A discriminating probe of gravity at cosmological scales

Abstract

The standard cosmological model is based on general relativity and includes dark matter and dark energy. An important prediction of this model is a fixed relationship between the gravitational potentials responsible for gravitational lensing and the matter overdensity. Alternative theories of gravity often make different predictions for this relationship. We propose a set of measurements which can test the lensing/matter relationship, thereby distinguishing between dark energy/matter models and models in which gravity differs from general relativity. Planned optical, infrared and radio galaxy and lensing surveys will be able to measure $E_G$, an observational quantity whose expectation value is equal to the ratio of the Laplacian of the Newtonian potentials to the peculiar velocity divergence, to percent accuracy. We show that this will easily separate alternatives such as $Λ$CDM, DGP, TeVeS and $f(R)$ gravity.

Figures (1)

• Figure 1: $E_G$ as a smoking gun of gravity. Error estimation is based on $\Lambda$CDM and error bars are centered on the $\Lambda$CDM prediction (black solid straight line). We only show those $k$ modes well in the linear regime. For clarity, we shift the error bars of LAMOST/AS2+LSST and ADEPT+LSST slightly rightward. Irregularities in the error-bars are caused by irregularities in the available discrete ${\bf k}$ modes of redshift distortion. Dotted lines are the results of a flat DGP model with $\Omega_0=0.2$. Dashed lines are for $f(R)=-\lambda_1 H_0^2\exp(-R/\lambda_2H_0^2)$ with $\lambda_2=100$. Differences in expansion histories of these models are of percent level at $z<2$ and are not the main cause of differences in $E_G$. Solid lines with wiggles are for TeVeS with $K_B=0.08,0.09,0.1$, where the lines with most significant wiggles have $K_B=0.1$.