Testing gravity on cosmological scales with cosmic shear, cosmic microwave background anisotropies, and redshift-space distortions

We use a range of cosmological data to constrain phenomenological modifications to general relativity on cosmological scales, through modifications to the Poisson and lensing equations. We include cosmic microwave background anisotropy measurements from the Planck satellite, cosmic shear from CFHTLenS and DES-SV, and redshift-space distortions from BOSS data release 12 and the 6dF galaxy survey. We find no evidence of departures from general relativity, with the modified gravity parameters constrained to ${\mathrm{\Sigma }}_0=0.05_{-0.07}^{+0.05}$ and ${\mu }_0=-0.10_{-0.16}^{+0.20}$, where ${\mathrm{\Sigma }}_0$ and ${\mu }_0$ refer to deviations from general relativity today and are defined to be zero in general relativity. We also forecast the sensitivity to those parameters of the full five-year Dark Energy Survey and of an experiment like the Large Synoptic Survey Telescope, showing a substantial expected improvement in the constraint on ${\mathrm{\Sigma }}_0$.

Figure 1

The redshift evolution of ${\mathrm{\Sigma }}_0$ and ${\mu }_0$ in blue for a value of 0.5 at $z=0$. The kernels for CFHTLenS $W_{\mathrm{CFHTLenS}}$ and the CMB lensing $W_{\kappa }$ are shown in orange and green respectively, normalized by their maximum.

Figure 2

Angular 2-point correlation function ${\xi }_{+}(\theta )$ measurements from the full CFHTLenS sample used in Ref. [22] in redshift bin 3 (upper panel) and DES-SV in Ref. [23] (lower panel). The black curve represents the theoretical ${\xi }_{+}(\theta )$ for the case of general relativity [i.e., $({\mathrm{\Sigma }}_0,{\mu }_0)=(0,0)$]. In the upper panel, the blue dot-dashed curve shows ${\xi }_{+}(\theta )$ with $({\mathrm{\Sigma }}_0,{\mu }_0)=(0.5,0)$ and the red dashed curve $({\mathrm{\Sigma }}_0,{\mu }_0)=(0,0.5)$.

Figure 3

68% and 95% confidence contours on the modified gravity parameters ${\mathrm{\Sigma }}_0$ and ${\mu }_0$ using all the ${\xi }_{\pm }$ CFHTLenS measurements. Green shows marginalization over all cosmological parameters and systematics in green. Grey ignores the presence of a shear calibration bias, red ignores the presence of photometric redshift bias, and blue ignores the presence of intrinsic alignment.

Figure 4

The combination $f{\sigma }_8$ as a function of redshift $z$ for general relativity in black, ${\mu }_0=0.5$, $-0.2$, $-0.5$ respectively in blue dotted-dashed, red dashed and green dotted. The leftmost red point is the measurement from 6dFGS and the black points from BOSS DR12. The theory curves are uniformly shifted up or down when the power spectrum amplitude is varied.

Figure 5

The 1D posterior distribution of ${\mu }_0$, using BOSS DR12 data alone in black and combined with 6dFGS in red.

Figure 6

Theoretical temperature correlations for different values of ${\mathrm{\Sigma }}_0$ and ${\mu }_0$. The general relativity case is the black curve while ${\mathrm{\Sigma }}_0=-0.5$ corresponds to the red (dashed) curve and ${\mu }_0=0.5$ to the blue (dash-dotted) line.

Figure 7

68% and 95% confidence contours on ${\mathrm{\Sigma }}_0$ and ${\mu }_0$, using temperature and polarization Planck likelihood in red, and the same adding the Planck lensing likelihood in blue.

Figure 8

68% and 95% confidence contours on ${\mathrm{\Sigma }}_0$ and ${\mu }_0$ combining RSD data (BOSS $\mathrm{DR}12+6\mathrm{dFGS}$), CMB data ($\mathrm{TT}+\mathrm{lowP}+\mathrm{CMB}$ lensing from Planck) and cosmic shear data (CFHTLenS in blue and DES-SV in red).

Figure 9

Forecasted 68% and 95% confidence contours on $({\mathrm{\Sigma }}_0,{\mu }_0)$ for a DES Y5-like like survey in blue and for LSST-like in green.

Figure 10

Forecasted 68% and 95% confidence contours on $({\mathrm{\Sigma }}_0,{\mu }_0)$ for a future DES Y5 like survey, ignoring intrinsic alignment in green and taking it into account in blue.