Testing general relativity with cosmological large scale structure

Abstract

In this paper I investigate the possibility to test Einstein's equations with observations of cosmological large scale structure. I first show that we have not tested the equations in observations concerning only the homogeneous and isotropic Universe. I then show with several examples how we can do better when considering the fluctuations of both, the energy momentum tensor and the metric. This is illustrated with galaxy number counts, intensity mapping and cosmic shear, three examples that are by no means exhaustive.

Keywords: Cosmological Surveys; Cosmology; General Relativity; Large Scale Structure.

Fig. 1

The distance-redshift relation is shown. The variable plotted in the vertical axis is $2.5{log}_{10}[d_L(z)/d_L^{\mathrm{Milne}}(z)]$, where $d_L^{\mathrm{Milne}}(z)$ is the luminosity distance in an empty universe which only contains negative curvature, a so called ’Milne universe’. Figure from [9]

Fig. 2

Measurements of $f{\sigma }_8$ at different redshifts from different surveys. The grey line shows the behaviour of $f(z){\sigma }_8(z)$ for the best fit $\mathrm{\Lambda }$CDM model from Planck. Figure from [10]