Cosmology with spinor connection

Abstract

A general relativistic cosmological method is constructed in which the energy momentum tensor is derived from a tetrad of four spinor fields satisfying Dirac's equation associated with a universal length of order 10 −12 cm. The field equations are derived from the variation of the metric field in a curvature scalar action integral, under the auxiliary condition that in the varied metric the spinor fields should still satisfy Dirac's equation. The obtained metric is the well known zero pressure model of general relativity, or more realistically a model with negligibly small pressure. The gravitational constant appears as a Lagrange multiplier and is therefore a (possibly constant) function of time. It also depends on the normalization of the spinor fields which we may choose at every epoch so as to suit convenience. Using the usual normalization, the gravitational constant appears to be inversely proportional to the cosmological epoch, providing a new interpretation of the well known Dirac-Jordan hypothesis.