  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.
