Modelling Of Redshift-space Distortions Research Articles

Studying large-scale structure probes of modified gravity with COLA

We study the effect of two Modified Gravity (MG) theories, f(R) and nDGP, on three probes of large-scale structure, the real space power spectrum estimator Q 0, bispectrum and voids, and validate fast approximate COLA simulations against full N-body simulations for the prediction of these probes.We find that using the first three even multipoles of the redshift space power spectrum to estimate Q 0 is enough to reproduce the MG boost factors of the real space power spectrum for both halo and galaxy catalogues. By analysing the bispectrum and reduced bispectrum of Dark Matter (DM), we show that the strong MG signal present in the DM bispectrum is mainly due to the enhanced power spectrum. We warn about adopting screening approximations in simulations as this neglects non-linear contributions that can source a significant component of the MG bispectrum signal at the DM level, but we argue that this is not a problem for the bispectrum of galaxies in redshift space where the signal is dominated by the non-linear galaxy bias. Finally, we search for voids in our mock galaxy catalogues using the ZOBOV watershed algorithm.To apply a linear model for Redshift-Space Distortion (RSD) in the void-galaxy cross-correlation function, we first examine the effects of MG on the void profiles entering into the RSD model. We find relevant MG signals in the integrated-density, velocity dispersion and radial velocity profiles in the nDGP theory. Fitting the RSD model for the linear growth rate, we recover the linear theory prediction in an nDGP model, which is larger than the ΛCDM predictionat the 3σ level. In f(R) theory we cannot naively compare the results of the fit with the linear theory prediction as this is scale-dependent, but we obtain results that are consistent with the ΛCDM prediction.

Galaxy and Mass Assembly (GAMA): probing galaxy-group correlations in redshift space with the halo streaming model

ABSTRACT We have studied the galaxy-group cross-correlations in redshift space for the Galaxy And Mass Assembly (GAMA) Survey. We use a set of mock GAMA galaxy and group catalogues to develop and test a novel ‘halo streaming’ model for redshift-space distortions. This treats 2-halo correlations via the streaming model, plus an empirical 1-halo term derived from the mocks, allowing accurate modelling into the non-linear regime. In order to probe the robustness of the growth rate inferred from redshift-space distortions, we divide galaxies by colour, and divide groups according to their total stellar mass, calibrated to total mass via gravitational lensing. We fit our model to correlation data, to obtain estimates of the perturbation growth rate, fσ8, validating parameter errors via the dispersion between different mock realizations. In both mocks and real data, we demonstrate that the results are closely consistent between different subsets of the group and galaxy populations, considering the use of correlation data down to some minimum projected radius, rmin. For the mock data, we can use the halo streaming model to below $r_{\rm min} = 5{\, h^{-1}\, \rm Mpc}$, finding that all subsets yield growth rates within about 3 per cent of each other, and consistent with the true value. For the actual GAMA data, the results are limited by cosmic variance: fσ8 = 0.29 ± 0.10 at an effective redshift of 0.20; but there is every reason to expect that this method will yield precise constraints from larger data sets of the same type, such as the Dark Energy Spectroscopic Instrument (DESI) bright galaxy survey.

Redshift-space distortions with split densities

ABSTRACT Accurate modelling of redshift-space distortions (RSD) is challenging in the non-linear regime for two-point statistics e.g. the two-point correlation function (2PCF). We take a different perspective to split the galaxy density field according to the local density, and cross-correlate those densities with the entire galaxy field. Using mock galaxies, we demonstrate that combining a series of cross-correlation functions (CCFs) offers improvements over the 2PCF as follows: (1) The distribution of peculiar velocities in each split density is nearly Gaussian. This allows the Gaussian streaming model for RSD to perform accurately within the statistical errors of a ($1.5\, h^{-1}$ Gpc)3 volume for almost all scales and all split densities. (2) The probability distribution of the density contrast at small scales is non-Gaussian, but the CCFs of split densities capture the non-Gaussianity, leading to improved cosmological constraints over the 2PCF. We can obtain unbiased constraints on the growth parameter fσ12 at the per cent level, and Alcock–Paczynski (AP) parameters at the sub-per cent level with the minimal scale of $15\, h^{-1}{\rm Mpc}$. This is a ∼30 per cent and ∼6 times improvement over the 2PCF, respectively. The diverse and steep slopes of the CCFs at small scales are likely to be responsible for the improved constraints of AP parameters. (3) Baryon acoustic oscillations (BAO) are contained in all CCFs of split densities. Including BAO scales helps to break the degeneracy between the line-of-sight and transverse AP parameters, allowing independent constraints on them. We discuss and compare models for RSD around spherical densities.

The completed SDSS-IV extended Baryon Oscillation Spectroscopic Survey: N-body mock challenge for the eBOSS emission line galaxy sample

ABSTRACT Cosmological growth can be measured in the redshift space clustering of galaxies targeted by spectroscopic surveys. Accurate prediction of clustering of galaxies will require understanding galaxy physics, which is a very hard and highly non-linear problem. Approximate models of redshift space distortion (RSD) take a perturbative approach to solve the evolution of dark matter and galaxies in the universe. In this paper, we focus on extended Baryon Oscillation Spectroscopic (eBOSS) emission line galaxies (ELGs) that live in intermediate mass haloes. We create a series of mock catalogues using haloes from the Multidark and outer rim dark matter only N-body simulations. Our mock catalogues include various effects inspired by baryonic physics such as assembly bias and the characteristics of satellite galaxies kinematics, dynamics, and statistics deviating from dark matter particles. We analyse these mocks using the TNS RSD model in Fourier space and the convolution Lagrangian perturbation theory (CLPT) in configuration space. We conclude that these two RSD models provide an unbiased measurement of RSD within the statistical error of our mocks. We obtain the conservative theoretical systematic uncertainty of $3.3{{\ \rm per\ cent}}$, $1.8{{\ \rm per\ cent}}$, and $1.5{{\ \rm per\ cent}}$ in fσ8, α∥, and α⊥, respectively, for the TNS and CLPT models. We note that the estimated theoretical systematic error is an order of magnitude smaller than the statistical error of the eBOSS ELG sample and hence are negligible for the purpose of the current eBOSS ELG analysis.

Nonlinear redshift-space distortions in the harmonic-space galaxy power spectrum

Future high spectroscopic resolution galaxy surveys will observe galaxies with nearly full-sky footprints. Modeling the galaxy clustering for these surveys, therefore, must include the wide-angle effect with narrow redshift binning. In particular, when the redshift-bin size is comparable to the typical peculiar velocity field, the nonlinear redshift-space distortion (RSD) effect becomes important. A naive projection of the Fourier-space RSD model to spherical harmonic space leads to diverging expressions. In this paper we present a general formalism of projecting the higher-order RSD terms into spherical harmonic space. We show that the nonlinear RSD effect, including the fingers-of-God (FoG), can be entirely attributed to a modification of the radial window function. We find that while linear RSD enhances the harmonic-space power spectrum, unlike the three-dimensional case, the enhancement decreases on small angular-scales. The fingers-of-God suppress the angular power spectrum on all transverse scales if the bin size is smaller than $\Delta r \lesssim \pi \sigma_u$; for example, the radial bin sizes corresponding to a spectral resolution $R=\lambda/\Delta \lambda$ of a few hundred satisfy the condition. We also provide the flat-sky approximation which reproduces the full calculation to sub-percent accuracy.

Validating the methodology for constraining the linear growth rate from clustering anisotropies

ABSTRACT Redshift-space clustering distortions provide one of the most powerful probes to test the gravity theory on the largest cosmological scales. We perform a systematic validation study of the state-of-the-art statistical methods currently used to constrain the linear growth rate from redshift-space distortions in the galaxy two-point correlation function. The numerical pipelines are tested on mock halo catalogues extracted from large N-body simulations of the standard cosmological framework. We consider both the monopole and quadrupole multipole moments of the redshift-space two-point correlation function, as well as the radial and transverse clustering wedges, in the comoving scale range 10 < r[$h^{-1}\, \mbox{Mpc}$] < 55. Moreover, we investigate the impact of redshift measurement errors on the growth rate and linear bias measurements due to the assumptions in the redshift-space distortion model. Considering both the dispersion model and two widely used models based on perturbation theory, we find that the linear growth rate is underestimated by about $5\!-\! 10\, {\rm {per\ cent}}$ at $z$ < 1, while limiting the analysis at larger scales, r > 30 $h^{-1}\, \mbox{Mpc}$, the discrepancy is reduced below $5\, {\rm {per\ cent}}$. At higher redshifts, we find instead an overall good agreement between measurements and model predictions. Though this accuracy is good enough for clustering analyses in current redshift surveys, the models have to be further improved not to introduce significant systematics in RSD constraints from next-generation galaxy surveys. The effect of redshift errors is degenerate with the one of small-scale random motions, and can be marginalized over in the statistical analysis, not introducing any statistically significant bias in the linear growth constraints, especially at $z$ ≥ 1.

Developing a unified pipeline for large-scale structure data analysis with angular power spectra – I. The importance of redshift-space distortions for galaxy number counts

ABSTRACT We develop a cosmological parameter estimation code for (tomographic) angular power spectra analyses of galaxy number counts, for which we include, for the first time, redshift-space distortions (RSDs) in the Limber approximation. This allows for a speed-up in computation time, and we emphasize that only angular scales where the Limber approximation is valid are included in our analysis. Our main result shows that a correct modelling of RSD is crucial not to bias cosmological parameter estimation. This happens not only for spectroscopy-detected galaxies, but even in the case of galaxy surveys with photometric redshift estimates. Moreover, a correct implementation of RSD is especially valuable in alleviating the degeneracy between the amplitude of the underlying matter power spectrum and the galaxy bias. We argue that our findings are particularly relevant for present and planned observational campaigns, such as the Euclid satellite or the Square Kilometre Array, which aim at studying the cosmic large-scale structure and trace its growth over a wide range of redshifts and scales.

Radiative transfer distortions of Lyman α emitters: a new Fingers-of-God damping in the clustering in redshift space

ABSTRACT Complex radiative transfer (RT) of the Lyman α photons poses a theoretical challenge to galaxy surveys that infer the large-scale structure with Lyman α emitters (LAEs). Guided by RT simulations, prior studies investigated the impact of RT on the large-scale LAE clustering, and claimed that RT induces a selection effect which results in an anisotropic distortion even in real space but in an otherwise negligible effect in redshift space. However, our previous study, which relies on a full RT code run on the Illustris simulations, shows that the anisotropic selection effect was drastically reduced with higher spatial resolution. Adopting the same simulation framework, we further study the impact of RT on the LAE clustering in redshift space. Since we measure LAE’s radial position through a spectral peak of Lyman α emission, the frequency shift due to RT contaminates the redshift measurement and hence the inferred radial position in redshift space. We demonstrate that this additional RT offset suppresses the LAE clustering along the line of sight, which can be interpreted as a novel Fingers-of-God (FoG) effect. To assess the FoG effect, we develop a theoretical framework modelling the impact of the RT similar to that of the small-scale peculiar velocity which is commonly studied in the context of the redshift space distortion (RSD). Although our findings strongly encourage a more careful RSD modelling in LAE surveys, we also seek a method to mitigate the additional FoG effect due to RT by making use of other information in a Lyman α spectrum.

Study on the mapping of halo clustering from real space to redshift space

The mapping of galaxy clustering from real space to redshift space introduces the anisotropic property to the measured galaxy density power spectrum in redshift space, known as the redshift space distortion (RSD) effect. The mapping formula is intrinsically non-linear, which is complicated by the higher order polynomials due to indefinite orders of cross correlations between density and velocity fields, and the Finger-of-God (FoG) effect due to the randomness of the galaxy peculiar velocity field. In previous works, we have verified the robustness of advanced TNS mapping formula in our hybrid RSD model in dark matter case, where the halo bias models are not taken into account for the halo mapping formula in redshift space. Using 100 realizations of halo catalogs in N-body simulations, we find that our halo RSD model with the known halo bias model and the effective FoG function accurately predicts the halo power spectrum measurements, within 1∼2% accuracy up to k∼ 0.2 h Mpc-1, depending on different halo masses and redshifts.

Investigating the degeneracy between modified gravity and massive neutrinos with redshift-space distortions

There is a well known degeneracy between the enhancement of the growth of large-scale structure produced by modified gravity models and the suppression due to the free-streaming of massive neutrinos at late times. This makes the matter power-spectrum alone a poor probe to distinguish between modified gravity and the concordance ΛCDM model when neutrino masses are not strongly constrained. In this work, we investigate the potential of using redshift-space distortions (RSD) to break this degeneracy when the modification to gravity is scale-dependent in the form of Hu-Sawicki f(R). We find that if the linear growth rate can be recovered from the RSD signal, the degeneracy can be broken at the level of the dark matter field. However, this requires accurate modelling of the non-linearities in the RSD signal, and we here present an extension of the standard perturbation theory based model for non-linear RSD that includes both Hu-Sawicki f(R) modified gravity and massive neutrinos.

Large-scale redshift space distortions in modified gravity theories

Measurements of redshift space distortions (RSD) provide a means to test models of gravity on large-scales. We use mock galaxy catalogues constructed from large N-body simulations of standard and modified gravity models to measure galaxy clustering in redshift space. We focus our attention on two of the most representative and popular families of modified gravity models: the Hu \& Sawicki $f(R)$ gravity and the normal branch of the DGP model. The galaxy catalogues are built using a halo occupation distribution (HOD) prescription with the HOD parameters in the modified gravity models tuned to match with the number density and the real-space clustering of {\sc boss-cmass} galaxies. We employ two approaches to model RSD: the first is based on linear perturbation theory and the second models non-linear effects on small-scales by assuming standard gravity and including biasing and RSD effects. We measure the monopole to real-space correlation function ratio, the quadrupole to monopole ratio, clustering wedges and multipoles of the correlation function and use these statistics to find the constraints on the distortion parameter, $\beta$. We find that the linear model fails to reproduce the N-body simulation results and the true value of $\beta$ on scales $s < 40\Mpch$, while the non-linear modelling of RSD recovers the value of $\beta$ on the scales of interest for all models. RSD on large scales ($s\gtrsim20$-$40\Mpch$) have been found to show significant deviations from the prediction of standard gravity in the DGP models. However, the potential to use RSD to constrain $f(R)$ models is less promising, due to the different screening mechanism in this model.

An accurate linear model for redshift space distortions in the void–galaxy correlation function

Redshift space distortions within voids provide a unique method to test for environmental dependence of the growth rate of structures in low density regions, where effects of modified gravity theories might be important. We derive a linear theory model for the redshift space void-galaxy correlation that is valid at all pair separations, including deep within the void, and use this to obtain expressions for the monopole $\xi^s_0$ and quadrupole $\xi^s_2$ contributions. Our derivation highlights terms that have previously been neglected but are important within the void interior. As a result our model differs from previous works and predicts new physical effects, including a change in the sign of the quadrupole term within the void radius. We show how the model can be generalised to include a velocity dispersion. We compare our model predictions to measurements of the correlation function using mock void and galaxy catalogues modelled after the BOSS CMASS galaxy sample using the Big MultiDark $N$-body simulation, and show that the linear model with dispersion provides an excellent fit to the data at all scales, $0\leq s\leq120\;h^{-1}$Mpc. While the RSD model matches simulations, the linear bias approximation does not hold within voids, and care is needed in fitting for the growth rate. We show that fits to the redshift space correlation recover the growth rate $f(z=0.52)$ to a precision of $2.7\%$ using the simulation volume of $(2.5\;h^{-1}\mathrm{Gpc})^3$.

The impact of galaxy formation on satellite kinematics and redshift-space distortions

Galaxy surveys aim to map the large-scale structure of the Universe and use redshift space distortions to constrain deviations from general relativity and probe the existence of massive neutrinos. However, the amount of information that can be extracted is limited by the accuracy of theoretical models used to analyze the data. Here, by using the L-Galaxies semi-analytical model run over the MXXL N-body simulation, we assess the impact of galaxy formation on satellite kinematics and the theoretical modelling of redshift-space distortions. We show that different galaxy selection criteria lead to noticeable differences in the radial distributions and velocity structure of satellite galaxies. Specifically, whereas samples of stellar mass selected galaxies feature satellites that roughly follow the dark matter, emission line satellite galaxies are located preferentially in the outskirts of halos and display net infall velocities. We demonstrate that capturing these differences is crucial for modelling the multipoles of the correlation function in redshift space, even on large scales. In particular, we show how modelling small scale velocities with a single Gaussian distribution leads to a poor description of the measure clustering. In contrast, we propose a parametrization that is flexible enough to model the satellite kinematics, and that leads to and accurate description of the correlation function down to sub-Mpc scales. We anticipate that our model will be a necessary ingredient in improved theoretical descriptions of redshift space distortions, which together could result in significantly tighter cosmological constraints and a more optimal exploitation of future large datasets.

The VIMOS Public Extragalactic Redshift Survey (VIPERS)

We carry out a joint analysis of redshift-space distortions and galaxy-galaxy lensing, with the aim of measuring the growth rate of structure; this is a key quantity for understanding the nature of gravity on cosmological scales and late-time cosmic acceleration. We make use of the final VIPERS redshift survey dataset, which maps a portion of the Universe at a redshift of $z \simeq 0.8$, and the lensing data from the CFHTLenS survey over the same area of the sky. We build a consistent theoretical model that combines non-linear galaxy biasing and redshift-space distortion models, and confront it with observations. The two probes are combined in a Bayesian maximum likelihood analysis to determine the growth rate of structure at two redshifts $z=0.6$ and $z=0.86$. We obtain measurements of $f\sigma_8(0.6) = 0.48 \pm 0.12$ and $f\sigma_8(0.86) = 0.48 \pm 0.10$. The additional galaxy-galaxylensing constraint alleviates galaxy bias and $\sigma_8$ degeneracies, providing direct measurements of $[f(0.6),\sigma_8(0.6)] = [0.93 \pm 0.22, 0.52 \pm 0.06]$ and $f(0.86),\sigma_8(0.86)] = [0.99 \pm 0.19, 0.48 \pm 0.04]$. These measurements are statistically consistent with a Universe where the gravitational interactions can be described by General Relativity, although they are not yet accurate enough to rule out some commonly considered alternatives. Finally, as a complementary test we measure the gravitational slip parameter, $E_G$ , for the first time at $z>0.6$. We find values of $\smash{\overline{E}_G}(0.6) = 0.16 \pm 0.09$ and $\smash{\overline{E}_G}(0.86) = 0.09 \pm 0.07$, when $E_G$ is averaged over scales above $3 h^{-1} \rm{Mpc}$. We find that our $E_G$ measurements exhibit slightly lower values than expected for standard relativistic gravity in a {\Lambda}CDM background, although the results are consistent within $1-2\sigma$.

Improved model of redshift-space distortions around voids: Application to quintessence dark energy

Using cosmic voids to probe the growth rate of cosmic structure, and hence the nature of dark energy, is particularly interesting in the context of modified gravity theories that rely on the screening mechanism. In this work we improve the modelling of redshift-space distortions around voids in the dark matter density field, and thus reduce systematic errors in the derivation of cosmological parameters. We also show how specific types of voids can be used to better probe the growth rate, using a flexible void finder. We apply our results to test for a quintessence type of dark energy vs. a LCDM model, and find a good agreement with the fiducial cosmology after implementing an analytical correction to the radial velocity profiles around voids. We additionally outline characteristic imprints of dark energy in the dark matter velocity distributions around voids.

The VIMOS Public Extragalactic Redshift Survey (VIPERS)

We present measurements of the growth rate of cosmological structure from the modelling of the anisotropic galaxy clustering measured in the final data release of the VIPERS survey. The analysis is carried out in configuration space and based on measurements of the first two even multipole moments of the anisotropic galaxy auto-correlation function, in two redshift bins spanning the range $0.5 < z < 1.2$. We provide robust and cosmology-independent corrections for the VIPERS angular selection function, allowing recovery of the underlying clustering amplitude at the percent level down to the Mpc scale. We discuss several improvements on the non-linear modelling of redshift-space distortions (RSD) and perform detailed tests of a variety of approaches against a set of realistic VIPERS-like mock realisations. This includes using novel fitting functions to describe the velocity divergence and density power spectra $P_{\theta\theta}$ and $P_{\delta\theta}$ that appear in RSD models. These tests show that we are able to measure the growth rate with negligible bias down to separations of $5h^{-1}Mpc$. Interestingly, the application to real data shows a weaker sensitivity to the details of non-linear RSD corrections compared to mock results. We obtain consistent values for the growth rate times the matter power spectrum normalisation parameter of $f\sigma_8=0.55\pm 0.12$ and $0.40\pm0.11$ at effective redshifts of $z = 0.6$ and $z=0.86$ respectively. These results are in agreement with standard cosmology predictions assuming Einstein gravity in a $\Lambda \rm{CDM}$ background.

Quantification of the multi-streaming effect in redshift space distortion

Both multi-streaming (random motion) and bulk motion cause the Finger-of-God (FoG) effect in redshift space distortion (RSD). We apply a direct measurement of the multi-streaming effect in RSD from simulations, proving that it induces an additional, non-negligible FoG damping to the redshift space density power spectrum. We show that, including the multi-streaming effect, the RSD modelling is significantly improved. We also provide a theoretical explanation based on halo model for the measured effect, including a fitting formula with one to two free parameters. The improved understanding of FoG helps break the fσ8−σv degeneracy in RSD cosmology, and has the potential of significantly improving cosmological constraints.

Validating estimates of the growth rate of structure with modified gravity simulations

We perform a validation of estimates of the growth rate of structure, described by the parameter combination $f\sigma_8$, in modified gravity cosmologies. We consider an analysis pipeline based on the redshift-space distortion modelling of the clustering wedges statistic of the galaxy correlation function and apply it to mock catalogues of $\Lambda{\rm CDM}$ and the normal branch of DGP cosmologies. We employ a halo occupation distribution approach to construct our mocks, which we ensure resemble the CMASS sample from BOSS in terms of the total galaxy number density and large scale amplitude of the power spectrum monopole. We show that the clustering wedges model successfully recovers the true growth rate difference between DGP and $\Lambda{\rm CDM}$, even for cases with over 40\% enhancement in $f\sigma_8$ compared to $\Lambda{\rm CDM}$. The unbiased performance of the clustering wedges model allows us to use the growth rate values estimated from the BOSS DR12 data to constrain the cross-over scale $r_c$ of DGP gravity to $\left[r_cH_0\right]^{-1} < 0.97$ ($2\sigma$) or $r_c > 3090\ {\rm Mpc}/h$, cutting into the interesting region of parameter space with $r_c \sim H_0^{-1}$ using constraints from the growth of structure alone.

Improving the modelling of redshift-space distortions– II. A pairwise velocity model covering large and small scales

We develop a model for the redshift-space correlation function, valid for both dark matter particles and halos on scales $>5\,h^{-1}$Mpc. In its simplest formulation, the model requires the knowledge of the first three moments of the line-of-sight pairwise velocity distribution plus two well-defined dimensionless parameters. The model is obtained by extending the Gaussian-Gaussianity prescription for the velocity distribution, developed in a previous paper, to a more general concept allowing for local skewness, which is required to match simulations. We compare the model with the well known Gaussian streaming model and the more recent Edgeworth streaming model. Using N-body simulations as a reference, we show that our model gives a precise description of the redshift-space clustering over a wider range of scales. We do not discuss the theoretical prescription for the evaluation of the velocity moments, leaving this topic to further investigation.

The effect of baryons on redshift space distortions and cosmic density and velocity fields in the EAGLE simulation

Abstract We use the Evolution and Assembly of GaLaxies and their Environments (EAGLE) galaxy formation simulation to study the effects of baryons on the power spectrum of the total matter and dark matter distributions and on the velocity fields of dark matter and galaxies. On scales k ≳ 4 h Mpc−1 the effect of baryons on the amplitude of the total matter power spectrum is greater than 1 per cent. The back-reaction of baryons affects the density field of the dark matter at the level of ∼3 per cent on scales of 1 ≤ k/( h Mpc−1) ≤ 5. The dark matter velocity divergence power spectrum at k ≲ 0.5 h Mpc−1 is changed by less than 1 per cent. The 2D redshift space power spectrum is affected at the level of ∼6 per cent at $|\boldsymbol {k}|\gtrsim 1\,h\,{\rm Mpc}^{-1}$ (for μ &amp;gt; 0.5), but for $|\boldsymbol {k}|\le 0.4\,h\,{\rm Mpc}^{-1}$ it differs by less than 1 per cent. We report vanishingly small baryonic velocity bias for haloes: the peculiar velocities of haloes with M200 &amp;gt; 3 × 1011 M⊙ (hosting galaxies with M* &amp;gt; 109 M⊙) are affected at the level of at most 1 km s−1, which is negligible for 1 per cent-precision cosmology. We caution that since EAGLE overestimates cluster gas fractions it may also underestimate the impact of baryons, particularly for the total matter power spectrum. Nevertheless, our findings suggest that for theoretical modelling of redshift space distortions and galaxy velocity-based statistics, baryons and their back-reaction can be safely ignored at the current level of observational accuracy. However, we confirm that the modelling of the total matter power spectrum in weak lensing studies needs to include realistic galaxy formation physics in order to achieve the accuracy required in the precision cosmology era.