Abstract
We study the cosmology of dark energy in an extended theory of gravity in Lyra’s geometry. By analyzing a possible phenomenological interaction between the matter field with a constant equation-of-state parameter ωm (0≤ωm<1) and the geometric displacement field in Lyra’s geometry, we find that the displacement vector field engenders an effective time-dependent gravitational constant Geff constrained in the region 0<Geff(t)≤G. We show that the effective equation-of-state parameter ωeff(t) evolves in the same way as the effective time-dependent gravitational constant which, by decreasing with time, can give rise to the late-time cosmic acceleration with ω=-1 crossing in a flat Robertson-Walker background without adding dynamical ghost mode.
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