Spatially Closed FRW Model leads to Einstein’s Universe with Cosmological Constant

Abstract

Einstein revisited his equations and modified by introducing something known as a universal constant Einstein's 1917 concept has been with us ever since in various variants and incarnations, including the broader concept of 'Dark Energy.' The Einstein’s field equation have been studies under the assumption of a power law time variation of the expansion factor. The Hubble’s parameter and distance modulus in our descended model are in good concordance with recent data of astrophysical observations under appropriate conditions. Dynamical tests such as density and velocity profiles around clusters and virialization are employed to theoretically determine the cosmological constant Λ and the density parameter .In this paper, we discuss briefly other classes of models that have a close relationship with the Freidmann models, and these are models derived from modified Einstein equations containing the cosmological constant. Thus the cosmological constant is not any old value but rather simply the inverse of the scale factor squared, where the scale factor is a fixed value in static closed universe. Ultimately we derived to describe the final radius of a virialized cluster, in which a repulsive cosmological constant lambda (Λ) gives a smaller value. Two scenarios for the universe are suggested based on the results, one with a large amount of nonbaryonic matter and a zero cosmological constant and another in which all matter is baryonic. The cosmological constant is added to save inflation and build up a static universe model.