On a New Approach to Cosmology

An attempt is made to develop a new theory of cosmology based on a scalar field, in view of several weak points proper to the general relativistic cosmology. In our treatment,. a kind of correspondence principle plays the important role, together with the consideration of the scope of applicability of general relativity. Our cosmological field equation thus proposed not only has an intimate linkage with Einstein's equations, but also satisfies Mach's relation for the universe as a whole in a covariant and intrinsic manner