Brans-Dicke gravity with scalar matter coupling and its cosmological probe

In this work we investigate the Brans-Dicke gravity with self-interacting potential and potentialess model, the scalar field depends on redshift. But our model includes both potential and coupling, so we put the redshift dependence of the scalar in other form. Making use of CMB, BAO and SNIa observational data, we probe the model and determine model parameters, but our main concern is the dependence of model parameters on the temporal and spatial scales. Therefore we separate the probes for high(CMB) and low (BAO + SN) redshift observational data.