Dynamics and cosmological constraints on Brans-Dicke cosmology

Abstract

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{ń}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 ${\omega }_{\text{BD}}=-0.8606_{-0.1341}^{+0.8281}$, for an oscillatory approach to the de Sitter state ${\omega }_{\text{BD}}=-1.1103_{-0.1729}^{+0.1872}$, and for the transient de Sitter state represented by a saddle-type critical point ${\omega }_{\text{BD}}=-2.3837_{-4.5459}^{+0.4588}$. We obtain the mass of the Brans-Dicke scalar field at the present epoch as $m_{\varphi }\sim H_0$. The Bayesian methods of model comparison are used to discriminate between obtained models. We show that observational data point toward vales of the ${\omega }_{\text{BD}}$ parameter close to the value suggested by the low-energy limit of the bosonic string theory.

arXiv comment13 pages, 5 figs; (v2) new analysis, refs. added, PhysRevD (in press)

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