Lensed cosmic microwave background constraints on post-general-relativity parameters

The constraints on departures from general relativity (GR) at cosmological length scales due to cosmic microwave background (CMB) data are discussed. The departure from GR is measured by the ratio, parametrized as $1+{\varpi }_0(1+z{)}^{-S}$, between the gravitational potentials conventionally appearing in the geodesic equation and the Poisson equation. Current CMB data indicate ${\varpi }_0={1.67}_{-1.87}^{+3.07}$ at the $2\sigma$ confidence level, while $S$ remains unconstrained. The departure from GR affects the lensing conversion of E-mode into B-mode polarization. Hence, the lensing measurements from CMBpol alone should be able to improve the constraint to ${\varpi }_0<0.52$ ($2\sigma$) for a fiducial ${\varpi }_0=0$ model independent of $S$.

Figure 1

The effect of the modified gravity parameters on the temperature, B-mode polarization, and lensing potential power spectra for the best-fit $\Lambda \mathrm{CDM}$ model from $\mathrm{WMAP}5+\mathrm{ACBAR}$ [18]; we also show the measurement error for B-mode polarization measurements with Planck and CMBpol and the CMBpol noise for lensing reconstruction (up to $l=700$).

Figure 2

Two-dimensional contours at $1\sigma$ (dark) and $2\sigma$ (light) in the plane ${\varpi }_0\mathrm{\text{−}}S$ for WMAP+ACBAR (top panel) and CMBpol (bottom panel). We marginalized over the other cosmological parameters considered in the analysis. The closing contours in the upper panel are due to the lacking of sampling points for the low-likelihood region at $S\sim 0$.