Fourth-rank gravity and cosmology

Details Fourth-rank gravity and cosmology Fourth-rank gravity and cosmology

Jul 1992

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1992stin...9330918m&link_type=abstract

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Mathematics

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

Scientific paper

We consider the consequences of describing the metric properties of space-time through a quartic line element. The associated 'metric' is a fourth-rank tensor Gmu(upsilonlambda(pi)). In order to recover a Riemannian behavior of the geometry, it is necessary to have Gmu(upsilonlambda(pi)) = g (mu(upsilon)glambda(pi)). We construct a theory for the gravitational field based on the fourth-rank metric Gmu(upsilonlambda(pi)). In the absence of matter, the fourth-rank 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 kOBS = O and OmegaOBS 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 tCLAS approximately = 1020tPLANCK approximately = 10-23s. 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.

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