Dynamics and cosmological constraints on Brans-Dicke cosmology

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-Paczy{\'n}ski 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 $\omega_{\textrm{BD}}=-0.8606^{+0.8281}_{-0.1341}$, for an oscillatory approach to the de Sitter state $\omega_{\textrm{BD}}=-1.1103^{+0.1872}_{-0.1729}$, and for the transient de Sitter state represented by a saddle-type critical point $\omega_{\textrm{BD}}=-2.3837^{+0.4588}_{-4.5459}$. 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 $\omega_{\textrm{BD}}$ parameter close to the value suggested by the low-energy limit of the bosonic string theory.