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.
Categories: astro-ph.CO gr-qc hep-th