Cosmological dynamical systems of non-minimally coupled fluids and scalar fields

In the present work we consider the existence and stability of Einstein static ES Universe in Brans–Dicke (BD) theory with non-vanishing spacetime torsion. In this theory, torsion field can be generated by the BD scalar field as well as the intrinsic angular momentum (spin) of matter. Assuming the matter content of the Universe to be a Weyssenhoff fluid, which is a generalization of perfect fluid in general relativity (GR) in order to include the spin effects, we find that there exists a stable ES state for a suitable choice of the model parameters. We analyze the stability of the solution by considering linear homogeneous perturbations and discuss the conditions under which the solution can be stable against these type of perturbations. Moreover, using dynamical system techniques and numerical analysis, the stability regions of the ES Universe are parametrized by the BD coupling parameter and first and second derivatives of the BD scalar field potential, and it is explicitly shown that a large class of stable solutions exists within the respective parameter space. This allows for non-singular emergent cosmological scenarios where the Universe oscillates indefinitely about an initial ES solution and is thus past eternal.

We consider the equations of motion for classical point particles moving in an external long-range attractive scalar field. Taking into account the effects of radiation damping leads to an integro-differential equation similar to the Lorentz--Dirac equation, except for the fact that the preacceleration time now depends on the external scalar field. If the external field is large enough, then the preacceleration time can become large enough to violate macroscopic causality in open systems in which the scalar field plays a part. (AIP)

First, the case of (0 + 1)-dimensional nonequilibrium quantum mechanics is analyzed using the Yukawa model in external scalar field $${{\phi }_{{{\text{cl}}}}}(t) = \frac{m}{{{\lambda }}} + \frac{{{\alpha }}}{{{\lambda }}}t$$ as an example. It is shown that the exact fermion propagators do not change with time, and the growth of bosonic propagators is determined by the contribution to the quantum mean of field $$\phi $$ and corresponds to the so-called "tadpole" diagrams. After that, the Yukawa theory of the interacting massive Dirac field and massless real scalar field in the (1 + 1)-dimensional Minkowski space with the signature (+1, –1) is examined. In this theory, a classical current is first calculated, and then quantum corrections for the Dirac field in an external coordinate-dependent scalar field with Yukawa interaction are determined. The response of fermion pair generation to an external bosonic field that linearly depends on the coordinate is studied.

An elementary example of fermion number fractionalization is given. The model considered is a massive Dirac fermion moving on the positive halfline in an external scalar Coulomb field. The theory is symmetric under charge conjugation. We demonstrate the existence of a nondegenerate, normalizable, and self-charge-conjugate zero energy solution in the theory. The vacuum thus has a fermion number $\ifmmode\pm\else\textpm\fi{}1/2$ depending on whether the lowest positive energy state without the external scalar field was filled or empty.

In this paper, we have constructed a five dimensional LRS Bianchi type I cosmological model with wet dark fluid (WDF) in general relativity with the matter field described as bulk viscosity. It is found that in presence of bulk viscosity an inflationary effective stiff fluid cosmological model is obtained, whereas in absence of bulk viscosity the wet dark fluid degenerate to stiff fluid. Some physical and geometrical properties of the model are also discussed.

We present results for the fermion determinant in an external Yukawa-coupled scalar field, a quantity relevant to instanton and sphaleron transition rates as well as bubble nucleation occuring in the electroweak phase transition when the scalar field is identified with the Higgs field. We calculate the determinant exactly and find an approximation (essentialy of the gradient expansion type) that reproduces the exact results very well if the fermion mass $m_F$ becomes larger than the inverse of the size $R$ of the background field configuration. The results are given for 2, 3 and 4 Euclidean dimensions.

The braneworld model of gravity is well-known for several notable\ncosmological features such as self-acceleration originating from a geometric\nand not matter source, effective dark energy behavior with phantom\ncharacteristics but not leading to a Big-Rip singularity, rough resemblance to\nthe $\\Lambda$CDM evolution, etc. The dynamical system tools usually allow us to\nobtain generic conclusions on the global dynamics of a system over a wide range\nof initial conditions. With this motivation, in order to recover the important\nfeatures of the braneworld model from a more global perspective, here, we\ninvestigate the global cosmological dynamics of the braneworld model using\ndynamical system techniques. We first analyze the case where there is just a\nnormal matter on the brane and then extend the analysis to the case with an\nextra scalar field also trapped on the brane. In the presence of a scalar\nfield, potentials belonging to different classes are considered. The stability\nbehavior of critical points is examined using linear stability analysis and\nwhen necessary center manifold theory as well as numerical perturbation\ntechniques are also used. To understand the global dynamics of a dynamical\nsystem, we utilized the Poincar\\'e compactification method to capture the\nproperties of all possible critical points. Applying dynamical system analysis,\nwe found that brane gravity is consistent with observed actions of the\nUniverse. In particular, our analysis shows that important cosmological\nbehaviors like the long-lasting matter-dominated era, late time acceleration as\nwell as the avoidance of\n Big-Rip singularity can be realized in brane gravity for a wide range of\ninitial conditions.\n

Cosmological models can be studied effectively using dynamical systems techniques. Starting from Brown’s formulation of the variational principle for relativistic fluids, we introduce new types of couplings involving a perfect fluid, a scalar field, and boundary terms. We describe three different coupling models, one of which turns out to be particularly relevant for cosmology. Its behaviour is similar to that of models in which dark matter decays into dark energy. In particular, for a constant coupling, the model mimics well-known dynamical dark energy models while the non-constant couplings offer a rich dynamical structure, unseen before. We are able to achieve this richness whilst working in a two-dimensional phase space. This is a significant advantage which allows us to provide a clear physical interpretation of the key features and draw analogies with previously studied models.

In this work we consider Randall-Sundrum brane-world type scenarios, in which the spacetime is described by a five-dimensional manifold with matter fields confined in a domain wall or three-brane. We present the results of a systematic analysis, using dynamical systems techniques, of the qualitative behavior of Friedmann-Lema\^{\i}tre-Robertson-Walker type models, whose matter is described by a scalar field with an exponential potential. We construct the state spaces for these models and discuss how their structure changes with respect to the general-relativistic case, and in particular, what new critical points appear and their nature and the occurrence of bifurcation.

A stability criterion is derived in general relativity for self-similar solutions with a scalar field and those with a stiff fluid, which is a perfect fluid with the equation of state P = ρ. A wide class of self-similar solutions turns out to be unstable against kink mode perturbation. According to the criterion, the Evans–Coleman stiff-fluid solution is unstable and cannot be a critical solution for the spherical collapse of a stiff fluid if we allow sufficiently small discontinuity in the density gradient field in the initial data sets. The self-similar scalar-field solution, which was recently found numerically by Brady et al (2002 Class. Quantum Grav. 19 6359), is also unstable. Both the flat Friedmann universe with a scalar field and that with a stiff fluid suffer from kink instability at the particle horizon scale.

We study a class of homogeneous and anisotropic geometries with affine equation of state (EoS) for different physically plausible scenarios of the universe evolution using dynamical system technique. We analyze the locally rotationally symmetric Bianchi I (LRS BI), Bianchi III (LRS BIII) and Bianchi V (LRS BV) geometry for the exhibition of the effects of affine EoS in the model. The model exhibits stable attractor which is also isotropic and thus, it may explain the late-time accelerated expansion of the universe. The model also possess stiff matter-, radiation- and matter-dominated phases prior to the dark energy assisted accelerating phase which are confirmed by the behaviours of effective equation of state and deceleration parameters. We use the statefinder diagnostic which is a geometrical diagnostic to explore model independent features of the cosmological dynamical system. The LRS BI, BIII and BV geometry based dynamical systems exhibit r=1,s=0(Lambda cold dark matter model) at late-times, which is compatible with the observations. The dynamical system for the Kantowski–Sachs model yields synchronous bounce on the basis of the model parameters. It also yields a late-time attractor which may explain the accelerated expansion of the universe in the model. The qualitative differences between LRS BIII and BV cosmological dynamical systems have also been discussed.

We parametrize a large class of corrections to general relativity which include a long-ranged gravitational scalar field as a dynamical degree of freedom in two ways: parametrizing the structure of the correction to the action, and parametrizing the scalar hair (multipole structure) that compact objects and black holes attain. The presence of this scalar hair violates the no-hair theorems present in general relativity, which leads to several important effects. The effects we consider are (i) the interaction between an isolated body and an external scalar field, (ii) the scalar multipole-multipole interaction between two bodies in a compact binary, (iii) the additional pericenter precession of a binary, (iv) the scalar radiation from a binary, and (v) the modification to the gravitational wave phase from a binary. We apply this framework to example theories including Einstein-dilaton-Gauss-Bonnet gravity and dynamical Chern-Simons gravity, and estimate the size of the effects. Finally, we estimate the bounds that can be placed on parameters of the theories from the precession of pulsar binaries and from gravitational waves.

The equilibrium thermodynamics of a many-particle assembly in the presence of an external scalar field is examined. Two types of scalar coupling are considered: an external field coupled to the particle density and an external scalar field coupled to the energy density. It is shown that the broken translational and rotational invariance of the system due to the external field is reflected in the macroscopic physics by loss of the usual extensivity property of the system and by means of anisotropy in the response of the system to changes in the system lengths or to the system shape. In addition, the assumptions used in local equilibrium analyses are shown to be incorrect in principle. Nonlocal effects due to the external field must be included in the determination of the equation of state. Simple model calculations for a system in an external gravitational field and an externally imposed temperature field are presented as illustrations.

Solutions obtained by Kramer (1984) for a rotating perfect fluid in general relativity are generalised. In the process a few results are noted that seem mathematically interesting and may be applicable elsewhere.

A previously discussed variational principle for a perfect fluid in general relativity was restricted to irrotational, isentropic motions of the fluid. It is proven that these restrictions can be dropped, and the original variational principle can be generalized to general motions of the perfect fluid. The form of the basic Lagrangian density is unchanged by these generalizations. An Eulerian fluid description is used throughout. As a by-product of our variational principle, the 4-velocity is required to have the generalized Clebsch form.