From General Relativity to A Simple-Harmonically Oscillating Universe, and Vice-Versa: A Review

Abstract

In this paper two different lines of reasoning are followed in order to discuss a Universe that belongs to the so-called oscillatory class. In the first section, we start from the general writing of the first Friedmann – Lemaître equation. Taking into account mass – energy equivalence, the so-called fluid equation is immediately deduced, with the usual hypotheses of homogeneity and isotropy, once identified the evolution of the Universe with an isentropic process. Considering equal to zero the curvature parameter, and carrying out an opportune position concerning the so-called cosmological constant, we obtain an oscillating class, to which a simple-harmonically oscillating Universe evidently belongs. In the second section, we start from a simple-harmonically oscillating Universe, hypothesized globally flat and characterized by at least a further spatial dimension. Once defined the density, taking into account a global symmetry elsewhere postulated, we carry out a simple but noteworthy position concerning the gravitational constant. Then, once established the dependence between pressure and density, we deduce, by means of simple mathematical passages, the equations of Friedmann – Lemaître, without using Einstein’s Relativity.