We investigate observational constraints on the Brans-Dicke cosmological model using observational data coming from distant supernovae type Ia , the Hubble function H ( z ) measurements , information coming from the Alcock-Paczyński test , and baryon acoustic oscillations .
Our analysis is based on the modified Friedmann function resulting form dynamical investigations of Brans-Dicke cosmology in the vicinity of a de Sitter state .
The qualitative theory of dynamical systems enables us to obtain three different behaviors in the vicinity of this state .
We find for a linear approach to the de Sitter state \omega _ { \textrm { \tiny BD } } = -0.8606 ^ { +0.8281 } _ { -0.1341 } , for an oscillatory approach to the de Sitter state \omega _ { \textrm { \tiny BD } } = -1.1103 ^ { +0.1872 } _ { -0.1729 } , and for the transient de Sitter state represented by a saddle-type critical point \omega _ { \textrm { \tiny BD } } = -2.3837 ^ { +0.4588 } _ { -4.5459 } .
We obtain the mass of the Brans-Dicke scalar field at the present epoch as m _ { \phi } \sim H _ { 0 } .
The Bayesian methods of model comparison are used to discriminate between obtained models .
We show that observational data point toward vales of the \omega _ { \textrm { \tiny BD } } parameter close to the value suggested by the low-energy limit of the bosonic string theory .