Integrable vectorial nonmetricity gravity is shown to be equivalent to purely kinetic quadratic k-essence, which fits late-time data as well as ΛCDM.
Integrability and Cosmological Solutions in Einstein-aether-Weyl theory
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abstract
We consider a Lorentz violating scalar field cosmological model given by the modified Einstein-aether theory defined in Weyl integrable geometry. The existence of exact and analytic solutions is investigated for the case of a spatially flat Friedmann--Lema\^{\i}tre--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.
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Geometric formulation of $k$-essence and late-time acceleration
Integrable vectorial nonmetricity gravity is shown to be equivalent to purely kinetic quadratic k-essence, which fits late-time data as well as ΛCDM.