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

A. S. M. Mohiul Islam

Department of Mathematics, University of Chittagong, 4331, Bangladesh.

Md. Habibur Rahman *

Department of Mathematics, University of Chittagong, 4331, Bangladesh.

*Author to whom correspondence should be addressed.


Einstein revisited his equations and altered 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’. Einstein’s field equation has been studying 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. Theoretically, the cosmological constant Λ and the density parameter  p are determined using dynamical tests like as density and velocity profiles around clusters and virialization. This paper, we discuss and 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. Based on the results, two scenarios for the universe are proposed, one with a huge proportion of nonbaryonic matter and a zero cosmological constant, and the other with all matter being baryonic. The cosmological constant is added to save inflation and build up a static universe model.

Keywords: Friedmann model, cosmological constant, Einstein’s universe, Ricci tensor, energy momentum tensor, Hubble’s parameter

How to Cite

Mohiul Islam, A. S. M., & Habibur Rahman, M. (2022). Spatially Closed FRW Model Leads to Einstein’s Universe with Cosmological Constant. International Astronomy and Astrophysics Research Journal, 4(1), 182–189. Retrieved from


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