Skewness as a test of dark energy perturbations

We investigate the role played by dark energy perturbations in the skewness $S_3$ of large-scale matter distribution. We consider a two-fluid universe composed by matter and dark energy, with perturbations in both components, and we estimate numerically the skewness of the matter density field as a function of the dark energy parameters. We characterize today’s $S_3$ value for quintessence and phantom dark energy cosmologies as well as its dependence on the matter density parameter ${\mathrm{\Omega }}_{m0}$ and the dark energy sound speed $c_s^2$ with accurate numerical fitting. These fits can be used to test cosmology against future high quality data on large scale structure.

Figure 1

Skewness evolution as a function of redshift. Solid lines represents $c_{de}^2=1$ cases, dot-dashed $c_{de}^2=0$, and dashed no DE perturbations. The colors represents the following cases: blue for a $\mathrm{\Lambda }\mathrm{CDM}$ case i.e., ${\mathrm{\Omega }}_{m0}=0.3$, $w_{de}=-1$ (cases for $w_{de}=-1$ and $c_{de}^2=0$, $c_{de}^2=1$ and no DE perturbation are indistinguishable); black for EdS case, i.e., ${\mathrm{\Omega }}_{m0}=1$. Then, always putting ${\mathrm{\Omega }}_{m0}=0.3$, we employ orange for $w_{de}=-0.8$: red for $w_{de}=-0.9$ and magenta for $w_{de}=-1.2$.

Figure 2

Dependence of the skewness on the density parameter ${\mathrm{\Omega }}_{m0}$. In the left panel the dot-dashed lines represent $c_{de}^2=0$, solid lines $c_{de}^2=1$ and dashed lines is the case without dark energy perturbations (${\delta }_{de}=0$). The colors refer to different $w_{de}$ values: blue for $w_{de}=-1$, magenta for $w_{de}=-1.2$, and orange for $w_{de}=-0.9$. The dashed and solid blue lines are indistinguishable. On the right side we show the skewness for $\mathrm{\Lambda }\ne 0$ by Bernardeau (1994) [15] (dashed blue) compared to our result (dashed black) for the $\mathrm{\Lambda }\mathrm{CDM}$ case ($w_{de}=-1$, ${\mathrm{\Omega }}_{m0}=0.3$ (black dot) and no dark energy perturbations ${\delta }_{de}=0$). The black line is for the EdS skewness value of $34/7=4.857$. The fit Eq. (16) is represented by the red cross symbols.

Figure 3

Dependence of $S_3$ on the dark energy equation of state $w_{de}$. The colored curves refers to different values of the matter density parameter, namely ${\mathrm{\Omega }}_{m0}=0.2$ (red), ${\mathrm{\Omega }}_{m0}=0.3$ (blue), and ${\mathrm{\Omega }}_{m0}=0.4$ (purple). The black line sets the Einstein–de Sitter value $34/7$. We assumed $c_{de}^2=1$ for solid lines, $c_{de}^2=0$ for dot-dashed lines, and no DE perturbations (${\delta }_{de}=0$) for dashed lines (hardly visible next to the solid curves).

Figure 4

Variation of skewness with ${\mathrm{\Omega }}_{m0}$ and $w_{de}$. On the left panels we fix ${\mathrm{\Omega }}_{m0}=0.3$; on the right panels we fix $w_{de}=-0.9$. The red line represents the fit from Eq. (17) and Table 2, and the black dots the data. Here we have the case for $c_{de}^2=0$ (top row) and $c_{de}^2=1$ (lower row).

Figure 5

Variation of skewness with $c_{de}^2$. The red line represents the fit Eq. (18) and Table 3 for ${\mathrm{\Omega }}_{m0}=0.3$ and $w_{de}=-0.9$; the black dots are the data.

Figure 6

Skewness compared to observational data from [20]. The red line represents the theoretical plot using our set of equations with ${\mathrm{\Omega }}_{m0}=0.27$ and $H_0=71\mathrm{km}/\mathrm{s}/\mathrm{Mpc}$ that was also used in [20]. The cases for different values of $w_{de}$ and $c_{de}^2$ are indistinguishable in this scale. Also the theoretical curve is almost independent of $z$; we plot here the $z=0.9$ case.