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Recently, a new alternative vector theory of gravity has been proposed whichassumes that universe has fixed background Euclidean geometry and gravity is avector field that alters this geometry [Phys. Scr. 92, 125001 (2017)]. It hasbeen shown that vector gravity passes all available gravitational tests andyields, with no free parameters, the value of cosmological constant inagreement with observations. Here we obtain substantially simplifiedgravitational field equations of vector gravity which are more suitable foranalytical and numerical analyses. We also provide a detailed explanation whyin vector gravity in the reference frame of observer that takes a snapshot ofthe universe at time $t_0$ the ratio of the cosmological constant to thecritical density is equal to 2/3 at $t=t_0$. We also show that dark energy doesnot affect universe evolution in the co-evolving reference frame. Thus, inreality, universe is expanding at a continually decelerating rate, withexpansion asymptotically approaching zero.

Simplified equations for gravitational field in the vector theory of gravity and new insights into dark energy