An Understanding of the Dark Matter in the Universe and the Variation of the Universal Gravitational Contant G with Time

Considering the fact that the present universe might have been formed out of a system of ficticious self-gravitating particles, fermionic in nature, each of mass m, we are able to obtain a compact expression for the radius R 0 of the universe by using a model density distribution ρ(r) for the particles which is singular at the origin. This singularity in ρ(r) can be considered to be consistent with the socalled Big Bang theory of the universe. By assuming that Mach's principle holds good in the evolution of the universe, we determine the number of particles, N , of the universe and its R 0 , which are obtained in terms of the mass m of the constituent particles and the Universal Gravitational constant