Estimations of total mass and density of the observable universe by dimensional analysis

Abstract

Abstarct The dimensional analysis has been carried out by means of three fundamental constants the speed of the light in vacuum (c), the universal gravitational constant (G) and the Hubble constant (H). The mass dimension quantity ) /( ~ 3 GH c m ~ 10 kg, derived by this approach, practically coincides with Hoyle-Carvalho formula for the mass of the observable universe, obtained by a totally different approach. It has been shown that this value is close to the mass of the Hubble sphere. Besides, by dimensional analysis it has been found that the total density of the universe, including the dark matter and the dark energy, is of the order of a magnitude of the critical density of the universe 26 2 10 ~ / ~   c G H   kg m .