Conservation laws and exact solutions in Brans–Dicke cosmology with a scalar field

Abstract

Scalar-tensor theories have drawn the attention of cosmologist for the past few years because they can provide mechanism to explain the observable phenomena. Moreover, the results of scalar-tensor theories can be applied in higher-order theories of gravity. In this work, we consider a Brans-Dicke scalar field cosmological model that includes a second scalar field minimally coupled to gravity. For the second scalar field we consider the two cases that there exist and there is not any interaction with the Brans-Dicke scalar field. For the two models of our consideration we prove the existence of scaling and de Sitter solutions. Furthermore, we perform an Obsiannikov's classification for the field equations, where we find all the point and contact transformations which leave the gravitational Action Integral invariant. Conservation laws are determined and we show how these can be applied to infer about the integrability of the cosmological models and find new analytic solutions. 95.35.+d, 95.36.+x

Generalized Brans-Dicke cosmology, noether symmetries and quantization

“…The role played by the dilaton field and by parameter ω can be put under investigation, to clarify the scope of these cosmologies. What we learn, in general, is that the results depend on the gravitational sources chosen [3][4][5][6][7]. To begin, what can be considered as gravitational source is a Klein-Gordon field with a self-interacting potential.…”

“…The generalization of the BD theory mentioned above can bring new possibilities in order to describe primordial-universe properties. We therefore investigate the role of a self-interacting bosonic field in a generalized BD early universe, as an extension of the analysis made in [4], with a ω parameter seen as a function of the model fields that also allows a quantum formulation. In particular, the Noether symmetries strategy permits to determine which functional form parameter ω possesses, imposing those conditions on the model equations of motion.…”

Lie symmetries for the cosmological field equations in brane-world gravitywith bulk scalar field

“…In cosmology, symmetry analysis has been widely employed to constrain the unknown functions of the theory and construct conservation laws using Noether's second theorem [26]. The derivation of conservation laws has led to the discovery of new analytic and exact solutions for various cosmological models, including those in scalar field theory [33,34], scalar-tensor theory [35][36][37], and modified theories of gravity [38,39], as discussed in the review article [40]. With this in mind, the structure of the paper is organized accordingly.…”

Analytic Solutions of Brans-Dicke Cosmology: Early Inflation and Late Time Accelerated Expansion

“…Parametric exact solutions for potential free universe filled with ordinary matter were given in [41]. On the other hand Noether's theorem was used to determine conservation laws in Brans-Dicke cosmology which includes two scalar fields and exact solutions were found [42]. An exact solutions of modified Brans-Dicke theory was studied in [43].…”