arXiv subjects
Publications and source records attributed to Joel Tossa.
In this paper, we study pseudo-Riemannian Hom-Lie algebras. We establish Hom-versions of the classical Bochner theorem in both the Riemannian and Lorentzian settings. Finally, we prove that the space of Killing vectors on a pseudo-Riemannian Hom-Lie algebra forms a totally geodesic Hom-Lie subalgebra.
In this note, we consider the resultant of systems of homogeneous multivariate polynomials which are equivariant under the action of direct product of two symmetric groups. We establish a decomposition formula for the resultant of such systems. Thanks to that decomposition formula we prove that the discriminant of an invariant multivariate homogeneous polynomial under a direct product of symmetric groups splits into smaller resultants that are easier to compute.
We investigate alternative candidates to dark energy that can explain the current state of the universe in the framework of the generalized teleparallel theory of gravity $f(T)$ where $T$ denotes the torsion scalar. To achieve this, we carried out a series of reconstruction taking into account to the ordinary and entropy-corrected versions of the holographic and new agegraphic dark energy models. These models used as alternative to dark energy in the literature in order describe the current state of our universe. It is remarked that the models reconstructed indicates behaviors like phantom or quintessence models. Furthermore, we also generated the EoS parameters associated to entropy-corrected models and we observed a transition phase between quintessence state and phantom state as showed by recent observational data. We also investigated on the stability theses models and we created the $\{r-s\}$. The behavior of certains physical parameters as speed of sound and the Statefinder parameters are compatible with current observational data.
The quantization of gravity coupled to a perfect fluid model leads to a Schrödinger-like equation, where the matter variable plays the role of time. The wave function can be determined, in the flat case, for an arbitrary barotropic equation of state $p = αρ$; solutions can also be found for the radiative non-flat case. The wave packets are constructed, from which the expectation value for the scale factor is determined. The quantum scenarios reveal a bouncing Universe, free from singularity. We show that such quantum cosmological perfect fluid models admit a universal classical analogue, represented by the addition, to the ordinary classical model, of a repulsive stiff matter fluid. The meaning of the existence of this universal classical analogue is discussed. The quantum cosmological perfect fluid model is, for a flat spatial section, formally equivalent to a free particle in ordinary quantum mechanics, for any value of $α$, while the radiative non-flat case is equivalent to the harmonic oscillator. The repulsive fluid needed to reproduce the quantum results is the same in both cases.
The non-minimal coupling of gravity to a scalar field can be transformed into a minimal coupling through a conformal transformation. We show how to connect the results of a perturbation calculation, performed around a Friedmann-Robertson-Walker background solution, before and after the conformal transformation. We work in the synchronous gauge, but we discuss the implications of employing other formalisms.