Cosmological Tests of General Relativity with Future Tomographic Surveys

Future weak lensing surveys will map the evolution of matter perturbations and gravitational potentials, yielding a new test of general relativity on cosmic scales. They will probe the relations between matter overdensities, local curvature, and the Newtonian potential. These relations can be modified in alternative gravity theories or by the effects of massive neutrinos or exotic dark energy fluids. We introduce two functions of time and scale which account for any such modifications in the linear regime. We use a principal component analysis to find the eigenmodes of these functions that cosmological data will constrain. The number of constrained modes gives a model-independent forecast of how many parameters describing deviations from general relativity could be constrained, along with $w(z)$. The modes’ scale and time dependence tell us which theoretical models will be better tested.

Figure 1

Uncertainties in the eigenmodes for current data and for future data sets including LSST (DES). The two upper panels show modes of $\mu$ and $\gamma$ with mutual marginalization. The lower panel shows uncertainties in the combined modes. The solid lines and the shaded region denote the thresholds $T_1$, $T_2$, and $T_3$. The filled symbols denote the redshift-dependent modes. In the lower panel, the dashed lines show the uncertainties for $\mu$ with $\gamma$ fixed.

Figure 2

Eigensurfaces for $\mu$ and $\gamma$, with mutual marginalization, for LSST (DES) along with Planck and JDEM.