We analyze the clustering of large scale structure in the Universe in a model independent method, accounting for anisotropic effects along and transverse to the line of sight. The Baryon Oscillation Spectroscopy Survey Data Release 11 provides a large sample of 690,000 galaxies, allowing determination of the Hubble expansion H, angular distance DA, and growth rate GΘ at an effective redshift of z = 0.57. After careful bias and convergence studies of the effects from small scale clustering, we find that cutting transverse separations below 40 Mpc/h delivers robust results while smaller scale data leads to a bias due to unmodelled nonlinear and velocity effects. The converged results are in agreement with concordance ΛCDM cosmology, general relativity, and minimal neutrino mass, all within the 68% confidence level. We also present results separately for the northern and southern hemisphere sky, finding a slight tension in the growth rate -potentially a signature of anisotropic stress, or just covariance with small scale velocities -but within 68% CL.PACS numbers: 98.80.-k,95.36.+x
Abstract. Both multi-streaming (random motion) and bulk motion cause the Finger-ofGod (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 f σ 8 − σ v degeneracy in RSD cosmology, and has the potential of significantly improving cosmological constraints.
Our observations of the Universe are fundamentally anisotropic, with data from galaxies separated transverse to the line of sight coming from the same epoch while that from galaxies separated parallel to the line of sight coming from different times. Moreover, galaxy velocities along the line of sight change their redshift, giving redshift space distortions. We perform a full two-dimensional anisotropy analysis of galaxy clustering data, fitting in a substantially model independent manner the angular diameter distance DA, Hubble parameter H, and growth rate dδ/d ln a without assuming a dark energy model. The results demonstrate consistency with ΛCDM expansion and growth, hence also testing general relativity. We also point out the interpretation dependence of the effective redshift z eff , and its cosmological impact for next generation surveys. 95.36.+x
The observed power spectrum in redshift space appears distorted due to the peculiar motion of galaxies, known as redshift-space distortions (RSD). While all the effects in RSD are accounted for by the simple mapping formula from real to redshift spaces, accurately modeling redshift-space power spectrum is rather difficult due to the non-perturbative properties of the mapping. Still, however, a perturbative treatment may be applied to the power spectrum at large-scales, and on top of a careful modeling of the Finger-of-God effect caused by the small-scale random motion, the redshift-space power spectrum can be expressed as a series of expansion which contains the higher-order correlations of density and velocity fields. In our previous work [JCAP 8 (Aug., 2016) 050], we provide a perturbation-theory inspired model for power spectrum in which the higher-order correlations are evaluated directly from the cosmological N -body simulations. Adopting a simple Gaussian ansatz for Finger-of-God effect, the model is shown to quantitatively describe the simulation results. Here, we further push this approach, and present an accurate power spectrum template which can be used to estimate the growth of structure as a key to probe gravity on cosmological scales. Based on the simulations, we first calibrate the uncertainties and systematics in the pertrubation theory calculation in a fiducial cosmological model. Then, using the scaling relations, the calibrated power spectrum template is applied to a different cosmological model. We demonstrate that with our new template, the best-fitted growth functions are shown to reproduce the fiducial values in a good accuracy of 1 % at k < 0.18 h Mpc −1 for cosmologies with different Hubble parameters.
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. Theoretical RSD model for halo clusteringUnderstanding the halo clustering in redshift space is a key stepstone towards theoretically describing the observed galaxy clustering in the Universe. In our previous work [96], the RSD model for dark matter clustering in redshift space was studied in detail. The model has been proved to accurately reconstruct the linear growth rate within 1% at k < 0.18 h Mpc −1 for simulations of different cosmologies with different Hubble parameters [97]. This theoretical RSD model will be applied to the halo clustering case in this manuscript. We will describe the RSD model in this section. Besides, the halo density bias model [108] and halo velocity bias model [105] adopted in this paper will be presented as well. The advanced TNS model for halosMatter distribution in the universe is inhomogeneous at small scales. The gravitational attraction arising from this inhomogeneity perturbs galaxies and causes their motions deviating from the Hubble flow. These deviations, named peculiar velocities of galaxies, disturb the galaxy redshifts and hence the galaxy distribution in redshift space in an anisotropic way.
The anisotropic galaxy clustering of large scale structure observed by the Baryon Oscillation Spectroscopic Survey Data Release 11 is analyzed to probe the sum of neutrino mass in the small mν < ∼ 1 eV limit in which the early broadband shape determined before the last scattering surface is immune from the variation of mν. The signature of mν is imprinted on the altered shape of the power spectrum at later epoch, which provides an opportunity to access the non-trivial mν through the measured anisotropic correlation function in redshift space (hereafter RSD instead of Redshift Space Distortion). The non-linear RSD corrections with massive neutrinos in the quasi linear regime are approximately estimated using one-loop order terms computed by tomographic linear solutions. We suggest a new approach to probe mν simultaneously with all other distance measures and coherent growth functions, exploiting this deformation of the early broadband shape of the spectrum at later epoch. If the origin of cosmic acceleration is unknown, mν is poorly determined after marginalising over all other observables. However, we find that the measured distances and coherent growth functions are minimally affected by the presence of mild neutrino mass. Although the standard model of cosmic acceleration is assumed to be the cosmological constant, the constraint on mν is little improved. Interestingly, the measured CMB distance to the last scattering surface sharply slices the degeneracy between the matter content and mν, and the hidden mν is excavated to be mν = 0.19 +0.28 −0.17 eV which is different from massless neutrino more than 68% confidence.PACS numbers: 98.80.-k,95.36.+x
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