Tensor stability in Born-Infeld determinantal gravity

We consider the transverse-traceless tensor perturbation of a spatial flat homogeneous and isotropic spacetime in Born-Infeld determinantal gravity, and investigate the evolution of the tensor mode for two solutions in the early universe. For the first solution where the initial singularity is replaced by a regular geometric de Sitter inflation of infinite duration, the evolution of the tensor mode is stable for the parameter spaces $\alpha<-1$, $\omega\geq-1/3$ and $\alpha=-1$, $\omega>0$. For the second solution where the initial singularity is replaced by a primordial brusque bounce, which suffers a sudden singularity at the bouncing point, the evolution of the tensor mode is stable for all regions of the parameter space. Our calculation suggests that the tensor evolution can hold stability in large parameter spaces, which is a remarkable property of Born-Infeld determinantal gravity. We also constrain the theoretical parameter $|\lambda|\geq 10^{-38} \text{m}^{-2}$ by resorting to the current bound on the speed of the gravitational waves.Comment: 14 pages, added a general discussion on the tensor stability in Sec. 3, and added Sec. 5 on the parameter constraint, published versio

Full linear perturbations and localization of gravity on f(R,T)f(R,T) brane

We study the thick brane world system constructed in the recently proposed $f(R,T)$ theories of gravity, with $R$ the Ricci scalar and $T$ the trace of the energy-momentum tensor. We try to get the analytic background solutions and discuss the full linear perturbations, especially the scalar perturbations. We compare how the brane world model is modified with that of general relativity coupled to a canonical scalar field. It is found that some more interesting background solutions are allowed, and only the scalar perturbation mode is modified. There is no tachyon state exists in this model and only the massless tensor mode can be localized on the brane, which recovers the effective four-dimensional gravity. These conclusions hold provided that two constraints on the original formalism of the action are satisfied.Comment: v3: 8 pages, 2 figures, improved version with minor corrections, accepted by EPJ

SU(5) Symmetry of spdfg Interacting Boson Model

The extended interacting boson model with s-, p-, d-, f- and g-bosons being included (spdfg IBM) are investigated. The algebraic structure including the generators, the Casimir operators of the groups at the SU(5) dynamical symmetry and the branching rules of the irreducible representation reductions along the group chain are obtained. The typical energy spectrum of the Symmetry is given.Comment: 12 pages, 2 figure