Testing Dvali-Gabadadze-Porrati Gravity with Planck

Abstract: Recently, the Planck collaboration has released the first cosmological papers providing the highest resolution, full sky, maps of the cosmic microwave background (CMB) temperature anisotropies. In this paper we study a phenomenological model which interpolates between the pure $\Lambda$CDM model and the Dvali-Gabadadze-Porrati (DGP) braneworld model with an additional parameter $\alpha$. Firstly, we calculate the "distance information" of Planck data which includes the "shift parameter" $R$, the "acoustic scale" $l_A$, and the photon decoupling epoch $z_\ast$ in different cosmological models and find that this information is almost independent on the input models we use. Then, we compare the constraints on the free parameter $\alpha$ of the DGP model from the "distance information" of Planck and WMAP data and find that the Planck data with high precision do not improve the constraint on $\alpha$, but give the higher median value and the better limit on the current matter density fraction $\Omega_m$. Then, combining the "distance information" of Planck measurement, baryon acoustic oscillations (BAO), type Ia supernovae (SNIa) and the prior on the current Hubble constant (HST), we obtain the tight constraint on the parameter $\alpha < 0.20$ at $95\%$ confidence level, which implies that the flat DGP model has been ruled out by the current cosmological data. Finally, we allow the additional parameter $\alpha < 0$ in our calculations and interestingly obtain $\alpha=-0.29\pm0.20$ ($68\%$ C.L.), which means the current data slightly favor the effective equation of state $w_{\rm eff}<-1$. More importantly, the tension between constraints on $H_0$ from different observational data has been eased.