Abstract
We consider a Lorentz violating scalar field cosmological model given by the modified Einstein-æther theory defined in Weyl integrable geometry. The existence of exact and analytic solutions is investigated for the case of a spatially flat Friedmann–Lemaître–Robertson–Walker background space. We show that the theory admits cosmological solutions of special interests. In addition, we prove that the cosmological field equations admit the Lewis invariant as a second conservation law, which indicates the integrability of the field equations.
Highlights
A plethora of modified or alternative theories to Einstein’s gravity [1,2] have been proposed during the last years in order to explain the cosmological observations
We consider the Einstein-æther theory defined in Weyl integrable geometry [37]
In this work we considered a spatially flat FLRW background space in Einstein-æther theory defined in Weyl integrable geometry
Summary
A plethora of modified or alternative theories to Einstein’s gravity [1,2] have been proposed during the last years in order to explain the cosmological observations. In this work we are interest on the existence of exact and analytic solutions for a Lorentz-violating scalar field cosmological model. A set of differential equations describing a physical system is said to be integrable if there exist a sufficient number of invariant functions such that the dynamical system can be written in algebraic form. we present the cosmological model under consideration which is that of Einstein-æther defined in Weyl integrable geometry assuming a spatially flat Friedmann–Lemaître–Robertson–Walker (FLRW) background space without any matter source terms. we present for the first time analytic and exact solutions for this cosmological model, we focus on the existence of exact solutions where the scale factor describes inflationary models of special interests We obtain those solutions which are determined as the general analytic solutions for the corresponding scalar field potentials.
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