Entropy and Cosmological Constant of a Universe Calculated by Means of Dimensional Analysis, Margolus-Levitin Theorem and Landauer’s Principle

Abstract

By means of the dimensional analysis a spherically simmetric universe with a mass M = c 3 /(2 HG ) and radius equal to c / H is considered, where H is the Hubble constant, c the speed of light and G the Newton gravitational constant. The density corresponding to this mass is equal to the critical density ρ cr = 3 H 2 /(8 π G ) . This universe evolves according to a Bondi-Gold-Hoyle scenario, with continuous creation of matter at a rate such to maintain, during the expansion, the density always critical density. Using the Margolus-Levitin theorem and the Landauer’s principle, an entropy is associated with this universe, obtaining a formula having the same structure as the Bekenstein-Hawking formula of the entropy of a black hole. Furthermore, a time-dependent cosmological constant Λ, function of the Hubble constant and the speed of light, is proposed.