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arXiv 1807.04656gr-qcastro-ph.CO
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Extended family of generalized Chaplygin gas models

V. M. C. Ferreira, P. P. Avelino

备注：
5 pages
发表信息：
Phys. Rev. D 98, 043515 (2018)
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英文摘要：

The generalized Chaplygin gas is usually defined as a barotropic perfect fluid with an equation of state $p=-A ρ^{-α}$, where $ρ$ and $p$ are the proper energy density and pressure, respectively, and $A$ and $α$ are positive real parameters. It has been extensively studied in the literature as a quartessence prototype unifying dark matter and dark energy. Here, we consider an extended family of generalized Chaplygin gas models parameterized by three positive real parameters $A$, $α$ and $β$, which, for two specific choices of $β$ [$β=1$ and $β=\left(1+α\right)/(2α)$], is described by two different Lagrangians previously identified in the literature with the generalized Chaplygin gas. We show that, for $β> 1/2$, the linear stability conditions and the maximum value of the sound speed $c_s$ are regulated solely by $β$, with $0 \le c_s \le 1$ if $β\ge 1$. We further demonstrate that in the non-relativistic regime the standard equation of state $p=-A ρ^{-α}$ of the generalized Chaplygin gas is always recovered, while in the relativistic regime this is true only if $β=\left(1+α\right)/(2α)$. We present a regularization of the ($α\rightarrow 0$, $A \rightarrow \infty$) limit of the generalized Chaplygin gas, showing that it leads to a logarithmic Chaplygin gas model with an equation of state of the form $p = {\mathcal A} \ln\left(ρ/ρ_{*}\right)$, where ${\mathcal A}$ is a real parameter and $ρ_*>0$ is an arbitrary energy density. We finally derive its Lagrangian formulation.

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