Extended family of generalized Chaplygin gas models
2018, Physical review
https://doi.org/10.1103/PHYSREVD.98.043515Abstract
The generalized Chaplygin gas is usually defined as a barotropic perfect fluid with an equation of state p = −Aρ −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 = (1 + α) /(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 cs are regulated solely by β, with 0 ≤ cs ≤ 1 if β ≥ 1. We further demonstrate that in the nonrelativistic regime the standard equation of state p = −Aρ −α of the generalized Chaplygin gas is always recovered, while in the relativistic regime this is true only if β = (1 + α) /(2α). We present a regularization of the (α → 0, A → ∞) 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 = A ln (ρ/ρ *), where A is a real parameter and ρ * > 0 is an arbitrary energy density. We finally derive its Lagrangian formulation.
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