Abstract
We study the Einstein-aether theory in Weyl integrable geometry. The scalar field which defines the Weyl affine connection is introduced in the gravitational field equation. We end up with an Einstein-aether scalar field model where the interaction between the scalar field and the aether field has a geometric origin. The scalar field plays a significant role in the evolution of the gravitational field equations. We focus our study on the case of homogeneous and isotropic background spacetimes and study their dynamical evolution for various cosmological models.
Highlights
Alternative theories of gravity [1], where the Lorentz symmetry is violated, have drawn the attention of gravitation physicists in the last decades
We considered the extension of Einstein-aether theory in Weyl geometry
The scalar field plays a significant role in the geometry since it defines
Summary
Alternative theories of gravity [1], where the Lorentz symmetry is violated, have drawn the attention of gravitation physicists in the last decades. It has been proposed a nonminimally coupling of a scalar field with the aether field, where the Einstein-aether coefficients become functions of the scalar field In this model, the inflationary stage is divided into two parts; the Lorentz-violating stage and the standard slow-roll stage. The universe expands as an exact de Sitter spacetime, the inflaton field is rolling down the potential Another Einstein-aether scalarfield inflaton model coupled bilinearly to the expansion of the aether was proposed by Donnelly and Jacobson in [30]. As we shall see from the following analysis, in our approach we are able to introduce a geometric scalar field coupled to the aether field, by considering the Einstein-æther action in Weyl geometry.
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