Is modified gravity required by observations? An empirical consistency test of dark energy models

We apply the technique of parameter-splitting to existing cosmological data sets, to check for a generic failure of dark energy models. Given a dark energy parameter, such as the energy density Omega_Lambda or equation of state w, we split it into two meta-parameters with one controlling geometrical distances, and the other controlling the growth of structure. Observational data spanning Type Ia Supernovae, the cosmic microwave background (CMB), galaxy clustering, and weak gravitational lensing statistics are fit without requiring the two meta-parameters to be equal. This technique checks for inconsistency between different data sets, as well as for internal inconsistency within any one data set (e.g., CMB or lensing statistics) that is sensitive to both geometry and growth. We find that the cosmological constant model is consistent with current data. Theories of modified gravity generally predict a relation between growth and geometry that is different from that of general relativity. Parameter-splitting can be viewed as a crude way to parametrize the space of such theories. Our analysis of current data already appears to put sharp limits on these theories: assuming a flat universe, current data constrain the difference Omega_Lambda(geom) - Omega_Lambda(grow) to be -0.0044 +/- 0.0058 (68% C.L.); allowing the equation of state w to vary, the difference w(geom) - w(grow) is constrained to be 0.37 +/- 0.37 (68% C.L.). Interestingly, the region w(grow) > w(geom), which should be generically favored by theories that slow structure formation relative to general relativity, is quite restricted by data already. We find w(grow) < -0.80 at 2 sigma. As an example, the best-fit flat Dvali-Gabadadze-Porrati (DGP) model approximated by our parametrization lies beyond the 3 sigma contour for constraints from all the data sets.