Distance-redshift and growth-redshift relations as two windows on acceleration and gravitation: Dark energy or new gravity?

Small distortions in the observed shapes of distant galaxies, a cosmic shear due to gravitational lensing, can be used to simultaneously determine the distance-redshift relation, $r(z)$, and the density contrast growth factor, $g(z)$. Both of these functions are sensitive probes of the acceleration. Their simultaneous determination allows for a consistency test and provides sensitivity to physics beyond the standard dark energy paradigm.

Figure 1

Dependence of the $z=1$ shear auto power spectrum on $g(z)$ and $r(z)$. There are $n-1$ more auto power spectra and $n(n-1)/2$ cross power spectra not shown here. The solid line is the shear power spectrum for sources at $z=1$. The dashed lines show the contributions to this shear power spectrum from lens slices of width $\Delta z=0.2$ centered at $z=0.1$, 0.3, 0.5, 0.7 and 0.9. Their sum gives the solid line. The lower panel shows the $z=0.5$ contribution again (dashed line), how it would look with an increase in $g(z=0.5)$ (dotted line) and how it would look with an increase in $r(z=0.5)$ (dot-dashed line).

Figure 2

Reconstructed distances (left panels), and growth factors (right panels). The lower left panel shows the fractional residual distances, $[r(z)-r_{\mathrm{fid}}(z)]/r_{\mathrm{fid}}(z)$, where $r(z)$ are the reconstructed distances and $r_{\mathrm{fid}}(z)$ are the distances in the fiducial DGP model. The lower right panel shows the residual growth factor, $g(z)-g_{\mathrm{fid}}(z)$. The curves in the right panels are $g_{\mathrm{fid}}(z)$ (solid) and $g(z)$ for the Einstein gravity model (dashed) with the same $H(z)$ and ${\rho }_m$ as the DGP model. Although these two models have the same $r(z)$ they are distinguishable by their significantly different growth factors.