Fourthrank gravity and cosmology
Abstract
We consider the consequences of describing the metric properties of spacetime through a quartic line element. The associated 'metric' is a fourthrank tensor G_{mu(upsilon}lambda(pi)). In order to recover a Riemannian behavior of the geometry, it is necessary to have G_{mu(upsilon}lambda(pi)) = g _{(mu(upsilon})g_{lambda(pi})). We construct a theory for the gravitational field based on the fourthrank metric G_{mu(upsilon}lambda(pi)). In the absence of matter, the fourthrank metric becomes separable and the theory coincides with General Relativity. In the presence of matter, we can maintain Riemmanianicity, but now gravitation couples, as compared to General Relativity, in a different way to matter. We develop a simple cosmological model based on a FRW metric with matter described by a perfect fluid. For the present time, the field equations are compatible with k_{OBS} = O and Omega_{OBS} less than 0.18, and they imply p/(rho) less than 0.038 which corresponds to an almost pressureless perfect fluid. Therefore, the flatness problem is solved. However, our approach is valid only for p/(rho) less than 0.236. Therefore, we consider an early universe in which the state equation of matter is p/(rho) = 0.236 rather than p/p = 1/3. There is no violation of causality, no horizon problem, for t greater than t_{CLAS} approximately = 10^{20}t_{PLANCK} approximately = 10^{23}s. Our final and most important result is the fact that the entropy is an increasing function of time. When interpreted at the light of General Relativity, the treatment is shown to be almost equivalent to that of the standard model of cosmology combined with the inflationary scenario.
 Publication:

NASA STI/Recon Technical Report N
 Pub Date:
 July 1992
 Bibcode:
 1992STIN...9330918M
 Keywords:

 Astronomical Models;
 Cosmology;
 Equations Of State;
 Gravitation;
 Gravitation Theory;
 Gravitational Fields;
 Mathematical Models;
 Metric Space;
 Relativity;
 Riemann Manifold;
 SpaceTime Functions;
 Universe;
 Entropy;
 Ideal Fluids;
 Manifolds (Mathematics);
 Operators (Mathematics);
 Tensors;
 Time Dependence;
 Astrophysics