Observational Tests of Modified Gravity

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). Disciplines Physical Sciences and Mathematics | Physics Comments Suggested Citation: B. Jain and P. Zhang. (2008). "Observational tests of modified gravity." Physical Review D. 78, 063503. © 2008 The American Physical Society http://dx.doi.org/10.1103/PhysRevD.78.063503 This journal article is available at ScholarlyCommons: http://repository.upenn.edu/physics_papers/85 Observational tests of modified gravity Bhuvnesh Jain and Pengjie Zhang* Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA Shanghai Astronomical Observatory, Shanghai, China 200030 Joint Institute for Galaxy and Cosmology (JOINGC) of Shanghai Astronomical Observatory (SHAO) and University of Science and Technology of China (USTC), 80 Nandan Road, Shanghai, China 200030 (Received 8 October 2007; published 2 September 2008) 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 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). DOI: 10.1103/PhysRevD.78.063503 PACS numbers: 98.65.Dx, 04.50.Kd, 95.36.+x