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L\\'aszl\\'o \\'A Gergely
Publication date
2009
fields
Physics
and research's language is
English
Authors
Laszlo A. Gergely
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The high value of brane tension has a crucial role in recovering Einsteins general relativity at low energies. In the framework of a recently developed formalism with variable brane tension one can pose the question, whether it was always that high? In analogy with fluid membranes, in this paper we allow for temperature dependent brane tension, according to the corresponding law established by Eotvos. For cosmological branes this assumption leads to several immediate consequences: (a) The brane Universe was created at a finite temperature $T_{c}$ and scale factor $a_{min}$. (b) Both the brane tension and the 4-dimensional gravitational coupling constant increase with the scale factor from zero to asymptotic values. (c) The 4-dimensional cosmological constant evolves with $a$, starting with a huge negative value, passing through zero, finally reaching a small positive value. Such a scale-factor dependent cosmological constant is able to generate a surplus of attraction at small $a$ (as dark matter does) and a late-time repulsion at large $a$ (dark energy). In the particular toy model discussed here the evolution of the brane tension is compensated by energy interchange between the brane and the fifth dimension, such that the continuity equation holds for the cosmological fluid. The resulting cosmology closely mimics the standard model at late times, a decelerated phase being followed by an accelerated expansion. The energy absorption of the brane drives the 5D space-time towards maximal symmetry, becoming Anti de Sitter.
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We introduce brane-worlds with non-constant tension, strenghtening the analogy with fluid membranes, which exhibit a temperature-dependence according to the empirical law established by Eotvos. This new degree of freedom allows for evolving gravitational and cosmological constants, the latter being a natural candidate for dark energy. We establish the covariant dynamics on a brane with variable tension in full generality, by considering asymmetrically embedded branes and allowing for non-standard model fields in the 5-dimensional space-time. Then we apply the formalism for a perfect fluid on a Friedmann brane, which is embedded in a 5-dimensional charged Vaidya-Anti de Sitter space-time.
We construct a generalized dynamics for particles moving in a symmetric space-time, i.e. a space-time admitting one or more Killing vectors. The generalization implies that the effective mass of particles becomes dynamical. We apply this generalized dynamics to the motion of test particles in a static, spherically symmetric metric. A significant consequence of the new framework is to generate an effective negative pressure on a cosmological surface whose expansion is manifest by the particle trajectory via embedding geometry cite{bwg,embed2,embed,pal}. This formalism thus may give rise to a source for dark energy in modeling the late accelerating universe.
We consider the collision of self-gravitating n-branes in a (n+2)-dimensional spacetime. We show that there is a geometrical constraint which can be expressed as a simple sum rule for angles characterizing Lorentz boosts between branes and the intervening spacetime regions. This constraint can then be re-interpreted as either energy or momentum conservation at the collision.
We consider here a robust study of stellar dynamics for White Dwarf Stars with polytropic matter in the weak field approximation using the Lane-Emden equation from the brane-world scenario. We also derive an analytical solution to the nonlocal energy density and show the behavior and sensitivity of these stars to the presence of extra dimensions. Similarly, we analyze its stability and compactness, in order to show whether it is possible to be close to the conventional wisdom of white dwarfs dynamics. Our results predicts an average value of brane tension as: $langlelambdaranglegtrsim84.818;rm MeV^4$, with a standard deviation $sigmasimeq82.021;rm MeV^4$ which comes from a sample of dwarf stars, being weaker than other astrophysical observations but remaining above of cosmological results provided by nucleosynthesis among others.
In this paper, we study the thick brane scenario constructed in the recently proposed $f(T,mathcal{T})$ theories of gravity, where $T$ is called the torsion scalar, and $mathcal{T}$ is the trace of the energy-momentum tensor. We use the first-order formalism to find analytical solutions for models that include a scalar field as a source. In particular, we describe two interesting cases in which, in the first, we obtain a double-kink solution, which generates a splitting in the brane. In the second case, proper management of a kink solution obtained generates a splitting in the brane intensified by the torsion parameter, evinced by the energy density components satisfying the weak and strong energy conditions. In addition, we investigate the behavior of the gravitational perturbations in this scenario. The parameters that control the torsion and the trace of the energy-momentum tensor tend to shift the massive modes to the core of the brane, keeping a gapless non-localizable and stable tower of massive modes and producing more localized massless modes.
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