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Extended family of generalized Chaplygin gas models

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

Abstract
The generalized Chaplygin gas is usually defined as a barotropic perfect fluid with an equation of state p = -A ρ, where rho 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 parametrized by three positive real parameters A, α, and β, which, for two specific choices of β [β = 1 and β = (1 + α)/(2 α)], 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 non-relativistic regime the standard equation of state p = -A ρ of the generalized Chaplygin gas is always recovered, while in the relativistic regime this is true only if β = (1 + α)/(2 α). We present a regularization of the (a -> 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.

Keywords
DARK ENERGY; FLUID; QUINTESSENCE; SUPERNOVAE; LAMBDA

Physical Review D
Volume 98, Issue 0435, Page 5
2018 August

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Instituto de Astrofísica e Ciências do Espaço Universidade do Porto Faculdade de Ciências da Universidade de Lisboa
Fundação para a Ciência e a Tecnologia COMPETE 2020 PORTUGAL 2020 União Europeia