We analyse the clustering of cosmic large scale structure using a consistent modified gravity perturbation theory, accounting for anisotropic effects along and transverse to the line of sight. The growth factor has a particular scale dependence in f(
R) gravity and we fit for the shape parameter f_{R0} simultaneously with the distance and the large scale (general relativity) limit of the growth function. Using more than 690,000 galaxies in the Baryon Oscillation Spectroscopy Survey Data Release 11, we find no evidence for extra scale dependence, with the 95% confidence upper limit |f_{R0}| <8 times 10^{-4}. Future clustering data, such as from the Dark Energy Spectroscopic Instrument, can use this consistent methodology to impose tighter constraints.
The apparent anisotropies of the galaxy clustering in observable redshift space provide a unique opportunity to simultaneously probe cosmic expansion and gravity on cosmological scales via the Alcock--Paczynski effect and redshift-space distortions.
While the improved theoretical models have been proposed and developed to describe the apparent anisotropic clustering at weakly non-linear scales, the applicability of these models is still limited in the presence of the non--perturbative smearing effect caused by the randomness of the relative velocities. Although the cosmological constraint from the anisotropic clustering will be certainly improved with a more elaborate theoretical model, we here consider an alternative way by using the statistical power of both the power spectrum and bispectrum at large scales. Based on the Fisher matrix analysis, we estimate the benefit of combining the power spectra and bispectra, finding that the constraints on the cosmic expansion and growth of structure will be improved by a factor of two. This compensates for the loss of constraining power using the power spectrum alone due to the randomness of the relative velocities.
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 larg
e sample of 690,000 galaxies, allowing determination of the Hubble expansion H, angular distance D_A, and growth rate G_T 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 LCDM 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.
Baryon acoustic oscillations (BAO), known as one of the largest cosmological objects, is now recognized as standard cosmological tool to measure geometric distances via the Alcock-Paczynski effect, by which the observed BAO exhibits characteristic an
isotropies in addition to the redshift distortions. This implies that once we know the correct distances to the observed BAO, the tip points of baryon acoustic peaks in the anisotropic correlation function of galaxies, $xi(sigma,pi)$, can form a great circle (hereafter 2D BAO circle) in the $sigma$ and $pi$ plane, where $sigma$ and $pi$ are the separation of galaxy pair parallel and perpendicular to the line-of-sight, respectively. This 2D BAO circle remains unchanged under the variations of the unknown galaxy bias and/or coherent motion, while it varies transversely and radially with respect to the variations of $D_A$ and $H^{-1}$, respectively. Hereby the ratio between transverse distance $D_A$ and the radial distance $H^{-1}$ reproduces the intrinsic shape of 2D BAO circle, which is {it a priori} given by the known broadband shape of spectra. All BAO peaks of $xi(sigma,pi)$ are precisely calculated with the improved theoretical model of redshift distortion. We test this broadband Alcock--Paczynski method using BOSS--like mock catalogues. The transverse and radial distances are probed in precision of several percentage fractional errors, and the coherent motion is observed to match with the fiducial values accurately.
The cosmological power spectrum of the coherent matter flow is measured exploiting an improved prescription for the apparent anisotropic clustering pattern in redshift space. New statistical analysis is presented to provide an optimal observational p
latform to link the improved redshift distortion theoretical model to future real datasets. The statistical power as well as robustness of our method are tested against 60 realizations of 8 Gpc/h^3 dark matter simulation maps mocking the precision level of upcoming wide--deep surveys. We showed that we can accurately extract the velocity power spectrum up to quasi linear scales of k~0.1 h/Mpc at z = 0.35 and up to k~0.15 h/Mpc at higher redshifts within a couple of percentage precision level. Our understanding of redshift space distortion is proved to be appropriate for precision cosmology, and our statistical method will guide us to righteous path to meet the real world.
We investigate the direct determination of expansion history using redshift distortions without plugging into detailed cosmological parameters. The observed spectra in redshift space include a mixture of information: fluctuations of density-density a
nd velocity-velocity spectra, and distance measures of perpendicular and parallel components to the line of sight. Unfortunately it is hard to measure all the components simultaneously without any specific prior assumption. Common prior assumptions include a linear/quasi-linear model of redshift distortions or a model for the shape of the power spectra, which eventually breaks down on small scales at later epochs where nonlinear structure formation disturbs coherent growth. The degeneracy breaking, between the effect of cosmic distances and redshift distortions for example, depends on the prior we assume. An alternative approach is to utilize the cosmological principle inscribed in the heart of the Friedmann-Lematre-Robertson-Walker (hereafter FLRW) universe, that is, the specific relation between the angular diameter distance and the Hubble parameter, in this degeneracy breaking. We show that utilizing this FLRW prior early in the step of distinguishing the distance effect from redshift distortions helps us improve the detectability of power spectra and distance measures with no leaning on a combination of other experiments.
We explore the complementarity of weak lensing and galaxy peculiar velocity measurements to better constrain modifications to General Relativity. We find no evidence for deviations from GR on cosmological scales from a combination of peculiar velocit
y measurements (for Luminous Red Galaxies in the Sloan Digital Sky Survey) with weak lensing measurements (from the CFHT Legacy Survey). We provide a Fisher error forecast for a Euclid-like space-based survey including both lensing and peculiar velocity measurements, and show that the expected constraints on modified gravity will be at least an order of magnitude better than with present data, i.e. we will obtain 5% errors on the modified gravity parametrization described here. We also present a model--independent method for constraining modified gravity parameters using tomographic peculiar velocity information, and apply this methodology to the present dataset.
Measuring the statistics of galaxy peculiar velocities using redshift-space distortions is an excellent way of probing the history of structure formation. Because galaxies are expected to act as test particles within the flow of matter, this method a
voids uncertainties due to an unknown galaxy density bias. We show that the parameter combination measured by redshift-space distortions, $fsigma_8^{rm mass}$ provides a good test of dark energy models, even without the knowledge of bias or $sigma_8^{rm mass}$ required to extract $f$ from this measurement (here $f$ is the logarithmic derivative of the linear growth rate, and $sigma_8^{rm mass}$ is the root-mean-square mass fluctuation in spheres with radius $8h^{-1}$Mpc). We argue that redshift-space distortion measurements will help to determine the physics behind the cosmic acceleration, testing whether it is related to dark energy or modified gravity, and will provide an opportunity to test possible dark energy clumping or coupling between dark energy and dark matter. If we can measure galaxy bias in addition, simultaneous measurement of both the overdensity and velocity fields can be used to test the validity of equivalence principle, through the continuity equation.
Using the linear theory of perturbations in General Relativity, we express a set of consistency relations that can be observationally tested with current and future large scale structure surveys. We then outline a stringent model-independent program
to test gravity on cosmological scales. We illustrate the feasibility of such a program by jointly using several observables like peculiar velocities, galaxy clustering and weak gravitational lensing. After addressing possible observational or astrophysical caveats like galaxy bias and redshift uncertainties, we forecast in particular how well one can predict the lensing signal from a cosmic shear survey using an over-lapping galaxy survey. We finally discuss the specific physics probed this way and illustrate how $f(R)$ gravity models would fail such a test.
We construct a consistency test of General Relativity (GR) on cosmological scales. This test enables us to distinguish between the two alternatives to explain the late-time accelerated expansion of the universe, that is, dark energy models based on G
R and modified gravity models without dark energy. We derive the consistency relation in GR which is written only in terms of observables - the Hubble parameter, the density perturbations, the peculiar velocities and the lensing potential. The breakdown of this consistency relation implies that the Newton constant which governs large-scale structure is different from that in the background cosmology, which is a typical feature in modified gravity models. We propose a method to perform this test by reconstructing the weak lensing spectrum from measured density perturbations and peculiar velocities. This reconstruction relies on Poissons equation in GR to convert the density perturbations to the lensing potential. Hence any inconsistency between the reconstructed lensing spectrum and the measured lensing spectrum indicates the failure of GR on cosmological scales. The difficulties in performing this test using actual observations are discussed.
