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

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 > 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 > 3 × 1011 M⊙ (hosting galaxies with M* > 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.

We study the non-linear evolution of baryon acoustic oscillations in the matter power spectrum and correlation function from the improved perturbation theory (PT). Based on the framework of renormalized PT, we apply the {\it closure approximation} that truncates the infinite series of loop contributions at one-loop order, and obtain a closed set of integral equations for power spectrum and non-linear propagator. The resultant integral expressions keep important non-perturbative properties which can dramatically improve the prediction of non-linear power spectrum. Employing the Born approximation, we then derive the analytic expressions for non-linear power spectrum and the predictions are made for non-linear evolution of baryon acoustic oscillations in power spectrum and correlation function. A detailed comparison between improved PT results and N-body simulations shows that a percent-level agreement is achieved in a certain range in power spectrum and in a rather wider range in correlation function. Combining a model of non-linear redshift-space distortion, we also evaluate the power spectrum and correlation function in correlation function. In contrast to the results in real space, the agreement between N-body simulations and improved PT predictions tends to be worse, and a more elaborate modeling for redshift-space distortion needs to be developed. Nevertheless, with currently existing model, we find that the prediction of correlation function has a sufficient accuracy compared with the cosmic-variance errors for future galaxy surveys with volume of a few (Gpc/h)^3 at z>=0.5.

Massive spectroscopic surveys will measure the redshift space distortion\n(RSD) induced by galaxy peculiar velocity to unprecedented accuracy. We develop\na new method to improve the RSD modeling and to carry out robust reconstruction\nof the 3D large scale peculiar velocity through galaxy redshift surveys, in\nlight of RSD. (1) We propose a mathematically unique and physically motivated\ndecomposition of peculiar velocity into three eigen-components of different\norigins, different scale dependences and different impacts on RSD. (2) This\ndecomposition has the potential to simplify and improve the RSD modeling. We\nderive a new formula for the redshift space power spectrum. Under the velocity\ndecomposition scheme, all high order Gaussian corrections and non-Gaussian\ncorrection of order $\\delta^3$ can be taken into account without introducing\nextra model uncertainties. We find that the leading order contribution $\\propto\n(1+f\\tilde{W}(k)u^2)^2$ differs from the Kaiser formula by a function\n$\\tilde{W}(k)\\leq 1$. We hence identify a significant systematic error causing\nunderestimation of the structure growth parameter $f$ by as much as $O(10%)$\neven at relatively large scale $k=0.1h/$Mpc. The velocity decomposition also\nreveals the three origins of the finger of God (FOG) effect. (3) The velocity\ndecomposition clarifies issues in peculiar velocity reconstruction through 3D\ngalaxy distribution. We discuss two possible ways to carry out the velocity\nreconstruction. Both use the otherwise troublesome RSD in velocity\nreconstruction as a valuable source of information. Both have the advantage to\nrender the reconstruction of a stochastic 3D field into the reconstruction of a\ndeterministic window function $W^s(k,u)$ of limited degrees of\nfreedom...[abridged]\n

Future spectroscopic and photometric surveys will measure accurate positions and shapes of an increasing number of galaxies. In the previous paper of this series we studied the effects of Redshift Space Distortions (RSD), baryon acoustic oscillations (BAO) and Weak gravitational Lensing (WL) using angular cross-correlation. Here, we provide a new forecast that explores the contribution of including different observables, physical effects (galaxy bias, WL, RSD, BAO) and approximations (non-linearities, Limber approximation, covariance between probes). The radial information is included by using the cross-correlation of separate narrow redshift bins. For the auto correlation the separation of galaxy pairs is mostly transverse, while the cross-correlations also includes a radial component. We study how this information adds to our figure of merit (FoM), which includes the dark energy equation of state $w(z)$ and the growth history, parameterized by $\gamma$. We show that the Limber approximation and galaxy bias are the most critical ingredients to the modelling of correlations. Adding WL increases our FoM by 4.8, RSD by 2.1 and BAO by 1.3. We also explore how overlapping surveys perform under the different assumption and for different figures of merit. Our qualitative conclusions depend on the survey choices and scales included, but we find some clear tendencies that highlight the importance of combining different probes and can be used to guide and optimise survey strategies.

We have quantified the degree of nonlinearity and stochasticity of the clustering of biased objects using cosmological $N$-body simulations. Adopting the peaks and the halos as representative biasing models, we focused on the two-point correlation of the biased objects, dark matter and their cross-correlation. Especially, we took account of the effect of redshift-space distortion and attempted to clarify the scale dependence and the time dependence by analyzing the biasing factor and the cross-correlation factor. On small scales, stochasticity and nonlinearity become appreciable and strongly object-dependent, especially in redshift space due to the pair-wise velocity dispersion of the biased objects. Nevertheless, an approximation of deterministic linear biasing, $\delta_\mathrm{obj}\simeq b_\mathrm{obj} \delta_\mathrm{mass}$, works reasonably well even in the quasi-linear regime, $r \gtrsim 10\,h^{-1} \textrm{Mpc}$, and linear redshift-space distortion explains the clustering amplitudes in redshift space in this regime.

Forward modeling the galaxy density within the Effective Field Theory of Large Scale Structure (EFT of LSS) enables field-level analyses that are robust to theoretical uncertainties. At the same time, they can maximize the constraining power from galaxy clustering on the scales amenable to perturbation theory. In order to apply the method to galaxy surveys, the forward model must account for the full observational complexity of the data. In this context, a major challenge is the inclusion of redshift space distortions (RSDs) from the peculiar motion of galaxies. Here, we present improvements in the efficiency and accuracy of the RSD modeling in the perturbative LEFTfield forward model. We perform a detailed quantification of the perturbative and numerical error for the prediction of momentum, velocity and the redshift-space matter density. Further, we test the recovery of cosmological parameters at the field level, namely the growth rate f, from simulated halos in redshift space. For a rigorous test and to scan through a wide range of analysis choices, we fix the linear (initial) density field to the known ground truth but marginalize over all unknown bias coefficients and noise amplitudes. With a third-order model for gravity and bias, our results yield < 1 % statistical and < 1.5 % systematic error. The computational cost of the redshift-space forward model is only ∼ 1.5 times of the rest frame equivalent, enabling future field-level inference that simultaneously targets cosmological parameters and the initial matter distribution.

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 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 fσ8(0.6) = 0.48 ± 0.12 and fσ8(0.86) = 0.48 ± 0.10. The additional galaxy-galaxy lensing constraint alleviates galaxy bias and σ8degeneracies, providing direct measurements of f and σ8: [f(0.6),σ8(0.6)] = [0.93 ± 0.22,0.52 ± 0.06] and [f(0.86),σ8(0.86)] = [0.99 ± 0.19,0.48 ± 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, EG, for the first time at z &amp;gt; 0.6. We find values of EG(0.6) = 0.16±0.09 and EG(0.86) = 0.09±0.07, when EGis averaged over scales above 3 h-1Mpc. We find that our EGmeasurements exhibit slightly lower values than expected for standard relativistic gravity in a ΛCDM background, although the results are consistent within 1-2σ.

Redshift space distortions are an important probe of the growth of large-scale structure and for constraining cosmological parameters in general. As galaxy redshift surveys approach per cent level precision in their observations of the two point clustering statistics, it is timely to review what effects baryons and associated processes such as feedback may have on small-scale clustering in redshift space. Contrary to previous studies in the literature, we show using the large-volume Bahamas hydrodynamic simulations that the effect of baryons can be as much as 1 per cent in the $k \sim 0.1\, h\,$Mpc$^{-1}$ range for the monopole and 5 per cent for quadrupole, and that this could rise to as much as 10 per cent at $k \sim 10 \, h\,$Mpc$^{-1}$ in both measurements. For the halo power spectra, this difference can be as much 3-4 per cent in the monopole on scales of $0.05 \lt k \lt 0.3 \, h\,$Mpc$^{-1}$ for 10$^{13}\, h^{-1}$ M$_{\odot }$ haloes. We find that these deviations can be mitigated to the sub- per cent level in the both the monopole and quadrupole up to $k\sim 0.3\, h$ Mpc$^{-1}$ if the baryon corrected halo masses are used to calculate the redshift space power spectra. Finally, we use the cosmo-OWLS simulation suite to explore the changes in the redshift space power spectra with different feedback prescriptions, finding that there is a maximum of 15–20 per cent difference between the redshift space monopole and quadrupole with and without baryons at $k \sim 1\!-\!2\, h\,$Mpc$^{-1}$ within these models.

We present an emulator that accurately predicts the power spectrum of galaxies in redshift space as a function of cosmological parameters. Our emulator is based on a second-order Lagrangian bias expansion that is displaced to Eulerian space using cosmological N-body simulations. Redshift space distortions are then imprinted using the non-linear velocity field of simulated particles and haloes. We build the emulator using a forward neural network trained with the simulations of the BACCO project, which covers an eight-dimensional parameter space including massive neutrinos and dynamical dark energy. We show that our emulator provides unbiased cosmological constraints from the monopole, quadrupole, and hexadecapole of a mock galaxy catalogue that mimics the BOSS-CMASS sample down to non-linear scales ($k\sim 0.6{h\, {\rm Mpc}^{-1}}$). This work opens up the possibility of robustly extracting cosmological information from small scales using observations of the large-scale structure of the universe.

The peculiar velocities of galaxies distort the clustering pattern anisotropically in redshift space. This effect on the statistics of isodensity contours is examined by linear theory. The statistics considered in this paper are the three- and two-dimensional genus of isodensity contours, the area of isodensity contours, the length of isodensity contours in the 2-dimensional slice and the level crossing statistics on the line. We find that all these statistics in redshift space as functions of density threshold of contours have the same shape as in real space. The redshift space distortion affects only amplitudes of these statistics. The three-dimensional genus and the area hardly suffer from the redshift space distortion for $0 \leq \Omega b^{-5/3} \leq 1$, where $b$ is a linear bias parameter. The other statistics are defined in one- or two-dimensional slices of the sample volume and depend on the direction of these slices relative to the line of sight. This dependence on direction of these statistics provides a way to determine the density parameter of the universe.

The clustering ratio is defined as the ratio between the correlation function and the variance of the smoothed overdensity field. In LCDM cosmologies not accounting for massive neutrinos, it has already been proved to be independent from bias and redshift space distortions on a range of linear scales. It therefore allows for a direct comparison of measurements (from galaxies in redshift space) to predictions (for matter in real space). In this paper we first extend the applicability of such properties of the clustering ratio to cosmologies that include massive neutrinos, by performing tests against simulated data. We then investigate the constraining power of the clustering ratio when cosmological parameters such as the total neutrino mass and the equation of state of dark energy are left free. We analyse the joint posterior distribution of the parameters that must satisfy, at the same time, the measurements of the galaxy clustering ratio in the SDSS DR12, and the angular power spectrum of temperature and polarization anisotropies of the CMB measured by the Planck satellite. We find the clustering ratio to be very sensitive to the CDM density parameter, but not very much so to the total neutrino mass. Lastly, we forecast the constraining power the clustering ratio will achieve with forthcoming surveys, predicting the amplitude of its errors in a Euclid-like galaxy survey. In this case, we find it is expected to improve the constraint at 95% level on the CDM density by 40% and on the total neutrino mass by 14%.

The velocity profile of galaxies around voids is a key ingredient for redshift space distortion (RSD) measurements made using the void–galaxy correlation function. In this paper, we use simulations to test whether the velocity profile of the tracers used to find the voids matches the velocity profile of the dark matter around these voids. A mismatch is expected and found in the inner part of voids, where tracers are very sparse. We discuss how this difference is caused by a selection effect where the void centre positions are correlated to the particular realization of the sparse tracers and their spatial distribution. In turn, this then affects the RSD void–galaxy correlation analysis. We show this by evaluating the Jacobian of the real to redshift space mapping using the tracer or matter velocity profile. Differences of the order of 20 per cent in the velocity profile translate into differences of the order of few per cent in the Jacobian. This small discrepancy propagates to the monopole and quadrupole of the void–tracer correlation function, producing modifications of comparable magnitude to those from changes in fσ8 at the level of the statistical uncertainties from current analyses.

We report on the first measurement of the three-point function with the position-dependent correlation function from the SDSS-III Baryon Oscillation Spectroscopic Survey (BOSS) Data Release 10 CMASS sample. This new observable measures the correlation between two-point functions of galaxy pairs within different subvolumes, ξ̂(ř,řL), where řL is the location of a subvolume, and the corresponding mean overdensities, δ̄(řL). This correlation, which we call the “integrated three-point function”, iζ(r)≡⟨ξ̂(ř,řL)δ̄(řL)⟩, measures a three-point function of two short- and one long-wavelength modes, and is generated by nonlinear gravitational evolution and possibly also by the physics of inflation. The iζ(r) measured from the BOSS data lies within the scatter of those from the mock galaxy catalogs in redshift space, yielding a ten-percent-level determination of the amplitude of iζ(r). The tree-level perturbation theory in redshift space predicts how this amplitude depends on the linear and quadratic nonlinear galaxy bias parameters (b1 and b2), as well as on the amplitude and linear growth rate of matter fluctuations (σ8 and f). Combining iζ(r) with the constraints on b1σ8 and fσ8 from the global two-point correlation function and that on σ8 from the weak lensing signal of BOSS galaxies, we measure b2=0.41±0.41 (68% C.L.) assuming standard perturbation theory at the tree level and the local bias model.

The highly redshifted 21 cm line of neutral hydrogen has become recognized as\na unique probe of cosmology from relatively low redshifts (z ~ 1) up through\nthe Epoch of Reionization (z ~ 8) and even beyond. To date, most work has\nfocused on recovering the spherically averaged power spectrum of the 21 cm\nsignal, since this approach maximizes the signal-to-noise in the initial\nmeasurement. However, like galaxy surveys, the 21 cm signal is affected by\nredshift space distortions, and is inherently anisotropic between the\nline-of-sight and transverse directions. A measurement of this anisotropy can\nyield unique cosmological information, potentially even isolating the matter\npower spectrum from astrophysical effects. However, in interferometric\nmeasurements, foregrounds also have an anisotropic footprint between the\nline-of-sight and transverse directions: the so-called foreground "wedge".\nAlthough foreground subtraction techniques are actively being developed, a\n"foreground avoidance" approach of simply ignoring contaminated modes has\narguably proven most successful to date. In this work, we analyze the effect of\nthis foreground anisotropy in recovering the redshift space distortion\nsignature in 21 cm measurements at both high and intermediate redshifts. We\nfind the foreground wedge corrupts nearly all of the redshift space signal for\neven the largest proposed EoR experiments (HERA and the SKA), making\ncosmological information unrecoverable without foreground subtraction. The\nsituation is somewhat improved at lower redshifts, where the redshift-dependent\nmapping from observed coordinates to cosmological coordinates significantly\nreduces the size of the wedge. Using only foreground avoidance, we find that a\nlarge experiment like CHIME can place non-trivial constraints on cosmological\nparameters.\n

The observed density field in redshift space is directly affected by the radial motions generated from mass fluctuations outside the volumeoccupied by a given galaxy redshift survey. These motions introduce redshift space anisotropies which are more pronounced at larger distances from thesurvey's center, thus offering clues to the nature of mass fluctuations on super-survey scales. Furthermore, we note that all estimates of the growthfactor derived from redshift space distortions are based on relations which explicitly assume that the velocity field is generated by mass fluctuationsinside the survey volume. This may cause uncertainties in these estimates which are on the order of a few percent.