Nöther's symmetries and exact solutions in flat non-minimally coupled cosmological models

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.

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“…which are similar to the solutions given by Capozziello & de Ritis (1994). Furthermore for n = 2 and c 1 = 1/4, we obtain the solutions…”

Section: Solutionsupporting

confidence: 84%

Exact scalar-tensor cosmological solutions via Noether symmetry

Belinchón

Harkó

Mak

2016

Astrophys Space Sci

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“…(65) We have plotted the quantities a, φ and the deceleration parameter q defined as q = This solution has been already obtained one by Capozziello and the Ritis [31], with A = 0 :…”

Section: Noether Symmetriesmentioning

confidence: 96%

Exact scalar–tensor cosmological models

Belinchón

Harkó

Mak

2017

Int. J. Mod. Phys. D

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Scalar-tensor gravitational theories are important extensions of standard general relativity, which can explain both the initial inflationary evolution, as well as the late accelerating expansion of the Universe. In the present paper we investigate the cosmological solution of a scalar-tensor gravitational theory, in which the scalar field φ couples to the geometry via an arbitrary function F (φ). The kinetic energy of the scalar field as well as its self-interaction potential V (φ) are also included in the gravitational action. By using a standard mathematical procedure, the Lie group approach, and Noether symmetry techniques, we obtain several exact solutions of the gravitational field equations describing the time evolutions of a flat Friedman-Robertson-Walker Universe in the framework of the scalar-tensor gravity. The obtained solutions can describe both accelerating and decelerating phases during the cosmological expansion of the Universe.

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“…This method underlies f (R)-gravity. [1][2] This theory of gravity could allow to explain Dark Energy (DE) and Dark Matter (DM) by changing the geometry of a space-time and each scale demonstrates its specific geometry. This fact fully agrees with the early spirit of GR that could not act in the same way at all scales.…”

Section: Introductionmentioning

confidence: 99%