Generalized Chaplygin Gas, Accelerated Expansion and Dark Energy-Matter Unification

TL;DR

This work generalizes the Chaplygin gas by introducing an equation of state $p = -A/\rho^{\alpha}$ with $0<\alpha\le 1$, providing a unified framework for dark matter and dark energy that evolves from a dust-dominated era to a cosmological-constant–dominated phase via an intermediate regime where $p = \alpha\rho$. The authors derive a generalized Born–Infeld (d-brane) Lagrangian from a Thomas–Fermi approximation of a massive complex scalar, obtaining the density evolution $\rho(a) = \left(A + B a^{-3(1+\alpha)}\right)^{1/(1+\alpha)}$ and connecting it to a brane description. They analyze linear inhomogeneities using a Zeldovich-inspired approach, deriving a perturbation equation for the deformation function and showing that the density contrast remains close to CDM at early times and decays toward ΛCDM-like growth at late times, for any $\alpha$ in the allowed range. Overall, the generalized Chaplygin gas offers a brane-based, single-fluid model capable of matching structure formation and CMB constraints while providing a natural interpolation between matter and dark-energy–dominated epochs, potentially mitigating fine-tuning and coincidence issues in cosmic acceleration.

Abstract

We consider the scenario emerging from the dynamics of a generalized $d$-brane in a $(d+1, 1)$ spacetime. The equation of state describing this system is given in terms of the energy density, $ρ$, and pressure, $p$, by the relationship $p = - A/ρ^α$, where $A$ is a positive constant and $0 < α\le 1$. We discuss the conditions under which homogeneity arises and show that this equation of state describes the evolution of a universe evolving from a phase dominated by non-relativistic matter to a phase dominated by a cosmological constant via an intermediate period where the effective equation of state is given by $p = αρ$.

Figures (4)

• Figure 1: Cosmological evolution of a universe described by a generalized Chaplygin gas equation of state.
• Figure 2: Evolution of $b(a)/b(a_{eq})$ for the generalized Chaplygin gas model, for different values of $\alpha$, as compared with CDM and $\Lambda$CDM.
• Figure 3: Evolution of $b(a)/b(a_{eq})$ for the generalized Chaplygin gas model, for different values of $\alpha$, as compared with $\Lambda$CDM.
• Figure 4: Density contrast for different values of $\alpha$, as compared with $\Lambda$CDM.