  Recently, a new alternative vector theory of gravity has been proposed which
assumes that universe has fixed background Euclidean geometry and gravity is a
vector field that alters this geometry [Phys. Scr. 92, 125001 (2017)]. It has
been shown that vector gravity passes all available gravitational tests and
yields, with no free parameters, the value of cosmological constant in
agreement with observations. Here we obtain substantially simplified
gravitational field equations of vector gravity which are more suitable for
analytical and numerical analyses. We also provide a detailed explanation why
in vector gravity in the reference frame of observer that takes a snapshot of
the universe at time $t_0$ the ratio of the cosmological constant to the
critical density is equal to 2/3 at $t=t_0$. We also show that dark energy does
not affect universe evolution in the co-evolving reference frame. Thus, in
reality, universe is expanding at a continually decelerating rate, with
expansion asymptotically approaching zero.
