WMAP and the Generalized Chaplygin Gas

TL;DR

This study tests the generalized Chaplygin gas as both a dark energy component and a unified dark matter candidate using the WMAP CMB power spectrum and SNIa data, accounting for adiabatic perturbations with a Jeans-length governed by $\alpha$. By exploring a flat cosmology with a broad parameter grid and applying CMBFAST-based predictions, the authors derive tight constraints: $\alpha<0.2$ and $w_X<-0.8$ (95% CL), with the Chaplygin gas ($\alpha=1$) ruled out at >99.99% CL as a DE candidate. The analysis shows that a unified dark matter scenario ($\Omega_c=0$) is strongly disfavored by CMB data relative to GCG as DE, though a best-fit UDM is not completely excluded at the ~2σ level. Incorporating SN Ia constraints weakens the leverage on $\alpha$ and $w_X$, while mass power spectrum considerations reveal the important role of baryons and nonlinear effects in reconciling CMB and LSS observations. Overall, standard quintessence-like models remain favored, with GCG providing strong predictive power and being tightly constrained by high-precision CMB data.

Abstract

We compare the WMAP temperature power spectrum and SNIa data to models with a generalized Chaplygin gas as dark energy. The generalized Chaplygin gas is a component with an exotic equation of state, p_X=-A/ρ^α_X (a polytropic gas with negative constant and exponent). Our main result is that, restricting to a flat universe and to adiabatic pressure perturbations for the generalized Chaplygin gas, the constraints at 95% CL to the present equation of state w_X = p_X / ρ_X and to the parameter αare -1\leq w_X < -0.8, 0 \leq α<0.2, respectively. Moreover, we show that a Chaplygin gas (α=1) as a candidate for dark energy is ruled out by our analysis at more than the 99.99% CL. A generalized Chaplygin gas as a unified dark matter candidate (Ω_{CDM}=0) appears much less likely than as a dark energy model, although its χ^2 is only two sigma away from the expected value.

Figures (8)

• Figure 1: The $C_{\ell }$ spectrum varying $w_{X}$ is plotted in comparison with a $\Lambda$CDM model (the upper curve): $w_{X}\simeq -0.8,-0.91,-0.99,-0.999$ from bottom to top, respectively. The other parameters are $\alpha =1$, $h=0.72$, $w_{b}=0.024$, $w_{c}=0.14$, $n_{s}=1$. The spectra are COBE normalized at $\ell =10$.
• Figure 2: The $C_{\ell }$ spectrum varying $\alpha$ is plotted in comparison with a $\Lambda$CDM model (the upper solid line): $\alpha =1,0.5,0.2,0$ from bottom to top, respectively. The other parameters are $w_{X}\simeq -0.99$, $h=0.72$, $w_{b}=0.024$, $w_{c}=0.14$, $n_{s}=1$. The spectra are COBE normalized at $\ell =10$. We note how the $\Lambda$CDM curve and $\alpha =0$ are very close, but not identical because of the different perturbation sectors.
• Figure 3: Marginalized likelihood functions for the six cosmological parameters. The dotted lines are for the HST prior on the Hubble constant. The horizontal long-dashed lines are the confidence levels at 68% and 95%. The vertical long-dashed lines in the panels for $\alpha \,, w_{X}$ mark the upper bounds at 68% and 95% CL.
• Figure 4: Likelihood in the plane $w_{X},\alpha$. The contours are at the 68%, 95% and 99% CL, inside to outside.
• Figure 5: Likelihood functions for the GCG model (full curve) and the unified model ($\Omega _{c}=0$ ; dashed curve). The horizontal long-dashed lines are the confidence levels at 68% and 95%. The vertical long-dashed lines in the panels for $\alpha \,, w_{X }$ mark the upper bounds at 68% and 95% CL.