Skewness as a Probe of Gravity: Real and Redshift Space Counts-In-Cells

We study the counts-in-cells reduced skewness $s_3$ for dark matter, halo, and galaxy distributions in both real and redshift space, using the ELEPHANT ($\mathit{\text{Extended}}\mathit{\text{LEnsing}}\mathit{\text{PHysics}}\mathit{\text{with}}\mathit{\text{ANalytical}}\mathit{\text{ray}}\mathit{\text{Tracing}}$) suite of $N$-body simulations. We compare General Relativity (GR) with two extended (EG) gravity models: $f(R)$ gravity with chameleon screening and the normal-branch Dvali-Gabadadze-Porrati (nDGP) model with Vainshtein screening. We quantify the suppression of $s_3$ by redshift-space distortions (RSD), finding that while small-scale skewness is strongly reduced, the $F5$ model retains a $\sim 4\mathrm{\%}$ deviation from GR in galaxy samples, corresponding to a $2\sigma$ significance. We show that the ratio $s_3^{\mathrm{R}\mathrm{S}\mathrm{D}}\mathrm{/}{s}_3^{\mathrm{r}\mathrm{e}\mathrm{a}\mathrm{l}}$ is approximately independent of the gravity model across tracers and redshifts. Our results demonstrate that real-space predictions can help reliably infer redshift-space skewness in both GR and extended gravity, providing a new tool for testing gravity with current and forthcoming galaxy redshift surveys.