Exact scalar-tensor cosmological solutions via Noether symmetry

Abstract

In this paper, we investigate the Noether symmetries of a generalized scalar-tensor, Brans-Dicke type cosmological model, in which we consider explicit scalar field dependent couplings to the Ricci scalar, and to the scalar field kinetic energy, respectively. We also include the scalar field self-interaction potential into the gravitational action. From the condition of the vanishing of the Lie derivative of the gravitational cosmological Lagrangian with respect to a given vector field we obtain three cosmological solutions describing the time evolution of a spatially flat Friedman-RobertsonWalker Universe filled with a scalar field. The cosmological properties of the solutions are investigated in detail, and it is shown that they can describe a large variety of cosmological evolutions, including models that experience a smooth transition from a decelerating to an accelerating phase.

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

“…From the latter conservation law it follows the radiation solution, a (t) = a 0 t 1 2 , which was found in the previous section. In addition for V (ψ) = V 0 ψ 2 , the field equations are invariant under the action of the Noether point symmetries X 1 P with conservation law (60). We search for contact symmetries and we find that for arbitrary V (ψ), the Killing tensors which provide conservation laws are the metric tensor and the X 2 p ∧ X 2 P with the corresponding conservation laws being the constraint equation (19) and I G 3 = (I 2 ) 2 .…”

Non-minimal coupling influence on the deviation from de Sitter cosmological expansion

“…Scalar-tensor gravity theories are important extensions of GR, which can explain both the initial inflationary evolution, as well as the late accelerating expansion of the Universe. The examples of inflationary models on the basis of scalar-tensor gravity theories with the exact solutions were considered in the works [25][26][27][28][29][30][31]. Also, in the articles [32,33] the equations of cosmological dynamics for STG were reduced to ones for the Einstein gravity in the case of the Friedman-Robertson-Walker metric by a specific choice of the coupling function and the kinetic function.…”

The Exact Solutions Construction in Cosmology Based on Horndeski Gravity

“…Scalar-tensor gravity with non-minimal coupling of a scalar field with curvature are important extensions of GR which can explain the initial inflationary evolution, as well as the late accelerating expansion of the universe [10,11]. The examples of inflationary models on the basis of scalar-tensor gravity (STG) theories with the exact solutions can be found in [10][11][12] and in many other works as well. Furthermore, the transformations of the dynamical equations from models based on STG to ones in frame of GR are presented in [13].…”