Generalizing the generalized Chaplygin gas

The generalized Chaplygin gas is characterized by the equation of state $p=-A/{\rho }^{\alpha }$, with $\alpha >-1$ and $w>-1$. We generalize this model to allow for the cases where $\alpha <-1$ or $w<-1$. This generalization leads to three new versions of the generalized Chaplygin gas: an early phantom model in which $w\ll -1$ at early times and asymptotically approaches $w=-1$ at late times, a late phantom model with $w\approx -1$ at early times and $w\to -\infty$ at late times, and a transient model with $w\approx -1$ at early times and $w\to 0$ at late times. We consider these three cases as models for dark energy alone and examine constraints from type Ia supernovae and from the subhorizon growth of density perturbations. The transient Chaplygin gas model provides a possible mechanism to allow for a currently accelerating universe without a future horizon, while some of the early phantom models produce $w<-1$ without either past or future singularities.

Figure 1

The energy density $\rho$ of the generalized Chaplygin gas (normalized to the present density ${\rho }_0$) as a function of the scale factor $a$ (taken to be $1$ at present). Solid curve is Case 2(a) (early phantom with $\alpha >0$: $A_s=1.1,\alpha =0.3$), dashed curve is Case 2(b) (early phantom with $-1<\alpha <0$: $A_s=1.2,\alpha =-0.95$), dashed-dot curve is Case 3 (transient GCG, with $A_s=0.9,\alpha =-1.5$) and dotted curve is Case 4 (late phantom, with $A_s=1.1,\alpha =-1.1$).

Figure 2

As Fig. 1, for the generalized Chaplygin gas equation of state parameter $w$, as a function of the scale factor $a$.

Figure 3

As Fig. 1, for the deceleration parameter $q$ as a function of the scale factor $a$, where we have taken ${\Omega }_{gcg0}=0.7$ and ${\Omega }_{m0}=0.3$.

Figure 4

Confidence contours in ${\Omega }_{m0}-A_s$ (left) and $\alpha -A_s$ (right) parameter space, marginalizing over $\alpha$ and ${\Omega }_{m0}$ respectively. Solid and dashed curves are the $68.3\%$ and $95\%$ confidence levels, respectively.

Figure 5

The $68.3\%$ confidence contours in $\alpha -A_s$ parameter space for different values of ${\Omega }_{m0}$. Solid, dashed, dash-dot and dotted lines are for ${\Omega }_{m0}=0.35,0.30,0.25$, and $0.20$, respectively

Figure 6

Evolution of the matter density perturbation $\delta$ as a function of the scale factor $a$ (normalized to $a=1$ at the present) for the standard GCG case with ${\Omega }_{m0}=0.3$.

Figure 7

Evolution of the matter density perturbation $\delta$ as a function of the scale factor $a$ (normalized to $a=1$ at the present) for the transient GCG case with ${\Omega }_{m0}=0.3$.

Figure 8

Evolution of the matter density perturbation $\delta$ as a function of the scale factor $a$ (normalized to $a=1$ at the present) for the late phantom GCG case with ${\Omega }_{m0}=0.3$.

Figure 9

Comparison of the evolution of the matter density perturbation $\delta$ for the transient and standard GCG cases with ${\Omega }_{m0}=0.3$.