Abstract
The recent astronomical observations indicate that the expanding universe is homogeneous, isotropic and asymptotically flat. The Euclidean geometry of the universe enables to determine the total gravitational and kinetic energy of the universe by Newtonian gravity in a flat space. By dimensional analysis, we have found the mass of the universe close to the Hoyle-Carvalho formula M ~ c^3/(GH). This value is independent from the cosmological model and infers a size (radius) of the universe close to Hubble distance. It has been shown that almost the entire kinetic energy of the universe ensues from the cosmological expansion. Both, the total gravitational and kinetic energies of the universe have been determined in relation to an observer at an arbitrary location. The relativistic calculations for total kinetic energy have been made and the dark energy has been excluded from calculations. The total mechanical energy of the universe has been found close to zero, which is a remarkable result. This result supports the conjecture that the gravitational energy of the universe is approximately balanced with its kinetic energy of the expansion.
Highlights
The problem for the average density of the universe ρ acquires significance when it has been shown that the General Relativity allows to reveal the geometry and evolution of the universe by simple cosmological models (Friedman, 1922; Lemaitre, 1927; Einstein and De Sitter, 1932)
The recent astronomical observations indicate that the expanding universe is homogeneous, isotropic and asymptotically flat
This value is independent from the cosmological model and infers a size of the observable universe close to Hubble distance
Summary
The problem for the average density of the universe ρ acquires significance when it has been shown that the General Relativity allows to reveal the geometry and evolution of the universe by simple cosmological models (Friedman, 1922; Lemaitre, 1927; Einstein and De Sitter, 1932). After recent CMB observations discovered that the global geometry of the universe is flat, some cosmological problems could be solved by Newtonian gravity in Euclidean space. This opportunity has been used in the paper to estimate total mechanical energy of the observable universe. From Equation 7 we have estimated the size (radius) of the observable universe R close to the Hubble distance cH−1: Any possible matter beyond the Hubble sphere recedes from the observer with superluminal velocity It does not affect the observer and it has no contribution in the mass and energy of the observable universe, calculated in relation to the observer. We can estimate the total rest energy of the observable universe from Equation 9 and Einstein equation: E0
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