Narrow Results

In this paper, the implications of considering interaction between Chaplygin gas and a barotropic fluid with constant equation of state have been explored. The unique feature of this work is that assuming an interaction $Q\propto H{\rho }_d$, analytic expressions for the energy density and pressure have been derived in terms of the hypergeometric ${}_2{\text{F}}_1$ function. It is worthwhile to mention that an interacting Chaplygin gas model was considered in 2006 by Zhang and Zhu, nevertheless, analytic solutions for the continuity equations could not be determined assuming an interaction proportional to $H$ times the sum of the energy densities of Chaplygin gas and dust. Our model can successfully explain the transition from the early decelerating phase to the present phase of cosmic acceleration. Arbitrary choice of the free parameters of our model through trial and error shows that recent observational data strongly favors $w_m=0$ and $w_m=-\frac{1}{3}$ over the $w_m=\frac{1}{3}$ case. Interestingly, the present model also incorporates the transition of dark energy into the phantom domain, however, future deceleration is forbidden.

The geodesics equations on de Sitter (dS) and anti-de Sitter (AdS) spacetimes of any dimensions, are the starting point for deriving the general form of the Boltzmann equation in terms of conserved quantities. The simple equation for the non-equilibrium Marle and Anderson–Witting models are derived and the distributions of the Boltzmann–Marle model on these manifolds are written down first in terms of conserved quantities and then as functions of canonical variables.

In high-energy heavy-ion collisions, a nearly perfect fluid, the so-called strongly coupled quark–gluon plasma (QGP), forms. After the short period of thermalization, the evolution of this medium can be described by the laws of relativistic hydrodynamics. The time evolution of the QGP can be understood through direct photon spectra measurements, which are sensitive to the entire period between the thermalization and the freeze-out of the medium. I present a new analytic formula that describes the thermal photon radiation and it is derived from an exact and finite solution of relativistic hydrodynamics with accelerating velocity field. Then I compare my calculations to the most recent nonprompt spectrum of direct photons for $\mathrm{\text{Au}}+\mathrm{\text{Au}}$ at $\sqrt{s_{NN}}=200$GeV collisions. I have found a convincing agreement between the model and the data, which allows to give an estimate of the initial temperature in the center of the fireball. My results predict hydrodynamic scaling behavior for the thermal photon spectra of high-energy heavy-ion collisions.

For a class of viable cosmological models in f(R) gravity in which deviation from the Einstein gravity decreases as an inverse power law of the Ricci scalar R for large R, an analytic solution for density perturbations in the matter component during the matter-dominated stage is obtained in terms of hypergeometric functions. An analytical expression for the matter transfer function at scales much smaller than the present Hubble scale is also obtained.