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Shortly after its discovery, General Relativity (GR) was applied to predict the behavior of our Universe on the largest scales, and later became the foundation of modern cosmology. Its validity has been verified on a range of scales and environments from the Solar system to merging black holes. However, experimental confirmations of GR on cosmological scales have so far lacked the accuracy one would hope for -- its applications on those scales being largely based on extrapolation and its validity sometimes questioned in the shadow of the unexpected cosmic acceleration. Future astronomical instruments surveying the distribution and evolution of galaxies over substantial portions of the observable Universe, such as the Dark Energy Spectroscopic Instrument (DESI), will be able to measure the fingerprints of gravity and their statistical power will allow strong constraints on alternatives to GR. In this paper, based on a set of $N$-body simulations and mock galaxy catalogs, we study the predictions of a number of traditional and novel estimators beyond linear redshift distortions in two well-studied modified gravity models, chameleon $f(R)$ gravity and a braneworld model, and the potential of testing these deviations from GR using DESI. These estimators employ a wide array of statistical properties of the galaxy and the underlying dark matter field, including two-point and higher-order statistics, environmental dependence, redshift space distortions and weak lensing. We find that they hold promising power for testing GR to unprecedented precision. The major future challenge is to make realistic, simulation-based mock galaxy catalogs for both GR and alternative models to fully exploit the statistic power of the DESI survey and to better understand the impact of key systematic effects. Using these, we identify future simulation and analysis needs for gravity tests using DESI., Comment: 69 pages, 36 figures, 6 tables; accepted for publication in JCAP. The modified gravity HOD galaxy catalogues used in this paper can be downloaded from http://icc.dur.ac.uk/data/, by searching for the title of this paper from the dataset table

We present an analytic approach to lift the mass-anisotropy degeneracy in clusters of galaxies by utilizing the line-of-sight velocity dispersion of clustered galaxies jointly with weak lensing inferred masses. More specifically, we solve the spherical Jeans equation by assuming a simple relation between the line-of-sight velocity dispersion and the radial velocity dispersion and recast the Jeans equation as a Bernoulli differential equation that has a well-known analytic solution. We first test our method in cosmological N-body simulations and then derive the anisotropy profiles for 35 archival data galaxy clusters with an average redshift of $\langle {z}_{c}\rangle =0.25$. The resulting profiles yield a weighted average global value of $\langle \beta (0.2\leqslant R/{R}_{200}\leqslant 1)\rangle =0.35\pm 0.28$ (stat) \pm 0.15 (sys). This indicates that clustered galaxies tend to globally fall on radially anisotropic orbits. We note that this is the first attempt to derive velocity anisotropy profiles for a cluster sample of this size utilizing joint dynamical and weak lensing data, Comment: 10 pages, 5 figures, published in ApJ

We use N-body simulations to quantify how the escape velocity in cluster-sized halos maps to the gravitational potential in a LambdaCDM universe. Using spherical density-potential pairs and the Poisson equation, we find that the matter density inferred gravitational potential profile predicts the escape velocity profile to within a few percent accuracy for group and cluster-sized halos (10^13 < M_200 < 10^15 M_sun, with respect to the critical density). The accuracy holds from just outside the core to beyond the virial radius. We show the importance of explicitly incorporating a cosmological constant when inferring the potential from the Poisson equation. We consider three density models and find that the Einasto and Gamma profiles provide a better joint estimate of the density and potential profiles than the Navarro, Frenk and White profile, which fails to accurately represent the escape velocity. For individual halos, the 1 sigma scatter between the measured escape velocity and the density-inferred potential profile is small (<5%). Finally, while the sub-halos show 15% biases in their representation of the particle velocity dispersion profile, the sub-halo escape velocity profile matches the dark matter escape velocity profile to high accuracy with no evidence for velocity bias outside 0.4r_200., Comment: Published in the Astrophysical Journal

We present a novel approach to constrain accelerating cosmologies with galaxy cluster phase spaces. With the Fisher matrix formalism we forecast constraints on the cosmological parameters that describe the cosmological expansion history. We find that our probe has the potential of providing constraints comparable to, or even stronger than, those from other cosmological probes. More specifically, with 1000 (100) clusters uniformly distributed in the redshift range $ 0 \leq z \leq 0.8$, after applying a conservative $80\%$ mass scatter prior on each cluster and marginalizing over all other parameters, we forecast $1\sigma$ constraints on the dark energy equation of state $w$ and matter density parameter $\Omega_M$ of $\sigma_w = 0.138 (0.431)$ and $\sigma_{\Omega_M} = 0.007 (0.025)$ in a flat universe. Assuming 40\% mass scatter and adding a prior on the Hubble constant we can achieve a constraint on the CPL parametrization of the dark energy equation of state parameters $w_0$ and $w_a$ with 100 clusters in the same redshift range: $\sigma_{w_0} = 0.191 $ and $\sigma_{w_a} = 2.712$. Dropping the assumption of flatness and assuming $w=-1$ we also attain competitive constraints on the matter and dark energy density parameters: $\sigma_{\Omega_M} = 0.101$ and $\sigma_{\Omega_{\Lambda}} = 0.197$ for 100 clusters uniformly distributed in the range $ 0 \leq z \leq 0.8$ after applying a prior on the Hubble constant. We also discuss various observational strategies for tightening constraints in both the near and far future., Comment: 20 pages, 13 figures, accepted for publication in PRD. In v2 we now take into account the cosmological dependence on the radial distance scale -- which breaks the degeneracy in the w0-wa parameter space; we also now take into account the mass-cosmological covariance in our prior matrix. For our Fisher matrix code, see https://github.com/alejostark/phase_space_cosmo_fisher

We derive the escape velocity profile for an Einasto density field in an accelerating universe and demonstrate its physical viability by comparing theoretical expectations to both light-cone data generated from N-body simulations and archival data on 20 galaxy clusters. We demonstrate that the projection function ($g(\beta )$) is deemed physically viable only for the theoretical expectation that includes a cosmology-dependent term. Using simulations, we show that the inferred velocity anisotropy is more than 6{\sigma} away from the expected value for the theoretical profile that ignores the acceleration of the universe. In the archival data, we constrain the average velocity anisotropy parameter of a sample of 20 clusters to be $\beta ={0.248}_{-0.360}^{+0.164}$ at the 68% confidence level. Lastly, we briefly discuss how our analytic model may be used as a novel cosmological probe based on galaxy clusters., Comment: 10 pages, 5 figures, accepted to ApJ

Modified theories of gravity provide us with a unique opportunity to generate innovative tests of gravity. In Chameleon f(R) gravity, the gravitational potential differs from the weak-field limit of general relativity (GR) in a mass dependent way. We develop a probe of gravity which compares high mass clusters, where Chameleon effects are weak, to low mass clusters, where the effects can be strong. We utilize the escape velocity edges in the radius/velocity phase space to infer the gravitational potential profiles on scales of 0.3-1 virial radii. We show that the escape edges of low mass clusters are enhanced compared to GR, where the magnitude of the difference depends on the background field value |fR0|. We validate our probe using N-body simulations and simulated light cone galaxy data. For a DESI (Dark Energy Spectroscopic Instrument) Bright Galaxy Sample, including observational systematics, projection effects, and cosmic variance, our test can differentiate between GR and Chameleon f(R) gravity models, |fR0| = 4e-6 (2e-6) at > 5{\sigma} (> 2{\sigma}), more than an order of magnitude better than current cluster-scale constraints., Comment: 9 pages, 4 figures, accepted to PRD