Jeans instability is analysed in an expanding universe within the framework of BGK model of the Boltzmann equation and Poisson equations. The background is characterized by a comoving Maxwellian distribution function and a space-time Newtonian gravitational potential which satisfy the BGK model of the Boltzmann and Poisson equations without the necessity to invoke "Jeans swindle". The perturbations of the distribution function and Newtonian gravitational potentials from their background states are represented by plane waves of small amplitudes and a differential equation for the density contrast is determined. The density contrast differential equation was solved numerically and it is shown: (i) Jeans instability is characterized by perturbation wavelengths larger than Jeans wavelength where the density contrast grows with time. The growth of the density contrast is less accentuated for the case where the particle collisions are considered due to an energy dissipation; (ii) for perturbation wavelengths smaller than Jeans wavelength the density contrast has an oscillatory behavior in time and the oscillations for the case where the collisions are taken into account fade away in time due to the energy dissipation.
Due to the nonlinearity of the Euler{Poisson equations, it is possible that the nonlinear Jeans instability may lead to a faster density growing rate than the rate in the standard theory of linearized Jeans instability, which motivates us to study the nonlinear Jeans instability. The aim of this article is to develop a method proving the Jeans instability for slightly nonlinear Euler-Poisson equations in the expanding Newtonian universe. The standard proofs of the Jeans instability rely on the Fourier analysis. However, it is difficult to generalize Fourier method to a nonlinear setting, and t…
A correction to the Jeans stability criterion due to heat conduction is established for the case of high temperature gases. This effect is only relevant for relativistic fluids and includes an additional term due to a density gradient driven heat flux. The result is obtained by thoroughly analyzing the exponentially growing modes present in the dynamics of density fluctuations in the linearized relativistic Navier-Stokes regime. The corrections to the corresponding Jeans mass and wavenumber are explicitly obtained and are compared to the non-relativistic and non-dissipative values using the tr…
We derive the metric for a Bianchi type I space-time with energy density that is dominated by that of a perfect fluid with equation of state $p=wρ$ and whose anisotropy is seeded by a fixed norm spacelike vector field. We solve for the evolution of perturbations about this space-time. In particular, the Jeans instability in an expanding flat Friedmann-Robertson-Walker universe is modified by the presence of the vector field so that energy density perturbations develop direction-dependent growth. We also briefly consider observational limits on the vector field vacuum expectation value, $m$. We…
The Jeans stability criterium for gravitational collapse is examined for the case of an inert binary mixture in local equilibrium, neglectinq dissipative effects. The corresponding transport equations are established using kinetic theory within the Euler regime approximation. It is shown that the corresponding dispertion relation is modified, yielding corrections to the Jeans wave number. This formalism that can be generalized for several interesting cases involving dissipation.
The problem of Jeans gravitational instability is investigated for static and expanding universes within the context of the five and thirteen field theories which account for viscous and thermal effects. For the five-field theory a general dispersion relation has been derived with the help of relevant linearized perturbation equations, showing that the shear viscosity parameter alters the propagating modes for large and small wavelengths. The behavior of density and temperature contrasts are analyzed for the hard-sphere model in detail. In the small wavelengths regime, increasing the amount of…
Typical observers in the universe do not follow the smooth Hubble expansion, but move relative to it. Such bulk peculiar motions introduce a characteristic scale that is closely analogous to the familiar Jeans length. This "peculiar Jeans length" marks the threshold below which relative-motion effects dominate the linear kinematics. There, cosmological measurements can vary considerably between the bulk-flow frame and that of the Hubble expansion, entirely due to the observers' relative motion. When dealing with the deceleration parameter, we find that the peculiar Jeans length varies between …
We discuss the diffusion equation resulting from a strong dissipation limit of the random wave equation arising in the models of warm inflation. We show that the long wave power spectrum of scalar perturbations in the model of an exponential expansion coincides with the spectrum of quantum fluctuations on this space time.
We consider the Jeans instability and the gravitational collapse of the rotating Bose-Einstein Condensate dark matter halos, described by the zero temperature non-relativistic Gross-Pitaevskii equation, with repulsive inter-particle interactions. In the Madelung representation of the wave function, the dynamical evolution of the galactic halos is described by the continuity and the hydrodynamic Euler equations, with the condensed dark matter satisfying a polytropic equation of state with index $n=1$. By considering small perturbations of the quantum hydrodynamical equations we obtain the dispe…
We examine the solutions of the equations of motion for an expanding Universe, taking into account the radiation of the inflaton field energy. We then analyze the question of the generality of inflationary solutions in this more general setting of a dissipative system. We find a surprisingly rich behavior for the solutions of the dynamical system of equations in the presence of dissipational effects. We also determine that a value of dissipation as small as $\sim 10^{-7} H$ can lead to a smooth exit from inflation to radiation.
A simple model of uniformly expanding, homogeneous Universe with a bulk viscosity is studied wherein the inflationary density decays due to viscous dissipation during the expansion phase of the Universe. The model is shown to generate the Cosmic Microwave Background radiation (CMB). We also demonstrate that, at late times, the inflationary density asymptotically approaches a small finite constant value.
With an aim to argue for the truly collisionless nature of cold dark matter between epochs of equality and recombination, we assume a model, wherein strongly coupled baryon-radiation plasma ejects out of small regions of concentrated cold dark matter without losing its equilibrium. We use the Meschersky equation to describe the dynamics of cold dark matter in the presence of varying mass of strongly coupled baryon-radiation plasma. Based on this model, we discuss the growth of perturbations in cold dark matter both in the Jeans theory and in the expanding universe using Newton's theory. We see…
Using a generalization of the Madelung transformation, we derive the hydrodynamic representation of the Klein-Gordon-Einstein equations in the weak field limit. We consider a complex self-interacting scalar field with a $λ|φ|^4$ potential. We study the evolution of the homogeneous background in the fluid representation and derive the linearized equations describing the evolution of small perturbations in a static and in an expanding universe. We compare the results with simplified models in which the gravitational potential is introduced by hand in the Klein-Gordon equation, and assumed to sat…
We study the dissipation of oscillating scalar backgrounds in a spatially flat Friedmann-Lemaître-Robertson-Walker universe using non-equilibrium quantum field theory. To be concrete, a $Z_2$-symmetric two-scalar model with quartic interactions is used. For quasi-harmonic oscillations, we adopt the multi-scale analysis to obtain analytical approximate expressions for the evolution of the scalar background in terms of the retarded self-energy and retarded proper four-vertex function. Different from the case in flat spacetime, we find that in an expanding universe the condensate decay in this mo…
Recently the formation of an expanding universe from the (1+3+6)-dimensional space-times has been proposed on the basis of super-string theory. The serious entropy problem must be solved for it to be realistic from the cosmological viewpoint. It is discussed here, taking account of the large dissipation due to the viscous motion between the collapsing inner space and the inflating outer space. It is shown that the large dissipation may be effective for the vast production of 3-dimensional entropy S_3 within the horizon, and that there are epochs when S_3 reaches the critical value 10^88 in the…
The Markovian diffusion theory in the phase space is generalized within the framework of the general theory of relativity. The introduction of moving orthonormal frame vectors both for the position as well the velocity space enables to bypass difficulties in the general relativistic stochastic calculus. The general relativistic Kramers equation in the phase space is derived both in the parametrization of phase space proper time and the coordinate time. The transformation of the obtained diffusion equation under hypersurface-preserving coordinate transformations is analyzed and diffusion in the…
We propose an interpretation of the expansion and acceleration of the Universe from an information theoretic viewpoint. We obtain the time evolution of the configuration entropy of the mass distribution in a static Universe and show that the process of gravitational instability leads to a rapid dissipation of configuration entropy during the growth of the density fluctuations making such a Universe entropically unfavourable. We find that in an expanding Universe, the configuration entropy rate is governed by the expansion rate of the Universe and the growth rate of density fluctuations. The co…
