A Look at the Abandoned Contributions to Cosmology of Dirac, Sciama and Dicke

Abstract

The separate contributions to cosmology of the above researchers are revisited and a cosmology encompassing their basic ideas is proposed. We study Dirac's article on the large number hypothesis (1938), Sciama's proposal of realizing Mach's principle (1953), and Dicke's considerations (1957) on a flat-space representation of general relativity with a variable speed of light (VSL). Dicke's tentative theory can be formulated in a way which is compatible with Sciama's hypothesis on the gravitational constant G. Additionally, such a cosmological model is shown to satisfy Dirac's second `large number' hypothesis on the total number of particles in the universe being proportional to the square of the epoch. In the same context, Dirac's first hypothesis on an epoch-dependent G-contrary to his prediction- does not necessarily produce a visible time dependence of G. While Dicke's proposalreproduces the classical tests of GR in first approximation, the cosmological redshift is described by a shortening of measuring rods rather than an expansion of space. Since the temporal evolution of the horizon R is governed by \dot R(t) =c(t), the flatness and horizon problems do not arise in the common form.