Skewness of matter distribution in clustering dark energy cosmologies

We calculate the skewness (the third moment $S_3$) of matter distribution in dynamical dark energy cosmologies. We pay particular attention to the impact of dark energy perturbations on this quantity. There is indeed a clear signature of dark energy perturbations on this quantity. By properly allowing dark energy perturbations we show that their impact on $S_3$ is strong enough (a factor $\sim 3$ greater) to easily discriminate between clustering and nonclustering dark energy cosmologies. This indicates that high order statistics of the cosmic density field are useful to the study of dark energy models and are potentially able to rule out clustering dark energy cosmologies.

Figure 1

Skewness as a function of the today’s fractionary matter density ${\mathrm{\Omega }}_{m0}$. Left panel: Dark energy perturbations are not considered. The LCDM curve is denoted by the red dashed line. The skewness assumes $S_3\approx 4.91$ for a ${\mathrm{\Omega }}_{m0}=0.315$ universe. We add the information on the impact of the dark energy equation of state. The stripe considers $w\mathrm{CDM}$ cosmologies without any dark energy perturbations with $w_0$ values given according to the color scheme shown in the inset of this panel. $w_0$ values $<-1(>-1)$ decreases (increases) $S_3$ but the impact is quite weak. Right panel: Dark energy perturbations are considered here. For ${\mathrm{\Omega }}_{m0}=0.315\pm 0.07$ values as given by the Planck best fit (which can be visualized by the vertical lines) the skewness assumes values $\sim 15$. The blue stripe also considers dark energy perturbations but its speed of sound is set to zero $c_a^2=0$. The black dot at ${\mathrm{\Omega }}_{m0}=1$ represents the Einstein the Sitter model (${\mathrm{\Omega }}_{m0}=1$) with its standard value $34/7\sim 4.857$. The $\mathrm{\Lambda }\mathrm{CDM}$ universe corresponds to the dotted red line.