Generalized power expansions in cosmology

It is given an algorithm to obtain generalized power asymptotic expansions of the solutions of the Einstein equations arising for several homogeneous cosmological models. This allows to investigate their behavior near the initial singularity or for large times. An implementation of this algorithm in the CAS system Maple V Release 4 is described and detailed calculations for three equations are shown.Comment: 22 pages, LaTeX, elsart.sty. To be published in Computer Physics Communications Thematic Issue "Computer Algebra in Physics Research

Unified model of baryonic matter and dark components

We investigate an interacting two-fluid cosmological model and introduce a scalar field representation by means of a linear combination of the individual energy densities. Applying the integrability condition to the scalar field equation we show that this "exotic quintessence" is driven by an exponential potential and the two-fluid mixture can be considered as a model of three components. These components are associated with baryonic matter, dark matter and dark energy respectively. We use the Simon, Verde & Jimenez (2005) determination of the redshift dependence of the Hubble parameter to constrain the current density parameters of this model. With the best fit density parameters we obtain the transition redshift between non accelerated and accelerated regimes z_{acc}=0.66 and the time elapsed since the initial singularity t_0= 19.8 Gyr. We study the perturbation evolution of this model and find that the energy density perturbation decreases with the cosmological time.Comment: 8 pages, 6 figures A new section adde

Quintessence as k-essence

Quintessence and k-essence have been proposed as candidates for the dark energy component of the universe that would be responsible of the currently observed accelerated expansion. In this paper we investigate the degree of resemblance between those two theoretical setups, and find that every quintessence model can be viewed as a k-essence model generated by a kinetic linear function. In addition, we show the true effects of k-essence begin at second order in the expansion of the kinetic function in powers of the kinetic energy.Comment: 14 pages, improved discussion, matches published versio

Comments on Unified dark energy and dark matter from a scalar field different from quintessence

In a recent paper by C. Gao, M. Kunz, A. Liddle and D. Parkinson [arXiv:0912.0949], the unification of dark matter and dark energy was explored within a theory containing a scalar field of non-Lagrangian type. This scalar field, different from the classic quintessence, can be obtained from the scalar field representation of an interacting two-fluid mixture described in the paper by L.P. Chimento and M. Forte [arXiv:0706.4142

Form Invariance of Differential Equations in General Relativity

Einstein equations for several matter sources in Robertson-Walker and Bianchi I type metrics, are shown to reduce to a kind of second order nonlinear ordinary differential equation $\ddot{y}+\alpha f(y)\dot{y}+\beta f(y)\int{f(y) dy}+\gamma f(y)=0$. Also, it appears in the generalized statistical mechanics for the most interesting value q=-1. The invariant form of this equation is imposed and the corresponding nonlocal transformation is obtained. The linearization of that equation for any $\alpha, \beta$ and $\gamma$ is presented and for the important case $f=by^n+k$ with $\beta=\alpha ^2 (n+1)/((n+2)^2)$ its explicit general solution is found. Moreover, the form invariance is applied to yield exact solutions of same other differential equations.Comment: 22 pages, RevTeX; to appear in J. Math. Phy

Big brake singularity is accommodated as an exotic quintessence field

We describe a big brake singularity in terms of a modified Chaplygin gas equation of state p=(\ga_{m}-1)\rho+\al\ga_{m}\rho^{-n}, accommodate this late-time event as an exotic quintessence model obtained from an energy-momentum tensor, and focus on the cosmological behavior of the exotic field, its kinetic energy and the potential energy. At the background level, the exotic field does not blow up whereas its kinetic energy and potential both grow without limit near the future singularity. We evaluate the classical stability of this background solution by examining the scalar perturbations of the metric along with the inclusion of entropy perturbation in the perturbed pressure. Within the Newtonian gauge, the gravitational field approaches a constant near the singularity plus additional regular terms. When the perturbed exotic field is associated with \al>0 the perturbed pressure and contrast density both diverge, whereas the perturbed exotic field and the divergence of the exotic field's velocity go to zero exponentially. When the perturbed exotic field is associated with \al<0 the contrast density always blows up, but the perturbed pressure can remain bounded. In addition, the perturbed exotic field and the divergence of the exotic field's velocity vanish near the big brake singularity. We also briefly look at the behavior of the intrinsic entropy perturbation near the singular event.Comment: 11 pages, no figures. Accepted for its publication in PR