Observational tests of modified gravity

Abstract

Modifications of general relativity provide an alternative explanation to dark energy for the observed acceleration of the Universe. Modified gravity theories have richer observational consequences for large scale structures than conventional dark energy models, in that different observables are not described by a single growth factor even in the linear regime. We examine the relationships between perturbations in the metric potentials, density and velocity fields, and discuss strategies for measuring them using gravitational lensing, galaxy cluster abundances, galaxy clustering/dynamics, and the integrated Sachs-Wolfe effect. We show how a broad class of gravity theories can be tested by combining these probes. A robust way to interpret observations is by constraining two key functions: the ratio of the two metric potentials, and the ratio of the gravitational ''constant'' in the Poisson equation to Newton's constant. We also discuss quasilinear effects that carry signatures of gravity, such as through induced three-point correlations. Clustering of dark energy can mimic features of modified gravity theories and thus confuse the search for distinct signatures of such theories. It can produce pressure perturbations and anisotropic stresses, which break the equality between the two metric potentials even in general relativity. With these two extra degrees of freedom, can a clustered dark energy model mimic modified gravity models in all observational tests? We show with specific examples that observational constraints on both the metric potentials and density perturbations can in principle distinguish modifications of gravity from dark energy models. We compare our result with other recent studies that have slightly different assumptions (and apparently contradictory conclusions). Modifications of general relativity provide an alternative explanation to dark energy for the observed acceleration of the Universe. Modified gravity theories have richer observational consequences for largescale structures than conventional dark energy models, in that different observables are not described by a single growth factor even in the linear regime. We examine the relationships between perturbations in the metric potentials, density and velocity fields, and discuss strategies for measuring them using gravitational lensing, galaxy cluster abundances, galaxy clustering/dynamics, and the integrated Sachs-Wolfe effect. We show how a broad class of gravity theories can be tested by combining these probes. A robust way to interpret observations is by constraining two key functions: the ratio of the two metric potentials, and the ratio of the gravitational ''constant'' in the Poisson equation to Newton's constant. We also discuss quasilinear effects that carry signatures of gravity, such as through induced three-point correlations. Clustering of dark energy can mimic features of modified gravity theories and thus confuse the search for distinct signatures of such theories. It can produce pressure perturbations and anisotropi...

Beyond the cosmological standard model

“…In general the scale force causes the dynamical masses of halos inferred from the virial theorem or hydrostatic equilibrium can be significantly larger than the lensing (or true) masses (see, for example, [953,997]). However, the force modifications can depend on halo mass and environment, so it is not straightforward to use dynamical and lensing masses to infer the maximal deviation in Φ/Ψ.…”

“…We summarize the primary observables that provide tests of gravity on cosmological scales in this sub-section, and consider galaxy and cluster scale tests in the following subsection. We follow the treatment of Jain & Zhang [953]. [954].…”

Observational probes of cosmic acceleration

“…More generally, many theories with f (R) modifications of the gravitational action can be written in a mathematically equivalent form of GR plus a scalar field with specified properties (Chiba, 2003;Kunz and Sapone, 2007). Relative to expectations for a cosmological constant or a simple scalar field model, models in which dark matter decays into dark energy can produce a mismatch between the histories of expansion and structure growth while maintaining GR (e.g., Jain and Zhang 2008;Wei and Zhang 2008). Thus, even perfect measurements of all relevant observables may not uniquely locate the explanation of cosmic acceleration in the gravitational or stress-energy sector.…”

Testing gravity using large-scale redshift-space distortions

“…The large-scale structure we see traced by the distribution of galaxies arises through gravitational instability, which amplifies primordial fluctuations that originated in the very early Universe; the rate at which structure grows from small perturbations offers a key discriminant between cosmological models, as different models predict measurable differences in the growth rate of large-scale structure with cosmic time (e.g. Jain & Zhang 2007;Song & Koyama 2009;Song & Percival 2009). For instance, dark energy models in which general relativity is unmodified predict different large-scale structure formation compared to Modified Gravity models with the same background expansion (e.g.…”