We present the one-loop 2-point function of biased tracers in redshift space computed with Lagrangian perturbation theory, including a full resummation of both long-wavelength (infrared) displacements and associated velocities. The resulting model accurately predicts the power spectrum and correlation function of halos and mock galaxies from two different sets of N-body simulations at the percent level for quasi-linear scales, including the damping of the baryon acoustic oscillation signal due to the bulk motions of galaxies. We compare this full resummation with other, approximate, techniques including the moment expansion and Gaussian streaming model. We discuss infrared resummation in detail and compare our Lagrangian formulation with the Eulerian theory augmented by an infrared resummation based on splitting the input power spectrum into "wiggle" and "no-wiggle" components. We show that our model is able to recover unbiased cosmological parameters in mock data encompassing a volume much larger than what will be available to future galaxy surveys. We demonstrate how to efficiently compute the resulting expressions numerically, making available a fast Python code capable of rapidly computing these statistics in both configuration and Fourier space.
We apply the Lagrangian perturbation theory with time-dependent growth functions at second and third order of perturbation with the aim to model the effect of dynamical dark energy on redshift-space distortions. Our fiducial galaxy redshift surveys are modeled after the upcoming SKA and DESI redshift surveys. We include PLANCK CMB priors and the 20\% uncertainty on the linear bias parameter, incorporating the unknown instrumentation noise. After the marginalizing, our results show that the constraints on the density parameter could potentially get better than $\sim$1\%, while the constraints o…
We compute a general expression for the contribution of vector perturbations to the redshift-space distortion of galaxy surveys. We show that they contribute to the same multipoles of the correlation function as scalar perturbations and should thus in principle be taken into account in data analysis. We derive constraints for next-generation surveys on the amplitude of two sources of vector perturbations, namely non-linear clustering and topological defects. While topological defects leave a very small imprint on redshift-space distortions, we show that the multipoles of the correlation functi…
We apply nonlinear reconstruction to the dark matter density field in redshift space and solve for the nonlinear mapping from the initial Lagrangian position to the final redshift space position. The reconstructed anisotropic field inferred from the nonlinear displacement correlates with the linear initial conditions to much smaller scales than the redshift space density field. The number of linear modes in the density field is improved by a factor of 30-40 after reconstruction. We thus expect this reconstruction approach to substantially expand the cosmological information including baryon ac…
Modified gravity and massive neutrino cosmologies are two of the most interesting scenarios that have been recently explored to account for possible observational deviations from the concordance $Λ$-cold dark matter ($Λ$CDM) model. In this context, we investigated the large-scale structure of the Universe by exploiting the \dustp simulations that implement, simultaneously, the effects of $f(R)$ gravity and massive neutrinos. To study the possibility of breaking the degeneracy between these two effects, we analysed the redshift-space distortions in the clustering of dark matter haloes at differ…
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 Fo…
Peculiar-velocity surveys of the low-redshift universe have significant leverage to constrain the growth rate of cosmic structure and test gravity. Wide-field imaging surveys combined with multi-object spectrographs (e.g. ZTF2, LSST, DESI, 4MOST) can use Type Ia supernovae as informative tracers of the velocity field, reaching few percent constraints on the growth rate $fσ_8$ at $z\lesssim0.2$ where density tracers cannot do better than $\sim10\%$. Combining the high-redshift DESI survey mapping redshift space distortions with a low-redshift supernova peculiar velocity survey using LSST and DE…
We present a new model for the cross-covariance between galaxy redshift-space distortions and peculiar velocities. We combine this with the auto-covariance models of both probes in a fully self-consistent, maximum-likelihood method, allowing us to extract enhanced cosmological parameter constraints. When applying our method to the 6-degree Field Galaxy Survey (6dFGS), our constraint on the growth rate of structure is $fσ_8 = 0.384 \pm 0.052 \rm{(stat)} \pm 0.061 \rm{(sys)}$ and our constraint for the redshift-space distortion parameter is $β= 0.289^{+0.044}_{-0.043} \rm{(stat)} \pm 0.049 \rm{(…
In this paper, we fully investigate cosmological scenarios in which dark matter is non-minimally coupled to an extra scalar degree of freedom. The interaction is realized by means of conformal and disformal terms in the transformed gravitational metric. Considering linear perturbation theory, we show that the growth rate of dark matter differs from the uncoupled case and that the well-known Kaiser formula undergoes modification. As a result, redshift space distortion measurements cease to be a direct probe of the linear growth rate of total matter, since the distortion factor has an extra, cou…
The anisotropy of the redshift space bispectrum contains a wealth of cosmological information. This anisotropy depends on the orientation of three vectors ${\bf k_1,k_2,k_3}$ with respect to the line of sight. Here we have decomposed the redshift space bispectrum in spherical harmonics which completely quantify this anisotropy. To illustrate this we consider linear redshift space distortion of the bispectrum arising from primordial non-Gaussianity. In the plane parallel approximation only the first four even $\ell$ multipoles have non-zero values, and we present explicit analytical expressions…
We measure the growth rate and its evolution using the anisotropic clustering of the extended Baryon Oscillation Spectroscopic Survey (eBOSS) Data Release 14 (DR14) quasar sample, which includes $148\,659$ quasars covering the wide redshift range of $0.8 < z < 2.2$ and a sky area of $2112.90$ $\rm deg^2$. To optimise measurements we deploy a redshift-dependent weighting scheme, which allows us to avoid binning, and perform the data analysis consistently including the redshift evolution across the sample. We perform the analysis in Fourier space, and use the redshift evolving power spectrum mul…
Redshift-space distortions (RSD) in galaxy redshift surveys generally break both the isotropy and homogeneity of galaxy distribution. While the former aspect is particularly highlighted as a probe of growth of structure induced by gravity, the latter aspect, often quoted as wide-angle RSD but ignored in most of the cases, will become important and critical to account for as increasing the statistical precision in next-generation surveys. However, the impact of wide-angle RSD has been mostly studied using linear perturbation theory. In this paper, employing the Zel'dovich approximation, i.e., f…
We apply the Minkowski tensor statistics to three dimensional Gaussian random fields. Minkowski tensors contain information regarding the orientation and shape of excursion sets, that is not present in the scalar Minkowski functionals. They can be used to quantify globally preferred directions, and additionally provide information on the mean shape of subsets of a field. This makes them ideal statistics to measure the anisotropic signal generated by redshift space distortion in the low redshift matter density field. We review the definition of the Minkowski tensor statistics in three dimension…
Redshift-space distortions are a sensitive probe of the growth of large-scale structure. In the linear regime, redshift-space distortions are fully described by the multipoles of the two-point correlation function. In the nonlinear regime, however, higher-order statistics are needed to capture the full information of the galaxy density field. In this paper, we show that the redshift-space line correlation function--which is a measure of Fourier phase correlations--is sensitive to the nonlinear growth of the density and velocity fields and to the nonlinear mapping between real and redshift spac…
We study the effect of large-scale tidal fields on internal halo properties using a set of N-body simulations. We measure significant cross-correlations between large-scale tidal fields and several non-scalar halo properties: shapes, velocity dispersion, and angular momentum. Selection effects that couple to these non-scalar halo properties can produce anisotropic clustering even in real-space. We investigate the size of this effect and show that it can produce a non-zero quadrupole similar in size to the one generated by linear redshift-space distortions (RSD). Finally, we investigate the clu…
The pairwise velocity generating function $G$ has deep connection with both the pairwise velocity probability distribution function and modeling of redshift space distortion (RSD). Its implementation into RSD modeling is often faciliated by expansion into series of pairwise velocity moments $\langle v_{12}^n\rangle$. Motivated by the logrithmic transformation of the cosmic density field, we investigate an alternative expansion into series of pairwise velocity cumulants $\langle v_{12}^n\rangle_c$ . We numerically evaluate the convergence rate of the two expansions, with three $3072^3$ particle…
We use a range of cosmological data to constrain phenomenological modifications to general relativity on cosmological scales, through modifications to the Poisson and lensing equations. We include cosmic microwave background anisotropy measurements from the Planck satellite, cosmic shear from CFHTLenS and DES-SV, and redshift-space distortions from BOSS data release 12 and the 6dF galaxy survey. We find no evidence of departures from general relativity, with the modified gravity parameters constrained to $Σ_0 = 0.05^{+0.05}_{-0.07}$ and $μ_0 = -0.10^{+0.20}_{-0.16}$, where $Σ_0$ and $μ_0$ refe…
We measure the scale dependence and redshift dependence of 21 cm line emitted from the neutral hydrogen gas at redshift 1<z<5 using full cosmological hydrodynamic simulations by taking the ratios between the power spectra of HI-dark matter cross correlation and dark matter auto-correlation. The neutral hydrogen distribution is computed in full cosmological hydrodynamic simulations including star formation and supernova feedback under a uniform ultra-violet background radiation. We find a significant scale dependence of HI bias at z>3 on scales of k>1h/Mpc, but it is roughly constant at lower r…
Observations of galaxy clustering are made in redshift space, which results in distortions to the underlying isotropic distribution of galaxies. These redshift-space distortions (RSD) not only degrade important features of the matter density field, such as the baryonic acoustic oscillation (BAO) peaks, but also pose challenges for the theoretical modelling of observational probes. Here we introduce an iterative nonlinear reconstruction algorithm to remove RSD effects from galaxy clustering measurements, and assess its performance by using mock galaxy catalogues. The new method is found to be a…
The gravitational coupling between large- and small-scale density perturbations leads to anisotropic distortions to the local small-scale matter fluctuations. Such local anisotropic distortions can be used to reconstruct the large-scale matter distribution, known as tidal reconstruction. In this paper, we apply the tidal reconstruction methods to simulated galaxies in redshift space. We find that redshift-space distortions lead to anisotropic reconstruction results. While the reconstructed radial modes are more noisy mainly due to the small-scale velocity dispersion, the transverse modes are s…
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 int…
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 (RSD) in the Limber approximation. This allows for a speed-up in computation time, and we emphasise 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 w…
We explore and compare different ways large-scale structure observables in redshift-space and real space can be connected. These include direct computation in Lagrangian space, moment expansions and two formulations of the streaming model. We derive for the first time a Fourier space version of the streaming model, which yields an algebraic relation between the real- and redshift-space power spectra which can be compared to earlier, phenomenological models. By considering the redshift-space 2-point function in both configuration and Fourier space, we show how to generalize the Gaussian streami…
We study the predictions for the matter redshift-space power spectrum and correlation function of a Lagrangian-space Gaussian ansatz introduced in a previous work. This model is a natural extension of the Zeldovich approximation, where the displacement and velocity power spectra are determined by the equations of motion, instead of being set equal to the linear power spectrum. It does not contain any free parameter. As for the real-space statistics, we find that this Lagrangian-space approach is much more efficient for the correlation functions than for the power spectra. The damping of the BA…
