Unified cosmological scale versus Planck scale: As above, so below!

Abstract

We will demonstrate that the mass (equivalent mass) of the observable universe divided by the universe radius is exactly identical to the Planck mass divided by the Planck length. This only holds true in the Haug universe model that takes into account Lorentz’s relativistic mass, while in the Friedmann model of the universe, the critical mass of the universe divided by the Hubble radius is exactly equal to m p /(2l p ). Furthermore, in a recently suggested quantum gravity model, the mass of the universe divided by the radius of the universe is exactly identical to mp /lp ; that is, the Planck mass divided by the Planck length. This is much more than just a speculative approximation, for the findings are consistent with a new unified quantum gravity theory that links the cosmological scale directly to the Planck scale.