Cosmological constraints on a decomposed Chaplygin gas

TL;DR

The paper addresses whether a generalized Chaplygin gas can be represented as interacting dark matter and vacuum energy, and how two covariant interaction choices—barotropic (Q_V^μ ∝ ∇^μρ_dm) and geodesic (Q^μ_(dm) ∝ u^μ_(dm))—affect linear perturbations. It derives the perturbation equations for both decomposed models, analyzes their impact on CMB and LSS power spectra, and constrains the interaction parameter α using combinations of CMB, SNIa, BAO, LSS, and gISW data with CosmoMC/CAMB. The main result is that the barotropic model requires α to be extremely small (α ≲ 10^{-6}), effectively recovering ΛCDM, while the geodesic model allows a much broader α range (approximately -0.15 to 0.26 at 95% CL), making larger departures from ΛCDM compatible with current observations. This work demonstrates that perturbation evolution, particularly the effective sound speed, is crucial for distinguishing between decomposed interacting models and the standard ΛCDM framework, even when background expansion is degenerate.

Abstract

Any unified dark matter cosmology can be decomposed into dark matter interacting with vacuum energy, without introducing any additional degrees of freedom. We present observational constraints on an interacting vacuum plus dark energy corresponding to a generalised Chaplygin gas cosmology. We consider two distinct models for the interaction leading to either a barotropic equation of state or dark matter that follows geodesics, corresponding to a rest-frame sound speed equal to the adiabatic sound speed or zero sound speed, respectively. For the barotropic model, the most stringent constraint on $α$ comes from the combination of CMB+SNIa+LSS(m) gives $α<5.66\times10^{-6}$ at the 95% confidence level, which indicates that the barotropic model must be extremely close to the $Λ$CDM cosmology. For the case where the dark matter follows geodesics, perturbations have zero sound speed, and CMB+SNIa+gISW then gives the much weaker constraint $-0.15<α<0.26$ at the 95% confidence level.

Figures (11)

• Figure 1: The Hubble parameter as a function of redshift z for different values of parameter $\alpha$, where the solid line with $\alpha$ = 0 corresponds to $\Lambda$CDM model.
• Figure 2: The sound speed as a function of scale factor a for the barotropic model.
• Figure 3: The dark matter density perturbations on fixed scales: k = 0.001 $[\textmd{h~Mpc}^{-1}]$ (left panel) and k = 0.01 $[\textmd{h~Mpc}^{-1}]$ (right panel) as a function of scale factor for the barotropic model. The thin solid line, dashed line, dotted line, dot-dashed line and thick solid line correspond to $\alpha$ = 0.1, 0.05, 0.01, 0.001, 0 ($\Lambda$CDM model), respectively.
• Figure 4: The dark matter density perturbations on fixed scales: k = 0.001 $[\textmd{h~Mpc}^{-1}]$ (left panel) and k = 0.01 $[\textmd{h~Mpc}^{-1}]$ (right panel) as a function of scale factor for the geodesic model. The thin solid line, dashed line, thick solid line, dotted line and dot-dashed line correspond to $\alpha$ = 0.2, 0.1, 0 ($\Lambda$CDM model), -0.1, -0.2, respectively.
• Figure 5: CMB temperature power spectra vs multipole moment l. The solid line is for the $\Lambda$CDM model. Left panel: The thick lines and thin lines for the same values of parameter $\alpha$ correspond to the barotropic model and geodesic model, respectively. Right panel: The dashed line and dotted line correspond to $\alpha = 0.1$ and $\alpha = -0.1$ in the geodesic model, respectively.