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

TL;DR

This paper simplifies the gravitational field equations in a vector theory of gravity, providing new insights into dark energy and the universe's expansion, suggesting it is decelerating and unaffected by dark energy in a co-evolving frame.

Contribution

It derives simplified equations for vector gravity and explains the role of dark energy and the cosmological constant in universe evolution.

Findings

Simplified gravitational equations suitable for analysis.

Dark energy does not influence universe evolution in a co-evolving frame.

Universe's expansion is decelerating and approaches zero asymptotically.

Abstract

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.