Cosmological constraint on Brans-Dicke Model
  We combine new Cosmic Microwave Background (CMB) data from Planck with Baryon
Acoustic Oscillation (BAO) data to constrain the Brans-Dicke (BD) theory, in
which the gravitational constant $G$ evolves with time. Observations of type Ia
supernovae (SNeIa) provide another important set of cosmological data, as they
may be regarded as standard candles after some empirical corrections. However,
in theories that include modified gravity like the BD theory, there is some
risk and complication when using the SNIa data because their luminosity may
depend on $G$. In this paper, we assume a power law relation between the SNIa
luminosity and $G$, but treat the power index as a free parameter. We then test
whether the difference in distances measured with SNIa data and BAO data can be
reduced in such a model. We also constrain the BD theory and cosmological
parameters by making a global fit with the CMB, BAO and SNIa data set. For the
CMB+BAO+SNIa data set, we find $0.08\times10^{-2} < \zeta <0.33\times10^{-2} $
at the 68\% confidence level (CL) and $-0.01\times10^{-2} <\zeta <0.43\times
10^{-2} $ at the 95\% CL, where $\zeta$ is related to the {BD} parameter
$\omega$ by $\zeta=\ln(1+1/\omega)$.
