1993/03/03 by Victor Tapia, Tapia, Victor, A. L. Marrakchi +3
Physics and Astronomy · #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #gr-qc
paper · pdf · doi:10.48550/arxiv.gr-qc/9303009
39 pages, plain TEX
arxiv created 1993/03/03 · arxiv updated 2009/11/30
We consider the consequences of describing the metric properties of space- time through a quartic line element ds4=Gμνλρdxμdxνdxλdxρ. The associated "metric" is a fourth-rank tensor Gμνλρ. We construct a theory for the gravitational field based on the fourth-rank metric Gμνλρ which is conformally invariant in four dimensions. In the absence of matter the fourth-rank metric becomes of the form Gμνλρ=g(μνgλρ) therefore we recover a Riemannian behaviour of the geometry; furthermore, the theory coincides with General Relativity. In the presence of matter we can keep Riemannianicity, but now gravitation couples in a different way to matter as compared to General Relativity. We develop a simple cosmological model based on a FRW metric with matter described by a perfect fluid. Our field equations predict that the entropy is an increasing function of time. For kobs=0 the field equations predict Ω≈ 4y, where y=p\overρ; for Ωsmall=0.01 we obtain ypred=2.5× 10-3. y can be estimated from the mean random velocity of typical galaxies to be yrandom=1×10-5. For the early universe there is no violation of causality for t>tclass≈1019tPlanck≈ 10-24s.