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Changes in the law of gravity have far-reaching implications for the formation and evolution of galaxy clusters, and appear as peculiar signatures in their mass-observable relations, structural properties, internal dynamics, and abundance. We review the outstanding progress made in recent years towards constraining deviations from General Relativity with galaxy clusters, and give an overview of the yet untapped information becoming accessible with forthcoming surveys that will map large portions of the sky in great detail and unprecedented depth.
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In modified gravity theories that seek to explain cosmic acceleration, dwarf galaxies in low density environments can be subject to enhanced forces. The class of scalar-tensor theories, which includes f(R) gravity, predict such a force enhancement (massive galaxies like the Milky Way can evade it through a screening mechanism that protects the interior of the galaxy from this fifth force). We study observable deviations from GR in the disks of late-type dwarf galaxies moving under gravity. The fifth-force acts on the dark matter and HI gas disk, but not on the stellar disk owing to the self-screening of main sequence stars. We find four distinct observable effects in such disk galaxies: 1. A displacement of the stellar disk from the HI disk. 2. Warping of the stellar disk along the direction of the external force. 3. Enhancement of the rotation curve measured from the HI gas compared to that of the stellar disk. 4. Asymmetry in the rotation curve of the stellar disk. We estimate that the spatial effects can be up to 1 kpc and the rotation velocity effects about 10 km/s in infalling dwarf galaxies. Such deviations are measurable: we expect that with a careful analysis of a sample of nearby dwarf galaxies one can improve astrophysical constraints on gravity theories by over three orders of magnitude, and even solar system constraints by one order of magnitude. Thus effective tests of gravity along the lines suggested by Hui et al (2009) and Jain (2011) can be carried out with low-redshift galaxies, though care must be exercised in understanding possible complications from astrophysical effects.
Modifications of general relativity provide an alternative explanation to dark energy for the observed acceleration of the universe. We review recent developments in modified gravity theories, focusing on higher dimensional approaches and chameleon/f(R) theories. We classify these models in terms of the screening mechanisms that enable such theories to approach general relativity on small scales (and thus satisfy solar system constraints). We describe general features of the modified Friedman equation in such theories. The second half of this review describes experimental tests of gravity in light of the new theoretical approaches. We summarize the high precision tests of gravity on laboratory and solar system scales. We describe in some detail tests on astrophysical scales ranging from ~kpc (galaxy scales) to ~Gpc (large-scale structure). These tests rely on the growth and inter-relationship of perturbations in the metric potentials, density and velocity fields which can be measured using gravitational lensing, galaxy cluster abundances, galaxy clustering and the Integrated Sachs-Wolfe effect. A robust way to interpret observations is by constraining effective parameters, such as the ratio of the two metric potentials. Currently tests of gravity on astrophysical scales are in the early stages --- we summarize these tests and discuss the interesting prospects for new tests in the coming decade.
Modifications to gravity can provide attractive alternatives to the dark components of the standard model of cosmology. These modifications to general relativity (GR) must be hidden at small scales where theory is well tested, and so one naturally looks to the large scales in order to detect any deviations from GR. One particularly promising avenue in testing gravity at cosmological scales is within the anisotropy of galaxy clustering in redshift space. This thesis presents a framework for consistently constructing large scale structure observables in redshift space for gravitational theories that include an additional scalar degree of freedom, specifically, the Horndeski class of theories with a generalized potential term. The relevance of such a framework in the context of next generation spectroscopic surveys is then investigated using N-body simulations. The thesis concludes with ongoing and recently completed extensions to this framework, including interacting dark energy models and the effective field theory of large scale structure.
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.
We present the radial distribution of the dark matter in two massive, X-ray luminous galaxy clusters, Abell~2142 and Abell~2319, and compare it with the quantity predicted as apparent manifestation of the baryonic mass in the context of the Emergent Gravity scenario, recently suggested from Verlinde (2016). Thanks to the observational strategy of the xmm Cluster Outskirt Programme (X-COP), using the X-ray emission mapped with xmm and the SZ signal in the Planck survey, we recover the gas density, temperature and thermal pressure profiles up to $sim R_{200}$, allowing to constrain at unprecedented level the total mass through the hydrostatic equilibrium equation. We show that, also including systematic uncertainties related to the X-ray based mass modelling, the apparent dark matter shows a radial profile that has a shape different from the traditional dark matter distribution, with larger discrepancies (by a factor 2--3) in the inner ($r<200$ kpc) clusters regions and a remarkable agreement only across $R_{500}$.
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