ABSTRACT
Cosmology is the branch of physics where the Universe is studied as a whole. The dimension of Universe is associated with a length scale of a billion light-years. At this large scale, gravitation is the only realizable interaction. Hence, both the Newtonian theory of gravity and Einstein’s theory could be used to describe the dynamics of the galaxies in the Universe. But since in Einstein’s general theory of relativity the curvature of space-time and gravitation are complementary to each other in the sense that the geometry (or curvature) of space-time is determined by gravitation and vice versa, Einstein’s theory is more appropriate for cosmological calculations of galactic dynamics. However, in general, the theory of general relativity is a necessity where the curvature of space-time is considerably large, which can happen in the presence of a massive compact object like a neutron star or black hole. On this count Newtonian gravity should work well for an ordinary stellar system where the effect of General Relativity (GR) is negligible. An estimate, where Einstein’s GR theory is required and where the Newtonian theory suffices, can be made by defining a dimensionless quantity ε = GNM
c2R and then analyzing the value of ε for the considered heavenly bodies. Here, GN and M denote the gravitational constant and mass, respectively, c is the velocity of light, and R is the distance scale. Typically for the case of the sun, εsun ∼O(10−6), which is rather low and Newtonian gravity very much suffices. But for the case when ε ∼ O(1), Newtonian mechanics break down and cosmological studies require the framework of GR. For the Universe, the distance scale R is very large and simultaneously the mass M is also considerably large, making ε not a very small quantity. Therefore, it is wise to use principles of GR for cosmological calculations.
