Hamilton-Jacobi Approach for Power-Law Potentials

The classical and relativistic Hamilton-Jacobi approach is applied to the one-dimensional homogeneous potential, $V(q)=\alpha q^n$, where $\alpha$ and $n$ are continuously varying parameters. In the non-relativistic case, the exact analytical solution is determined in terms of $\alpha$, $n$ and the total energy $E$. It is also shown that the non-linear equation of motion can be linearized by constructing a hypergeometric differential equation for the inverse problem $t(q)$. A variable transformation reducing the general problem to that one of a particle subjected to a linear force is also established. For any value of $n$, it leads to a simple harmonic oscillator if $E>0$, an "anti-oscillator" if $E<0$, or a free particle if E=0. However, such a reduction is not possible in the relativistic case. For a bounded relativistic motion, the first order correction to the period is determined for any value of $n$. For $n >> 1$, it is found that the correction is just twice that one deduced for the simple harmonic oscillator ($n=2$), and does not depend on the specific value of $n$.Comment: 12 pages, Late

Cosmographic constraints on a class of Palatini f(R) gravity

Modified gravity, known as $f(R)$ gravity, has presently been applied to Cosmology as a realistic alternative to dark energy. For this kind of gravity the expansion of the Universe may accelerate while containing only baryonic and cold dark matter. The aim of the present investigation is to place cosmographic constraints on the class of theories of the form $f(R)=R - \alpha/R^n$ within the Palatini approach. Although extensively discussed in recent literature and confronted with several observational data sets, cosmological tests are indeed inconclusive about the true signal of $n$ in this class of theories. This is particularly important to define which kind of corrections (infra-red or high-energy) to general relativity this class of theory indeed represent. We shed some light on this question by examining the evolution of the deceleration parameter $q(z)$ for these theories. We find that for a large range of $\alpha$, models based on $f(R) = R - \alpha/R^{n}$ gravity in the Palatini approach can only have positive values for $n$, placing thus a broad restriction on this class of gravity.Comment: 4 pages, 2 figures, Latex, Submitte

Is Λ\LambdaCDM an effective CCDM cosmology?

We show that a cosmology driven by gravitationally induced particle production of all non-relativistic species existing in the present Universe mimics exactly the observed flat accelerating $\Lambda$CDM cosmology with just one dynamical free parameter. This kind of scenario includes the creation cold dark matter (CCDM) model [Lima, Jesus & Oliveira, JCAP 011(2010)027] as a particular case and also provides a natural reduction of the dark sector since the vacuum component is not needed to accelerate the Universe. The new cosmic scenario is equivalent to $\Lambda$CDM both at the background and perturbative levels and the associated creation process is also in agreement with the universality of the gravitational interaction and equivalence principle. Implicitly, it also suggests that the present day astronomical observations cannot be considered the ultimate proof of cosmic vacuum effects in the evolved Universe because $\Lambda$CDM may be only an effective cosmology.Comment: 6 pages, 2 figures, changes in the abstract, introduction, new references and typo correction

New coupled quintessence cosmology

A component of dark energy has been recently proposed to explain the current acceleration of the Universe. Unless some unknown symmetry in Nature prevents or suppresses it, such a field may interact with the pressureless component of dark matter, giving rise to the so-called models of coupled quintessence. In this paper we propose a new cosmological scenario where radiation and baryons are conserved, while the dark energy component is decaying into cold dark matter (CDM). The dilution of CDM particles, attenuated with respect to the usual $a^{-3}$ scaling due to the interacting process, is characterized by a positive parameter $\epsilon$, whereas the dark energy satisfies the equation of state $p_x=\omega \rho_x$ ($\omega < 0$). We carry out a joint statistical analysis involving recent observations from type Ia supernovae, baryon acoustic oscillation peak, and Cosmic Microwave Background shift parameter to check the observational viability of the coupled quintessence scenario here proposed.Comment: 7 pages, 7 figures. Minor corrections to match published versio

Pair correlation function of short-ranged square-well fluids

We have performed extensive Monte Carlo simulations in the canonical (NVT) ensemble of the pair correlation function for square-well fluids with well widths $\lambda-1$ ranging from 0.1 to 1.0, in units of the diameter $\sigma$ of the particles. For each one of these widths, several densities $\rho$ and temperatures $T$ in the ranges $0.1\leq\rho\sigma^3\leq 0.8$ and $T_c(\lambda)\lesssim T\lesssim 3T_c(\lambda)$, where $T_c(\lambda)$ is the critical temperature, have been considered. The simulation data are used to examine the performance of two analytical theories in predicting the structure of these fluids: the perturbation theory proposed by Tang and Lu [Y. Tang and B. C.-Y. Lu, J. Chem. Phys. {\bf 100}, 3079, 6665 (1994)] and the non-perturbative model proposed by two of us [S. B. Yuste and A. Santos, J. Chem. Phys. {\bf 101}, 2355 (1994)]. It is observed that both theories complement each other, as the latter theory works well for short ranges and/or moderate densities, while the former theory does for long ranges and high densities.Comment: 10 pages, 10 figure

Comment on "Theory and computer simulation for the equation of state of additive hard-disk fluid mixtures"

A flaw in the comparison between two different theoretical equations of state for a binary mixture of additive hard disks and Monte Carlo results, as recently reported in C. Barrio and J. R. Solana, Phys. Rev. E 63, 011201 (2001), is pointed out. It is found that both proposals, which require the equation of state of the single component system as input, lead to comparable accuracy but the one advocated by us [A. Santos, S. B. Yuste, and M. L\'{o}pez de Haro, Mol. Phys. 96, 1 (1999)] is simpler and complies with the exact limit in which the small disks are point particles.Comment: 4 pages, including 1 figur

Nonlinear viscosity and velocity distribution function in a simple longitudinal flow

A compressible flow characterized by a velocity field $u_x(x,t)=ax/(1+at)$ is analyzed by means of the Boltzmann equation and the Bhatnagar-Gross-Krook kinetic model. The sign of the control parameter (the longitudinal deformation rate $a$) distinguishes between an expansion ($a>0$) and a condensation ($a<0$) phenomenon. The temperature is a decreasing function of time in the former case, while it is an increasing function in the latter. The non-Newtonian behavior of the gas is described by a dimensionless nonlinear viscosity $\eta^*(a^*)$, that depends on the dimensionless longitudinal rate $a^*$. The Chapman-Enskog expansion of $\eta^*$ in powers of $a^*$ is seen to be only asymptotic (except in the case of Maxwell molecules). The velocity distribution function is also studied. At any value of $a^*$, it exhibits an algebraic high-velocity tail that is responsible for the divergence of velocity moments. For sufficiently negative $a^*$, moments of degree four and higher may diverge, while for positive $a^*$ the divergence occurs in moments of degree equal to or larger than eight.Comment: 18 pages (Revtex), including 5 figures (eps). Analysis of the heat flux plus other minor changes added. Revised version accepted for publication in PR

On FRW Model in Conformal Teleparallel Gravity

In this paper we use the conformal teleparallel gravity to study an isotropic and homogeneous Universe which is settled by the FRW metric. We solve the field equations and we obtain the behavior of some cosmological parameters such as scale factor, deceleration parameter and the energy density of the perfect fluid which is the matter field of our model. The field equations, that we called modified Friedmann equations, allow us to define a dark fluid, with dark energy density and dark pressure, responsible for the acceleration in the Universe.Comment: Accepted in EPJ