Unified dark fluid with constant adiabatic sound speed: Including entropic perturbations

Abstract

In this paper, we continue to study a unified dark fluid model with a constant adiabatic sound speed but with the entropic perturbations. When the entropic perturbations are included, an effective sound speed, which reduces to the adiabatic sound speed when the entropic perturbations are zero, has to be specified as an additional free model parameter. Because of the relations between the adiabatic sound speed and equations of state ${c}_{s,ad}^{2}(a)=w(a)\ensuremath{-}d\mathrm{ln}(1+w(a))/3d\mathrm{ln}a$, the equation of state can be determined up to an integration constant, in principle, when an adiabatic sound speed is given. Then there are two degrees of freedom to describe the linear perturbations for a fluid. Its microscale properties are characterized by its equations of state or adiabatic sound speed and an effective sound speed. We take the effective sound speed and adiabatic sound speed as free model parameters and then use the currently available cosmic observational data sets, which include type Ia supernova Union 2.1, baryon acoustic oscillation, and WMAP 7-yr data of cosmic background radiation, to constrain the possible entropic perturbations and the adiabatic sound speed via the Markov Chain Monte Carlo method. The results show that the cosmic observations favor a small effective sound speed ${c}_{s,\mathrm{eff}}^{2}={0.00155}_{\ensuremath{-}0.00155}^{+0.000319}$ in the $1\ensuremath{\sigma}$ region.