New Developments on Gravitational Force and Nonlinear Oscillations of Space

This paper contains results obtained as solutions of the Unified Field Theory equations. It yields space nonlinear oscillations, a quartet of gravitational forces, quintessence, and replaces Einstein’s Cosmological Constant by an invariant parameter r0 which prevails over the entire evolution of the Universe. In the 1999 Coral Gables Conference I had reported on the latest observations, with regard to the expansion of the universe with increasing acceleration which theoretically was explained in terms of the existence of repulsive gravitational forces predicted in 1991 from the unified theory (see page 493 in this reference) and further that space itself was subjected to some nonlinear oscillations with variable frequencies. These predictions of the unified theory were published in the proceedings of the 1999 Coral Gables Conference. Contrary to the existing paradigm amongst most cosmologists and physicists, I strongly agree with Einstein’s regret for his introduction of the cosmological constant into (though for different reasons) his general relativistic theory of gravitation. In the unified theory the 16 component non-symmetric tensor ĝμv = gμv + εq Φμv where ε = ±1,±i contains the invariant parameter q, where q is an energy density and is related to an intrinsic fundamental length parameter r0 by the relation r 0q 2 = c/2G. (1) This relation was obtained in 1950 while a graduate student in Cambridge University and it is the condition for the non-symmetric theory to reduce to general relativity in the limit of ro = 0, the correspondence limit . The parameter q has the dimensions of an electric field and therefore the field tensor ĝμv is dimensionless. The relation (1) can also be regarded as an equation of state. The role of r0, which varies between zero and infinity, in this theory is as important as the role of h̄ in quantum theory. This is the missing link in Einstein and Schrödinger versions of the non-symmetric theory. Both Einstein (see the Appendix II page 146) and Schrödinger (see the letter to me in the Appendix of this reference) have commented on the subject of constants in a physical theory. The expansion of the universe is now linked up with the predicted existence of the quartet of gravitational forces. This multiplicity of the gravitational forces can be seen by studying the sign of the gravitational constant G in the equation of state (1). The four