Model independent tests of cosmic growth versus expansion

We use Gaussian processes to map the expansion history of the universe in a model-independent manner from the Union2.1 supernovae data and then apply these reconstructed results to solve for the growth history. By comparing this to Baryon Oscillation Spectroscopic Survey and WiggleZ large-scale structure data we examine whether growth is determined wholly by expansion, with the measured gravitational growth index testing gravity without assuming a model for dark energy. A further model-independent analysis looks for redshift-dependent deviations of growth from the general relativity solution without assuming the growth index form. Both approaches give results consistent with general relativity.

Figure 1

68 and 95% joint confidence limits on $\gamma$ and ${\Omega }_{m,0}$ are shown derived without assuming a dark energy model, using current supernovae distance and galaxy clustering growth data. The left contour of each pair has ${\sigma }_{8,0}=0.801$, the WMAP7 concordance value [22], and the right has ${\sigma }_{8,0}=0.78$ to show the effect of a small shift.

Figure 2

Reconstruction of the growth rate $f{\sigma }_8(z)$ is shown for the case when fixing $\gamma =0.55$ (light green curves) or allowing it to float (dark red curves). Current growth data is overplotted and we have fixed ${\sigma }_{8,0}=0.801$.

Figure 3

Limits on the amplitude of the deviation ${\sigma }_f$ from the GR growth relation (with model-independent dark energy) are shown in two-dimensional joint confidence contours with the present matter density.