Testing Einstein gravity with cosmic growth and expansion

We test Einstein gravity using cosmological observations of both expansion and structure growth, including the latest data from supernovae (Union2.1), cosmic microwave background (WMAP7), weak lensing (CFHTLS) and the peculiar velocity of galaxies (WiggleZ). We fit modified gravity parameters of the generalized Poisson equations simultaneously with the effective equation of state for the background evolution, exploring the covariances and model dependence. The results show that general relativity is a good fit to the combined data. Using a Padé approximant form for the gravity deviations accurately captures the time and scale dependence for theories like $f(R)$ and DGP gravity, and weights high and low redshift probes fairly. For current observations, cosmic growth and expansion can be fit simultaneously with little degradation in accuracy, while removing the possibility of bias from holding one aspect fixed.

Figure 1

1D PDF for the MG amplitude $c$ from the latest observational data. The left panel shows the scale-independent case, with $s$ either fixed to 1 or marginalized over, and the background either fixed to $\Lambda \mathrm{CDM}$ or marginalized over $w_0$, $w_a$. The right panel shows the analogous curves for the scale-dependent ($k^2$) case. All PDFs are consistent with $c=0$, corresponding to GR.

Figure 2

68% and 95% C.L. joint constraints on the MG parameters. Filled and unfilled contours represent the cases when the background cosmology is fixed to $\Lambda \mathrm{CDM}$, and the effective dark energy equation of state parameters $w_0$, $w_a$ are allowed to vary, respectively. GR corresponds to $c=0$, when the value of $s$ is moot. The left (right) panel corresponds to the scale-independent (-dependent, $k^2$) case.

Figure 3

The reconstructed $w(z)$ with 68% C.L. error are shown allowing for modified gravity (marginalized over $c$, $s$) in the scale-independent (left panel) and scale-dependent $k^2$ (right panel) cases by the filled bands. The reconstruction for true dark energy, with gravity fixed to GR, is shown by the dash-dotted curves, the same in each panel.