A Wasserstein approach to the one-dimensional sticky particle system

We present a simple approach to study the one-dimensional pressureless Euler system via adhesion dynamics in the Wasserstein space of probability measures with finite quadratic moments. Starting from a discrete system of a finite number of "sticky" particles, we obtain new explicit estimates of the solution in terms of the initial mass and momentum and we are able to construct an evolution semigroup in a measure-theoretic phase space, allowing mass distributions with finite quadratic moment and corresponding L^2-velocity fields. We investigate various interesting properties of this semigroup, in particular its link with the gradient flow of the (opposite) squared Wasserstein distance. Our arguments rely on an equivalent formulation of the evolution as a gradient flow in the convex cone of nondecreasing functions in the Hilbert space L^2(0,1), which corresponds to the Lagrangian system of coordinates given by the canonical monotone rearrangement of the measures.Comment: Added reference

Graviton production in the scaling of a long-cosmic-string network

In a previous paper [1] we considered the possibility that (within the early-radiation epoch) there has been (also) a short period of a significant presence of cosmic strings. During this radiation-plus-strings stage the Universe matter-energy content can be modelled by a two-component fluid, consisting of radiation (dominant) and a cosmic-string fluid (subdominant). It was found that, during this stage, the cosmological gravitational waves (CGWs) - that had been produced in an earlier (inflationary) epoch - with comoving wave-numbers below a critical value (which depends on the physics of the cosmic-string network) were filtered, leading to a distorsion in the expected (scale-invariant) CGW power spectrum. In any case, the cosmological evolution gradually results in the scaling of any long-cosmic-string network and, hence, after a short time-interval, the Universe enters into the late-radiation era. However, along the transition from an early-radiation epoch to the late-radiation era through the radiation-plus-strings stage, the time-dependence of the cosmological scale factor is modified, something that leads to a discontinuous change of the corresponding scalar curvature, which, in turn, triggers the quantum-mechanical creation of gravitons. In this paper we discuss several aspects of such a process, and, in particular, the observational consequences on the expected gravitational-wave (GW) power spectrum.Comment: 12 pages, 2 figures, accepted for publication in Physical Review

Nonlinear evolution of dark matter and dark energy in the Chaplygin-gas cosmology

The hypothesis that dark matter and dark energy are unified through the Chaplygin gas is reexamined. Using generalizations of the spherical model which incorporate effects of the acoustic horizon we show that an initially perturbative Chaplygin gas evolves into a mixed system containing cold dark matter-like gravitational condensate.Comment: 11 pages, 3 figures, substantial revision, title changed, content changed, added references, to appear in JCA

Dynamics of a thin shell in the Reissner-Nordstrom metric

We describe the dynamics of a thin spherically symmetric gravitating shell in the Reissner-Nordstrom metric of the electrically charged black hole. The energy-momentum tensor of electrically neutral shell is modelled by the perfect fluid with a polytropic equation of state. The motion of a shell is described fully analytically in the particular case of the dust equation of state. We construct the Carter-Penrose diagrams for the global geometry of the eternal black hole, which illustrate all possible types of solutions for moving shell. It is shown that for some specific range of initial parameters there are possible the stable oscillating motion of the shell transferring it consecutively in infinite series of internal universes. We demonstrate also that this oscillating type of motion is possible for an arbitrary polytropic equation of state on the shell.Comment: 17 pages, 7 figure