luminous galaxies, thus providing evidence that the "standard" halo model needs to be extended. This work opens the door to adding interesting freedom to the halo model and including additional clustering statistics as constraints.

astro-ph.CO↗

arXiv2018

Testing the consistency of three-point halo clustering in Fourier and configuration space

We compare reduced three-point correlations $Q$ of matter, haloes (as proxies for galaxies) and their cross correlations, measured in a total simulated volume of $\sim100 \ (h^{-1} \text{Gpc})^{3}$, to predictions from leading order perturbation theory on a large range of scales in configuration space. Predictions for haloes are based on the non-local bias model, employing linear ($b_1$) and non-linear ($c_2$, $g_2$) bias parameters, which have been constrained previously from the bispectrum in Fourier space. We also study predictions from two other bias models, one local ($g_2=0$) and one in which $c_2$ and $g_2$ are determined by $b_1$ via an approximately universal relation. Overall, measurements and predictions agree when $Q$ is derived for triangles with $(r_1r_2r_3)^{1/3} \gtrsim 60 h^{-1}\text{Mpc}$, where $r_{1-3}$ are the sizes of the triangle legs. Predictions for $Q_{matter}$, based on the linear power spectrum, show significant deviations from the measurements at the BAO scale (given our small measurement errors), which strongly decrease when adding a damping term or using the non-linear power spectrum, as expected. Predictions for $Q_{halo}$ agree best with measurements at large scales when considering non-local contributions. The universal bias model works well for haloes and might therefore be also useful for tightening constraints on $b_1$ from $Q$ in galaxy surveys. Such constraints are independent of the amplitude of matter density fluctuation ($σ_8$) and hence break the degeneracy between $b_1$ and $σ_8$, present in galaxy two-point correlations.

astro-ph.CO↗

arXiv2017

Effective Window Function for Lagrangian Halos

The window function for protohalos in Lagrangian space is often assumed to be a tophat in real space. We measure this profile directly and find that it is more extended than a tophat but less extended than a Gaussian; its shape is well-described by rounding the edges of the tophat by convolution with a Gaussian that has a scale length about 5 times smaller. This effective window $W_{\rm eff}$ is particularly simple in Fourier space, and has an analytic form in real space. Together with the excursion set bias parameters, $W_{\rm eff}$ describes the scale-dependence of the Lagrangian halo-matter cross correlation up to $kR_{\rm Lag} \sim 10 $, where $R_{\rm Lag}$ is the Lagrangian size of the protohalo. Moreover, with this $W_{\rm eff}$, all the spectral moments of the power spectrum are finite, allowing a straightforward estimate of the excursion set peak mass function. This estimate requires a prescription of the critical overdensity enclosed within a protohalo if it is to collapse, which we calibrate from simulations. We find that the resulting estimate of halo abundances is only accurate to about 20%, and we discuss why: A tophat in `infall time' towards the protohalo center need not correspond to a tophat in the initial spatial distribution, so models in which infall rather than smoothed overdensity is the relevant variable may be more accurate.

astro-ph.CO↗

arXiv2017

Accurate Estimators of Correlation Functions in Fourier Space

Efficient estimators of Fourier-space statistics for large number of objects rely on Fast Fourier Transforms (FFTs), which are affected by aliasing from unresolved small scale modes due to the finite FFT grid. Aliasing takes the form of a sum over images, each of them corresponding to the Fourier content displaced by increasing multiples of the sampling frequency of the grid. These spurious contributions limit the accuracy in the estimation of Fourier-space statistics, and are typically ameliorated by simultaneously increasing grid size and discarding high-frequency modes. This results in inefficient estimates for e.g. the power spectrum when desired systematic biases are well under per-cent level. We show that using interlaced grids removes odd images, which include the dominant contribution to aliasing. In addition, we discuss the choice of interpolation kernel used to define density perturbations on the FFT grid and demonstrate that using higher-order interpolation kernels than the standard Cloud in Cell algorithm results in significant reduction of the remaining images. We show that combining fourth-order interpolation with interlacing gives very accurate Fourier amplitudes and phases of density perturbations. This results in power spectrum and bispectrum estimates that have systematic biases below 0.01% all the way to the Nyquist frequency of the grid, thus maximizing the use of unbiased Fourier coefficients for a given grid size and greatly reducing systematics for applications to large cosmological datasets.

astro-ph.CO↗

arXiv2017

The imprint of neutrinos on clustering in redshift-space

(abridged) We investigate the signatures left by the cosmic neutrino background on the clustering of matter, CDM+baryons and halos in redshift-space using a set of more than 1000 N-body and hydrodynamical simulations with massless and massive neutrinos. We find that the effect neutrinos induce on the clustering of CDM+baryons in redshift-space on small scales is almost entirely due to the change in $σ_8$. Neutrinos imprint a characteristic signature in the quadrupole of the matter (CDM+baryons+neutrinos) field on small scales, that can be used to disentangle the effect of $σ_8$ and $M_ν$. We show that the effect of neutrinos on the clustering of halos is very different, on all scales, to the one induced by $σ_8$. We find that the effects of neutrinos of the growth rate of CDM+baryons ranges from $\sim0.3\%$ to $2\%$ on scales $k\in[0.01, 0.5]~h{\rm Mpc}^{-1}$ for neutrinos with masses $M_ν\leqslant 0.15$ eV. We compute the bias between the momentum of halos and the momentum of CDM+baryon and find it to be 1 on large scales for all models with massless and massive neutrinos considered. This point towards a velocity bias between halos and total matter on large scales that it is important to account for in order to extract unbiased neutrino information from velocity/momentum surveys such as kSZ observations. We show that baryonic effects can affect the clustering of matter and CDM+baryons in redshift-space by up to a few percent down to $k=0.5~h{\rm Mpc}^{-1}$. We find that hydrodynamics and astrophysical processes, as implemented in our simulations, only distort the relative effect that neutrinos induce on the anisotropic clustering of matter, CDM+baryons and halos in redshift-space by less than $1\%$. Thus, the effect of neutrinos in the fully non-linear regime can be written as a transfer function with very weak dependence on astrophysics.

astro-ph.CO↗