The evolution of the universe from an initial dramatic event, the Big-Bang, is firmly established. Hubble’s law  (HL) connects the velocity of galactic objects and their relative distance: v(r) = Hr, where H is the Hubble constant. In this work we suggest that HL is not valid at large distances because of total energy conservation. We propose an expansion of the velocity in terms of their relative distance and produce a better fit to the available experimental data. Using a simple “dust” universe model, we can easily calculate under which conditions an (unstable) equilibrium state can be reached and we estimate the values of the matter present in the universe as well as the “dark energy”. Within the same formalism we can derive the “deceleration parameter”. We do not need to invoke any “dark energy”, its role being played by the kinetic correction. The resulting picture is that the universe might reach an unstable equilibrium state whose fate will be decided by fluctuations: either collapse or expand forever.
E. Hubble, “A Relation between Distance and Radial Velocity among Extra-Galactic Nebulae,” The Proceedings of the National Academy of Sciences, Vol. 15, No. 3, 1929, pp. 168-173. doi:10.1073/pnas.15.3.168
A. G. Riess, et al., “New Hubble Space Telescope Discoveries of Type Ia Supernovae at z ≥ 1: Narrowing Constraints on the Early Behavior of Dark Energy,” The Astrophysical Journal, Vol. 659, No. 1, 2007, pp. 98-121.