Prof. Muni Mahendra Kumar
As we have already seen, Einstein considered it fallacious to picture the shape of the Universe on the basis of Euclidean geometry. He succeeded in showing that the light rays do not travel in straight lines when passing through a gravitational field. “The fact that they travel either along a curve or a great circle proves that the laws of Euclidean geometry do not hold true in a gravitational field. The Universe is filled with large gravitating bodies having large masses such as stars, planets, galaxies, etc. Now, since the structure of the gravitational field is shaped by the mass and the velocity of the gravitating bodies, the geometrical structure of the Universe as a whole must be shaped by the sum of its material contents. For each concentration of matter in the Universe, there is a corresponding distortion of the space-time continuum. Each celestial body gives curvature to its surrounding space. The total effect of all the matter of Universe is an overall curvature of space-time continuum. The result is that the Universe (space-time continuum) is so curved that it bends back on itself forming a closed cosmic curve. Thus the space (Universe) is finite. But as it is a closed curve, a ray of light will come to its starting place, after traveling round the universe. Thus the Universe of Dr. Einstein is finite and non-Euclidean.”[1]
Now the answer to the question as to “how big is the universe?” can only be given when the geometry of the Universe is known. The general theory of relativity gives the relation between the four-dimensional geometry in space and time and the distribution of the masses in the Universe. If this has been correctly given, then the astronomical observations of the distribution of galaxies in space can give us information about the geometry of the universe as a whole.[2] Several models-cosmological pictures-of the Universe have been suggested by the scientist.
