Interacting quintessence from new formalism of gravitoelectromagnetism formulated on a geometrical scalar–tensor gauge theory of gravity

Abstract

We derive an interacting quintessence model on the framework of a recently introduced new class of geometrical scalar-tensor theories of gravity formulated on a Weyl-Integrable geometry, where the gravitational sector is described by both a scalar and a tensor metric field. By using a Palatini variational principle we construct a scalar-tensor action invariant under the Weyl symmetry group of the background geometry, which in the Einstein-Riemann frame leads to a gravitoelectromagnetic theory. We use the gauge freedom of the theory and the fact that the Weyl scalar field couples with matter fields to formulate an interacting quintessential model with a non-canonical kinetic term, where the quintessence field has a geometrical origin. Due to this non-canonicity we obtain that the mass of the quintessence field in the past epochs results to be small enough not to cause modifications in the baryon to photon ratio during nucleosynthesis.

Non-perturbative gauge invariant scalar fluctuations of the metric in Higgs inflation from complex geometrical scalar–tensor theory of gravity

“…where f = f (x α ) is a well defined complex function of the space-time coordinates. Unfortunately, as it was shown in [19,23,24] the action (2) does not remain invariant under the symmetry group of the geometry (4)- (6). Thus it is proposed the action…”

“…However, for the particular choice f = −ϕ, we can define the effective metric h µν = ḡµν = e f +f † g µν , such that with respect to this new metric the condition (3) reduces to the effective Riemannian metricity condition: ∇ λ h αβ = 0. Consequently, the set (M, ḡ, φ = 0, φ † = 0, Bα ) = (M, h, Bα ) receives the name of Riemann frame [19,23,24]. It is important to emphasize here that in both frames geodesics are Weyl invariant and thus these frames are different from the tradictional Jordan and Einstein frames in scalar-tensor theories of gravity [22].…”

“…In this framework the inflaton scalar field is introduced as a part of the affine structure of the geometry and thus it results to be related to Weyl scalar field [19][20][21]. Some other topics like (2 + 1) gravity models, inflation and cosmic magnetic fields, quintessence and some cosmological models have been studied in this approach [22][23][24][25].…”

Higgs inflation in complex geometrical scalar-tensor theory of gravity

“…Hence, the ambiguity about the nature of the scalar field that usually arises in standard scalar-tensor theories and the controversy between the two frames is not present in this new approach [15,17,18]. In the framework of this theory topics like (2 + 1) gravity models, inflationary cosmology and cosmic magnetic fields, quintessence and some cosmological models have been studied [19][20][21][22].…”

Scalar field unification of interacting viscous dark fluid from a geometrical scalar–tensor theory of gravity

“…Different applications of these theories have been done. For example, inflationary cosmology [32,33], quintessence, cosmic magnetic fields, and some cosmological models have been studied topics of these theories [34][35][36].…”