The study of a self-consistent system of interacting spinor and scalar fields within the scope of a Bianchi type I (BI) gravitational field in presence of a viscous fluid and $Λ$ term has been carried out. The system of equations defining the evolution of the volume scale of BI universe, energy density and corresponding Hubble constant has been derived. The system in question has been thoroughly studied qualitatively. Corresponding solutions are graphically illustrated. The system in question is also studied from the view point of blow up. It has been shown that the blow up takes place only in presence of viscosity.
We consider a system of nonlinear spinor and a Bianchi type I gravitational fields in presence of viscous fluid. The nonlinear term in the spinor field Lagrangian is chosen to be $λF$, with $λ$ being a self-coupling constant and $F$ being a function of the invariants $I$ an $J$ constructed from bilinear spinor forms $S$ and $P$. Self-consistent solutions to the spinor and BI gravitational field equations are obtained in terms of $τ$, where $τ$ is the volume scale of BI universe. System of equations for $τ$ and $\ve$, where $\ve$ is the energy of the viscous fluid, is deduced. This system is so…
We consider a self-consistent system of spinor and scalar fields within the framework of a Bianchi type I gravitational field filled with viscous fluid in presence of a $Λ$ term. Exact self-consistent solutions to the corresponding spinor, scalar and BI gravitational field equations are obtained in terms of $τ$, where $τ$ is the volume scale of BI universe. System of equations for $τ$ and $\ve$, where $\ve$ is the energy of the viscous fluid, is deduced. Some special cases allowing exact solutions are thoroughly studied.
The study of a self-consistent system of nonlinear spinor and Bianchi type I gravitational fields in presence of a viscous fluid and $Λ$ term with the spinor field nonlinearity being some arbitrary functions of the invariants $I$ an $J$ constructed from bilinear spinor forms $S$ and $P$, generates a multi-parametric system of ordinary differential equations \cite{saharrp,grqcnlsp}. A qualitative analysis of the system in question has been thoroughly carried out. A complete qualitative classification of the mode of evolution of the universe given by the corresponding dynamic system has been ill…
The Full (non--truncated) Israel--Stewart theory of bulk viscosity is applied to dissipative FRW spacetimes. Dimensionless variables and dimensionless equations of state are used to write the Einstein--thermodynamic equations as a plane autonomous system and the qualitative behaviour of this system is determined. Entropy production in these models is also discussed.
Isotropic and spatially homogeneous viscous fluid cosmological models are investigated using the truncated Israel-Stewart theory of irreversible thermodynamics to model the bulk viscous pressure. The governing system of differential equations is written in terms of dimensionless variables and a set of dimensionless equations of state is then utilized to complete the system. The resulting dynamical system is analyzed using geometric techniques from dynamical systems theory to find the qualitative behaviour of the Friedmann-Robertson-Walker models with bulk viscosity. In these models there exist…
The nature of cosmological solutions for a homogeneous, anisotropic Universe given by a Bianchi type-I (BI) model in the presence of a Cosmological constant $Λ$ is investigated by taking into account dissipative process due to viscosity. The system in question is thoroughly studied both analytically and numerically. It is shown the viscosity, as well as the $Λ$ term exhibit essential influence on the character of the solutions. In particular a negative $Λ$ gives rise to an ever-expanding Universe, whereas, a suitable choice of initial conditions plus a positive $Λ$ can result in a singularity-…
The truncated Israel-Stewart theory of irreversible thermodynamics is used to describe the bulk viscous pressure and the anisotropic stress in a class of spatially homogeneous viscous fluid cosmological models. The governing system of differential equations is written in terms of dimensionless variables and a set of dimensionless equations of state is utilized to complete the system. The resulting dynamical system is then analyzed using standard geometric techniques. It is found that the presence of anisotropic stress plays a dominant role in the evolution of the anisotropic models. In particu…
We analyse the quantization procedure of the spinor field in the Rindler spacetime, showing the boundary conditions that should be imposed to the field, in order to have a well posed theory. We then investigate the relationship between this construction and the usual one in Minkowski spacetime. This leads to the concept of "Unruh effect", that is the thermal nature of the Minkowski vacuum state from the point of view of an accelerated observer. It is demostrated that the two constructions are qualitatively different and can not be compared and consequently the conventional interpretation of th…
We explore the dynamical properties of a cosmological model that includes viscous effects in the dark matter sector of the fluid equations in a flat Friedmann-Lemaitre-Robertson-Walker (FLRW) spacetime. The bulk viscous effects are described by a non linear extension of the full Israel-Stewart model. We allow the interchange of energy in the dark sector by means of the interaction term, namely $Q$. We establish the dynamical system corresponding to Friedmann and fluid set of equations associated to the model and study the linear stability of its critical points. From the dynamical system, we s…
We analyse the quantization procedure of the spinor field in the Rindler spacetime, showing the boundary conditions that should be imposed to the field, in order to have a well posed theory. Because of these boundary conditions we argue that this construction and the usual one in Minkowski spacetime are qualitatively different and can not be compared and consequently the conventional interpretation of the Unruh effect, that is the thermal nature of the Minkowski vacuum state from the point of view of an accelerated observer, is questionable. We also analyse in detail the Unruh quantization sch…
We study the evolution of a homogeneous, anisotropic Universe given by a Bianchi type-I cosmological model filled with viscous fluid, in the presence of a cosmological constant $Λ$. The role of viscous fluid and $Λ$ term in the evolution the BI space-time is studied. Though the viscosity cannot remove the cosmological singularity, it plays a crucial part in the formation of a qualitatively new behavior of the solutions near singularity. It is shown that the introduction of the $Λ$ term can be handy in the elimination of the cosmological singularity. In particular, in case of a bulk viscosity, …
The behaviour of solutions to the Einstein equations with a causal viscous fluid source is investigated. In this model we consider a spatially flat Robertson-Walker metric, the bulk viscosity coefficient is related to the energy density as $ζ= αρ^{m}$, and the relaxation time is given by $ζ/ρ$. In the case $m = 1/2$ we find the exact solutions and we verify whether they satisfy the energy conditions. Besides, we study analytically the asymptotic stability of several families of solutions for arbitrary $m$. We find that the qualitative asymptotic behaviour in the far future is not altered by re…
The evolution of an homogeneous and isotropic dissipative fluid is analyzed using dynamical systems techniques. The dissipation is driven by bulk viscous pressure and the truncated Israel-Stewart theory is used. Although almost all solutions inflate, we show that only few of them can be considered as physical solutions since the dominant energy condition is not satisfied.
The acoustic analogue of the geometry of curved spacetime realised in a classical fluid becomes Lorentz violating in the presence of viscosity. We study how this effective Lorentz violation affects acoustic superradiance from the ergosphere of a rotating sonic black hole formed in such a fluid. It turns out that Lorentz violation imposes an upper bound on frequencies of acoustic perturbations that can get scattered from the ergosphere. Incidentally, this upper bound is same as that on the spectrum of superradiant frequencies. This study also reveals how superradiance is in general modified whe…
We study the mini--superspace quantization of spatially homogeneous (Bianchi) cosmological universes sourced by a Dirac spinor field. The quantization of the homogeneous spinor leads to a finite-dimensional fermionic Hilbert space and thereby to a multi-component Wheeler-DeWitt equation whose main features are: (i) the presence of spin-dependent Morse-type potentials, and (ii) the appearance of a q-number squared-mass term, which is of order ${\cal O}(\hbar^2)$, and which is affected by ordering ambiguities. We give the exact quantum solution of the Bianchi type-II system (which contains both …
We discuss the equilibrium conditions of the gravitational collapse of a spherically symmetric matter cloud. We analyze the spinor structure of a general collapsing space-time and redefine the equilibrium conditions by using Cartan scalars. We qualitatively investigate the equilibrium configuration of a two-fluid system consisting of a dust-like fluid and a fluid with a negative equation of state. We use our results to investigate certain cosmological scenarios where dark energy can cluster inside the over-dense regions of dark matter and together reaches a stable configuration. We compare the…
We study the impact of the viscous effects of the primordial plasma on the evolution of the primordial gravitational waves (pGW) spectrum from Inflation until today, considering a self-consistent interaction that incorporates the back-reaction of the GW into the plasma. We use a relativistic causal hydrodynamic framework with a positive entropy production based on a Second-Order Theory (SOT) in which the viscous properties of the fluid are effectively described by a new set of independent variables. We study how the spin-2 modes typical of SOTs capture the simplest GW-fluid viscous interaction…
We model the dark sector of the cosmic substratum by a viscous fluid with an equation of state $p=-ζΘ$, where $Θ$ is the fluid-expansion scalar and $ζ$ is the coefficient of bulk viscosity for which we assume a dependence $ζ\propto ρ^ν$ on the energy density $ρ$. The homogeneous and isotropic background dynamics coincides with that of a generalized Chaplygin gas with equation of state $p = - A/ρ^α$. The perturbation dynamics of the viscous model, however, is intrinsically non-adiabatic and qualitatively different from the Chaplygin-gas case. In particular, it avoids short-scale instabilities a…
