The dynamics of the Brans-Dicke theory with a scalar field potential function is investigated. We show that the system with a barotropic matter content can be reduced to an autonomous three-dimensional dynamical system. For an arbitrary potential function we found the values of the Brans-Dicke parameter for which a global attractor in the phase space representing de Sitter state exists. Using linearized solutions in the vicinity of this critical point we show that the evolution of the Universe mimics the ΛCDM model. From the recent Planck satellite data, we obtain constraints on the variability of the effective gravitational coupling constant as well as the lower limit of the mass of the Brans-Dicke scalar field at the de Sitter state.

The dynamics of the Brans-Dicke theory with a quadratic scalar field potential function and barotropic matter is investigated. The dynamical system methods are used to reveal complexity of dynamical evolution in homogeneous and isotropic cosmological models. The structure of phase space crucially depends on the parameter of the theory ω BD as well as barotropic matter index w m . In our analysis these parameters are treated as bifurcation parameters. We found sets of values of these parameters which lead to generic evolutional scenarios. We show that in isotropic and homogeneous models in the Brans-Dicke theory with a quadratic potential function the de Sitter state appears naturally. Stability conditions of this state are fully investigated. It is shown that these models can explain accelerated expansion of the Universe without the assumption of the substantial form of dark matter and dark energy. The Poincare construction of compactified phase space with a circle at infinity is used to show that phase space trajectories in a physical region can be equipped with a structure of a vector field on nontrivial topological closed space. For ω BD < −3/2 we show new types of early and late time evolution leading from the anti-de Sitter to the de Sitter state through an asymmetric bounce. In the theory without a ghost we find bouncing solutions and the coexistence of the bounces and the singularity. Following the Peixoto theorem some conclusions about structural stability are drawn.

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 ωBD = −0.8606 −4.5459 . We obtain the mass of the Brans-Dicke scalar field at the present epoch as m φ ∼ H0. The Bayesian methods of model comparison are used to discriminate between obtained models. We show that observational data point toward vales of the ωBD parameter close to the value suggested by the low-energy limit of the bosonic string theory.PACS numbers: 04.50. Kd, 95.36.+x, 95.35.+d

In the paper we investigate observational constraints on coupling to gravity constant parameter ξ using distant supernovae SNIa data, baryon oscillation peak (BOP), the cosmic microwave background radiation (CMBR) shift parameter, and H(z) data set. We estimate the value of this parameter to constrain the extended quintessence models with nonminimally coupled to gravity phantom scalar field. The combined analysis of observational data favors a value of ξ which lies in close neighborhood of the conformal coupling. While our estimations are model dependent they give rise to a indirect bound on the Equivalence Principle.PACS numbers: 98.80. Es, 98.80.Cq, 95.36.+x At the present, scalar fields play the crucial role in modern cosmology. In the inflationary scenario they generate an exponential rate of evolution of the universe as well as a density fluctuations due to vacuum energy.Observations of distant supernovae support the cosmological constant term. But two problems emerge in this context. Namely, the fine tuning and cosmic coincidence problems. The lack of some fundamental mechanism which sets the cosmological constant almost zero is called the cosmological constant problem. The second problem called "cosmic conundrum" is the question why the energy densities of both dark energy and dark matter are nearly equal at the present epoch. One of the solutions to this problem offers the idea of quintessence [1,2] which is a version of the time varying cosmological constant conception.All these models base on the assumption that there is a minimal coupling of scalar field to gravity (ξ = 0). This a priori assumption requires some justification. There are many theoretical arguments suggesting that the non-minimal coupling (NC for short) should be considered. The nonzero ξ comes from quantum corrections [3], renormalization of classical theory that shifts it to one with nonzero ξ [4], in relativity the value of ξ = 1/6 (conformal coupling) is distinguished. Only in this case the Einstein equivalence principle is not violated (for details see [5] The main goal of this paper is a statistical estimation of the coupling parameter from the astronomical observations. For this aim we consider the spatially flat FRW model where the source of gravity is a noninteracting mixture of dust matter and non-minimally coupled phantom scalar field.We treat ξ as a free parameter in the model and we are looking for constraints on it's value from observational cosmology. For simplicity it is assumed a simple and natural form of the potential function of the scalar field. For the vanishing coupling constant (minimal coupling) this potential corresponds to chaotic inflation [9]. This paradigm of inflation can be extended by including NC [6]. Also the scalar field non-minimally coupled to gravity are simple, non-exotic models of phantoms give rise to superacceleration [10]. Tsujikawa and Gumjudpai [11] also investigated constraints on the NC parameter from the CMB observations. Recently Jankiewicz and Kephart [12] applied the method of WKB a...

In this publication we investigate dynamics of a flat FRW cosmological model with a nonminimally coupled scalar field with the coupling term ξRψ 2 in the scalar field action. The quadratic potential function V (ψ) ∝ ψ 2 is assumed. All the evolutional paths are visualized and classified in the phase plane, at which the parameter of non-minimal coupling ξ plays the role of a control parameter. The fragility of global dynamics with respect to changes of the coupling constant is studied in details. We find that the future big rip singularity appearing in the phantom scalar field cosmological models can be avoided due to non-minimal coupling constant effects. We have shown the existence of a finite scale factor singular point (future or past) where the Hubble function as well as its first cosmological time derivative diverge. PACS numbers: 98.80.-k, 98.80.Cq, 95.36.+x I. INTRODUCTIONRecently scalar fields have played a very important role in cosmology. They are used in many phenomenological models like quintessence [1,2]. Scalar fields are also very important in description of dynamics in the loop quantum cosmology, which base on the background independent theory without the canonical notion of time. In this theory one scalar field is chosen as an internal clock for other fields [3]. The scalar fields with a potential function are also very important in modelling of inflation. For example a scalar field with the simplest quadratic potential function was assumed * Electronic address: hrycyna@kul.lublin.pl † Electronic address: uoszydlo@cyf-kr.edu.pl