Relativistic radial expansion: do we need dark energy?

Abstract

The Hubble law, for which the radial expansion velocity is linear in the distance r, implies a visible Universe limited to a horizon at r = c/H. No information beyond this horizon can reach us.Here we suggest a modified Hubble law for the measured radial expansion velocity that does not put a limit on the radius of the visible Universe. The modified Hubble law is based on Einstein's well known addition of relativistic velocities, and differs from the (conventional linear) Hubble law in orders of Hr/c that are higher than the first order. The modified Hubble law solves the Olbers's paradox (as the linear Hubble law does), and the existence of dark energy becomes unnecessary for explaining existing astronomical data on dependence of luminosity as a function of redshift for type Ia supernovas.