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Register a new userFriedmann branes with variable tension
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Added by
L\\'aszl\\'o \\'A Gergely
Publication date
2008
fields
Physics
and research's language is
English
Authors
Laszlo A. Gergely
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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.
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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.
We consider spatially homogeneous and isotropic cosmologies with non-zero torsion. Given the high symmetry of these universes, we adopt a specific form for the torsion tensor that preserves the homogeneity and isotropy of the spatial surfaces. Employing both covariant and metric-based techniques, we derive the torsion
In this work a series of methods are developed for understanding the Friedmann equation when it is beyond the reach of the Chebyshev theorem. First it will be demonstrated that every solution of the Friedmann equation admits a representation as a roulette such that information on the latter may be used to obtain that for the former. Next the Friedmann equation is integrated for a quadratic equation of state and for the Randall--Sundrum II universe, leading to a harvest of a rich collection of new interesting phenomena. Finally an analytic method is used to isolate the asymptotic behavior of the solutions of the Friedmann equation, when the equation of state is of an extended form which renders the integration impossible, and to establish a universal exponential growth law.
We completely classify Friedmann-Lema^{i}tre-Robertson-Walker solutions with spatial curvature $K=0,pm 1$ and equation of state $p=wrho$, according to their conformal structure, singularities and trapping horizons. We do not assume any energy conditions and allow $rho < 0$, thereby going beyond the usual well-known solutions. For each spatial curvature, there is an initial spacelike big-bang singularity for $w>-1/3$ and $rho>0$, while no big-bang singularity for $w<-1$ and $rho>0$. For $K=0$ or $-1$, $-1<w<-1/3$ and $rho>0$, there is an initial null big-bang singularity. For each spatial curvature, there is a final spacelike future big-rip singularity for $w<-1$ and $rho>0$, with null geodesics being future complete for $-5/3le w<-1$ but incomplete for $w<-5/3$. For $w=-1/3$, the expansion speed is constant. For $-1<w<-1/3$ and $K=1$, the universe contracts from infinity, then bounces and expands back to infinity. For $K=0$, the past boundary consists of timelike infinity and a regular null hypersurface for $-5/3<w<-1$, while it consists of past timelike and past null infinities for $wle -5/3$. For $w<-1$ and $K=1$, the spacetime contracts from an initial spacelike past big-rip singularity, then bounces and blows up at a final spacelike future big-rip singularity. For $w<-1$ and $K=-1$, the past boundary consists of a regular null hypersurface. The trapping horizons are timelike, null and spacelike for $win (-1,1/3)$, $win {1/3, -1}$ and $win (-infty,-1)cup (1/3,infty)$, respectively. A negative energy density ($rho <0$) is possible only for $K=-1$. In this case, for $w>-1/3$, the universe contracts from infinity, then bounces and expands to infinity; for $-1<w<-1/3$, it starts from a big-bang singularity and contracts to a big-crunch singularity; for $w<-1$, it expands from a regular null hypersurface and contracts to another regular null hypersurface.
A Friedmann like cosmological model in Einstein-Cartan framework is studied when the torsion function is assumed to be proportional to a single $phi(t)$ function coming just from the spin vector contribution of ordinary matter. By analysing four different types of torsion function written in terms of one, two and three free parameters, we found that a model with $phi(t)=- alpha H(t) big({rho_{m}(t)}/{rho_{0c}}big)^n$ is totally compatible with recent cosmological data, where $alpha$ and $n$ are free parameters to be constrained from observations, $rho_m$ is the matter energy density and $rho_{0c}$ the critical density. The recent accelerated phase of expansion of the universe is correctly reproduced by the contribution coming from torsion function, with a deceleration parameter indicating a transition redshift of about $0.65$.
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