The basic theory underlying the quasi-steady-state cosmology

Abstract

Outside cosmology, the procedure normally followed in science requires the integration of hyperbolic partial differential equations subject to initial data given on a free surface, which is usually taken to be a time section of spacetime. The initial data are determined in experimental science from observation and the results of the integrations are also checked by observations. Friedmann (Big Bang) cosmology suffers, however, from the fact that the observations cannot determine initial conditions. Thus in that theory the initial conditions have only the weak status of guesses. There is also some question whether the correct equations are being used, since the gravitational equations of that cosmology are not scale invariant, a situation unlike the rest of physics. Since matter exists in what is supposed to be a space of finite temporal duration its origin should be explained, working from a suitable lagrangian and action. Otherwise the origin is placed outside science. This is what is done in Big Bang cosmology. In this paper we depart from the standard procedure by first deriving gravitational equations that are scale invariant, whence it is shown that in a scale invariant gravitational theory particles have the property that the two lengths associated with them, the Compton wavelength and gravitational radius, must be comparable, i.e. they are Planck particles. It is then shown that the theory has the scope to explain the genesis of the so-called cosmological constant, and the usually required magnitude of the cosmological constant is derived. When interactions other than gravitation are included, Planck particles are unstable. The effect of instability on newly created Planck particles is to introduce terms into the gravitational equations additional to those of general relativity. In particular, there are negative pressure terms which act to expand the universe. The energy terms are such as to suggest that particle creation must be of an explosive nature and that it must occur in the neighbourhoods of highly compacted bodies, a property which appears to provide a connection between cosmological theory and high-energy astrophysics.