88 research outputs found

    Incompressible Stars and Fractional Derivatives

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    Fractional calculus is an effective tool in incorporating the effects of non-locality and memory into physical models. In this regard, successful applications exist rang- ing from signal processing to anomalous diffusion and quantum mechanics. In this paper we investigate the fractional versions of the stellar structure equations for non radiating spherical objects. Using incompressible fluids as a comparison, we develop models for constant density Newtonian objects with fractional mass distributions or stress conditions. To better understand the fractional effects, we discuss effective values for the density, gravitational field and equation of state. The fractional ob- jects are smaller and less massive than integer models. The fractional parameters are related to a polytropic index for the models considered

    A Singularity-Free Cosmological Model with a Conformally Coupled Scalar Field

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    We explore the possibility of describing our universe with a singularity--free, closed, spatially homogeneous and isotropic cosmological model, using only general relativity and a suitable equation of state which produces an inflationary era. A phase transition to a radiation--dominated era occurs as a consequence of boundary conditions expressing the assumption that the temperature cannot exceed the Planck value. We find that over a broad range of initial conditions, the predicted value of the Hubble parameter is approximately 4747 km\cdot~s1^{-1}\cdot~Mpc1^{-1}. Inflation is driven by a scalar field, which must be conformally coupled to the curvature if the Einstein equivalence principle has to be satisfied. The form of the scalar field potential is derived, instead of being assumed a priori.Comment: 19 pages, figures and tables available from the author

    Do Rotations Beyond the Cosmological Horizon Affect the Local Inertial Frame?

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    If perturbations beyond the horizon have the velocities prescribed everywhere then the dragging of inertial frames near the origin is suppressed by an exponential factor. However if perturbations are prescribed in terms of their angular momenta there is no such suppression. We resolve this paradox and in doing so give new explicit results on the dragging of inertial frames in closed, flat and open universe with and without a cosmological constant.Comment: 12 page

    Quantum Tunneling Effect in Oscillating Friedmann Cosmology

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    It is shown that the tunneling effect in quantum cosmology is possible not only at the very beginning or the very end of the evolution, but also at the moment of maximum expansion of the universe. A positive curvature expanding Friedmann universe changes its state of evolution spontaneously and completely, {\it without} any changes in the matter content, avoiding recollapse, and falling into oscillations between the nonzero values of the scale factor. On the other hand, an oscillating nonsingular universe can tunnel spontaneously to a recollapsing regime. The probability of such kind of tunneling is given explicitly. It is inversely related to the amount of nonrelativistic matter (dust), and grows from a certain fixed value to unity if the negative cosmological constant approaches zero.Comment: 18 pages Latex + 2 figures available by fax upon reques

    Accelerated expansion from braneworld models with variable vacuum energy

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    In braneworld models a variable vacuum energy may appear if the size of the extra dimension changes during the evolution of the universe. In this scenario the acceleration of the universe is related not only to the variation of the cosmological term, but also to the time evolution of GG and, possibly, to the variation of other fundamental "constants" as well. This is because the expansion rate of the extra dimension appears in different contexts, notably in expressions concerning the variation of rest mass and electric charge. We concentrate our attention on spatially-flat, homogeneous and isotropic, brane-universes where the matter density decreases as an inverse power of the scale factor, similar (but at different rate) to the power law in FRW-universes of general relativity. We show that these braneworld cosmologies are consistent with the observed accelerating universe and other observational requirements. In particular, GG becomes constant and Λ(4)const×H2\Lambda_{(4)} \approx const \times H^2 asymptotically in time. Another important feature is that the models contain no "adjustable" parameters. All the quantities, even the five-dimensional ones, can be evaluated by means of measurements in 4D. We provide precise constrains on the cosmological parameters and demonstrate that the "effective" equation of state of the universe can, in principle, be determined by measurements of the deceleration parameter alone. We give an explicit expression relating the density parameters Ωρ\Omega_{\rho}, ΩΛ\Omega_{\Lambda} and the deceleration parameter qq. These results constitute concrete predictions that may help in observations for an experimental/observational test of the model.Comment: References added, typos correcte
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