arXiv subjects
Publications and source records attributed to A. L. Marrakchi.
In this paper we reconsider the supersymmetric hybrid inflation in the context of the braneworld scenario . The observational bounds are satisfied with an inflationary energy scale $μ\simeq 4\times 10^{-4}M_p$, without any fine-tuning of the coupling parameter, provided that the five-dimensional Planck scale is $M_5\stackrel{<}{\sim} 2\times 10^{-3}M_p$ . We have also obtained an upper bound on the the brane tension .
We propose a new realisation of hybrid inflation in supergravity where the inflaton field does not appear in the superpotential but contributes only through the Kahler potential. The scalar potential derived from an R-invariant superpotential has the same form as that of the Linde's original version. The correct magnitude of the density perturbations amplitude is found without any fine-tuning of the coupling parameter in the superpotential for an acceptable value of the fundamental energy scale of the theory. The eta-problem was also resolved in this model.
We consider the consequences of describing the metric properties of space- time through a quartic line element $ds^4=G_{μνλρ}dx^μdx^νdx^λdx^ρ$. The associated "metric" is a fourth-rank tensor $G_{μνλρ}$. We construct a theory for the gravitational field based on the fourth-rank metric $G_{μνλρ}$ which is conformally invariant in four dimensions. In the absence of matter the fourth-rank metric becomes of the form $G_{μνλρ}=g_{(μν}g_{λρ)}$ 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 $k_{obs}=0$ the field equations predict $Ω\approx 4y$, where $y={p\overρ}$; for $Ω_{small}=0.01$ we obtain $y_{pred}=2.5\times 10^{-3}$. $y$ can be estimated from the mean random velocity of typical galaxies to be $y_{random}=1\times10^{-5}$. For the early universe there is no violation of causality for $t>t_{class}\approx10^{19}t_{Planck}\approx 10^{-24}s$.