LAUSR

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 ω m ( 0 ≤ ω m 1 ) and the geometric displacement field in Lyra’s geometry, we find that the displacement vector field engenders an effective time-dependent gravitational constant G eff constrained in the region 0 G eff ( t ) ≤ G . We show that the effective equation-of-state parameter ω eff ( 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.