A low matter density decaying vacuum cosmology from a complex metric

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Abstract
A low matter density decaying vacuum cosmology is proposed on the assumption that the universe's radius is a complex quantity if it is regarded as having a zero energy - momentum tensor. But we find that when the radius is real, it contains matter. Using the Einstein - Hilbert action principle, the physical scale factor is obtained as equal to with representing the finite radius of the universe at t = 0. The resulting physical picture is roughly a theoretical justification of the old Ozer - Taha model. The new model is devoid of all cosmological problems. In particular, it confirms the bounds on , the present value of the Hubble parameter: and faces no age problem. We argue that the total energy density consists of parts corresponding to relativistic/non-relativistic matter, a positive vacuum energy, a negative energy and a form of matter with equation of state (textures or generally K-matter), and the following predictions are made for the present non-relativistic era: , , , where a parameter corresponding to K-matter is taken to be unity. It is shown that spacetime with a complex metric has signature changing properties. Using quantum cosmological considerations, it is shown that the wavefunction is peaked about the classical contour of evolution and the minimum radius of the non-singular model is predicted as comparable with the Planck length.
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