Arbitrary scalar field and quintessence cosmological models

The mechanism of the initial inflationary scenario of the universe and of its late-time acceleration can be described by assuming the existence of some gravitationally coupled scalar fields $\phi$, with the inflaton field generating inflation and the quintessence field being responsible for the late accelerated expansion. Various inflationary and late-time accelerated scenarios are distinguished by the choice of an effective self-interaction potential $V(\phi )$, which simulates a temporarily non-vanishing cosmological term. In this work, we present a new formalism for the analysis of scalar fields in flat isotropic and homogeneous cosmological models. The basic evolution equation of the models can be reduced to a first order non-linear differential equation. Approximate solutions of this equation can be constructed in the limiting cases of the scalar field kinetic energy and potential energy dominance, respectively, as well as in the intermediate regime. Moreover, we present several new accelerating and decelerating exact cosmological solutions, based on the exact integration of the basic evolution equation for scalar field cosmologies. More specifically, exact solutions are obtained for exponential, generalized cosine hyperbolic, and power law potentials, respectively. Cosmological models with power law scalar field potentials are also analyzed in detail.Comment: 22 pages, 4 figures; references added; major revision; accepted for publication in EPJ

A Chiellini type integrability condition for the generalized first kind Abel differential equation

The Chiellini integrability condition of the first order first kind Abel equation $dy/dx=f(x)y^2+g(x)y^3$ is extended to the case of the general Abel equation of the form $dy/dx=a(x)+b(x)y+f(x)y^{\alpha -1}+g(x)y^{\alpha}$, where $\alpha \in \Re$, and $\alpha > 1$. In the case $\alpha =2$ the generalized Abel equations reduces to a Riccati type equation, for which a Chiellini type integrability condition is obtained.Comment: 4 pages, no figure

Bianchi type I cosmological models in Eddington-inspired Born-Infeld gravity

We consider the dynamics of a barotropic cosmological fluid in an anisotropic, Bianchi type I space-time in Eddington-inspired Born-Infeld (EiBI) gravity. By assuming an isotropic pressure distribution, we obtain the general solution of the field equations in an exact parametric form. The behavior of the geometric and thermodynamic parameters of the Bianchi type I Universe is studied, by using both analytical and numerical methods, for some classes of high density matter, described by the stiff causal, radiation, and pressureless fluid equations of state. In all cases the study of the models with different equations of state can be reduced to the integration of a highly nonlinear second order ordinary differential equation for the energy density. The time evolution of the anisotropic Bianchi type I Universe strongly depends on the initial values of the energy density and of the Hubble function. An important observational parameter, the mean anisotropy parameter is also studied in detail, and we show that for the dust filled Universe the cosmological evolution always ends into an isotropic phase, while for high density matter filled universes the isotropization of Bianchi type I universes is essentially determined by the initial conditions of the energy density.Comment: 23 pages, 12 figures; to appear in a Special Issue of Galaxies: "Beyond Standard Gravity and Cosmology". V2: references added, 24 pages; matches published versio

Causal Bulk Viscous Dissipative Isotropic Cosmologies with Variable Gravitational and Cosmological Constants

We consider the evolution of a flat Friedmann-Robertson-Walker Universe, filled with a causal bulk viscous cosmological fluid, in the presence of variable gravitational and cosmological constants. The basic equation for the Hubble parameter, generalizing the evolution equation in the case of constant gravitational coupling and cosmological term, is derived, under the supplementary assumption that the total energy of the Universe is conserved. By assuming that the cosmological constant is proportional to the square of the Hubble parameter and a power law dependence of the bulk viscosity coefficient, temperature and relaxation time on the energy density of the cosmological fluid, two classes of exact solutions of the field equations are obtained. In the first class of solutions the Universe ends in an inflationary era, while in the second class of solutions the expansion of the Universe is non-inflationary for all times. In both models the cosmological "constant" is a decreasing function of time, while the gravitational "constant" increases in the early period of evolution of the Universe, tending in the large time limit to a constant value.Comment: 14 pages, 15 figure

Relativistic Compact Objects in Isotropic Coordinates

We present a matrix method for obtaining new classes of exact solutions for Einstein's equations representing static perfect fluid spheres. By means of a matrix transformation, we reduce Einstein's equations to two independent Riccati type differential equations for which three classes of solutions are obtained. One class of the solutions corresponding to the linear barotropic type fluid with an equation of state $p=\gamma \rho$ is discussed in detail.Comment: 9 pages, no figures, accepted for publication in Pramana-Journal of Physic

Modified-gravity wormholes without exotic matter

A fundamental ingredient in wormhole physics is the flaring-out condition at the throat which, in classical general relativity, entails the violation of the null energy condition. In this work, we present the most general conditions in the context of modified gravity, in which the matter threading the wormhole throat satisfies all of the energy conditions, and it is the higher order curvature terms, which may be interpreted as a gravitational fluid, that support these nonstandard wormhole geometries. Thus, we explicitly show that wormhole geometries can be theoretically constructed without the presence of exotic matter, but are sustained in the context of modified gravity.Comment: 4 pages. V2: Slight change in title, discussion on the stability and references added; version to appear in PRD. V3: reference adde