Mach's Principle and Matter Production Process in Non-Steady State Cosmological Model

Abstract

A Hoyle-Pryce tensor can be introduced into the Einstein field equations of general relativity as a possible inference from Mach's principle as formulated in Whitrow's relation. The set of equations obtained can be completely determined for the matter injection field, pressure, density and scaling functions in a dosed model universe with asymptotically limited expansion. This model presents a cosmic density higher than the usually accepted value for the smearing out of galactic matter. Hoyle and Narlikar considered the hypothesis of matter injection into the universe as a way out for the unsatisfactory status of Mach's principle. 1> It is well known that the energy-momentum tensor does not determine uniquely space­ time geometry so that non-Machian solutions are possible for the general theory of relativity. An example of this is Gi:idel's cosmological model2l in which the same energy-momentum tensor of the Einstein model universe determines a non­ stationary metric, which is incompatible with Mach's principle. In Hoyle and Narlikar's calculation it turns out that the matter injection field built into the Einstein field equations restrict its solutions to those compatible with the cos­ mological principle and W eyl's postulate which are necessary for Mach's principle. This result is obtained under conditions imposed on the cosmic stress and , the cosmic density: The former should be zero and the latter constant. It seems . that the hypothesis of cosmic zero pressure is somewhat unrealistic since the cosmic pressure which involves radiation and gas· stress may not be negligible. Besides, as is known, the field equations may afford negative stresses, which means that the cosmic pressure is not necessarily related only t.o gas and radiation. As will be shown afterwards, this is the case with the present cos­ mological model. Thus it is safer to keep p (t) different from zero in the field equations.