Symbolic analytical developments of the zero pressure cosmological model of the universe

Abstract

In the present paper, literal analytical solutions in power series forms are developed for the radius of curvature and the expansion velocity of the zero pressure cosmological models of the universe at any time t. Also, we develop literal analytical solutions in power series forms for the inverse problem of the zero pressure cosmological model, that is to find the time $t=\tilde{t}$ (say) at which the radius of curvature of the model $R=\tilde{R}$ (say) is known. The importance of these analytical power series representations is that, they are invariant under many operations because, addition, multiplication, exponent ion, integration, different ion, etc of a power series is also a power series. A fact which provides excellent flexibility in dealing with analytical as well as computational developments of the problems related to zero pressure cosmological models.For computational developments of these solutions, an efficient method using continued fraction theory is provided. By means of the present methods we able to analyze some known zero-pressure cosmological models, of these are Einstein and De Sitter models. In addition we also analyzed some other models by which one can know if the universe keep expanding forever, or will it reach a maximal size and then turn into contraction stage.