Abstract
The aim of this work is to study a scalar-tensor theory where owing to Palatini’s variational method the space-time is endowed with a geometrical structure of Weyl integrable type. The geometrical nature of the scalar field is related to the non-metricity so that the theory is known as geometrical scalar-tensor. On the framework of Weyl transformations, a non-minimally coupled scalar-tensor theory on the Jordan frame corresponds to a minimally coupled Einstein–Hilbert action on the Einstein frame. The scalar potential is selected by the Noether symmetry approach in order to obtain conserved quantities for the FRW cosmological model. Exact solutions are obtained and analyzed in the context of the cosmological scenarios consistent with an expanding universe. A particular case is matched in each frame and the role of scalar field as a dark energy component is discussed.
Highlights
Einstein’s theory of gravity is constantly being supported by current observational data [1], recent issues such as the accelerated expansion of the Universe and the possible existence of dark matter, can not be fully explained only based on general relativity
We conclude from this figure that in the Jordan frame the deceleration parameter has a positive sign, which may be interpreted as a matter dominated era
We started with the action in the Einstein frame and obtained the action in the Jordan frame through the use of the
Summary
Einstein’s theory of gravity is constantly being supported by current observational data [1], recent issues such as the accelerated expansion of the Universe and the possible existence of dark matter, can not be fully explained only based on general relativity. It was shown that the geometry that naturally appears when a symmetric affine connection is regarded is the so called integrable Weyl geometry, where the scalar field takes part together with the metric tensor in the description of the gravitational field. The potential term is obtained through the Noether symmetry approach, which allows making a choice that leads to a quantity conserved in the model [13,14,15,16] Such a conserved quantity will imply the existence of a cyclic variable useful to find exact solutions for the field equation. We will take the metric signature (+, −, −, −)
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