Skewness as a Test of the Equivalence Principle

The skewness of the large-scale distribution of matter has long been known to be a probe of gravitational clustering. Here we show that the skewness is also a probe of violation of the equivalence principle between dark matter and baryons. The predicted level of violation can be tested with the forthcoming data from the Sloan Digital Sky Survey.

Figure 1

Contour plot of the observable quantities $S_{3b}·(7/34)$, $S_{3c}·(7/34)$ calculated numerically as a function of ${\Omega }_m,\beta$. For $S_{3b}$, the lines correspond to the contour values 1.0, 1.002, 1.01, 1.03, 1.05, and 1.08, while for $S_{3c}$ they are 1, 1.001, 0.999, 0.995, 0.99, and 0.98, both from bottom to top. The short-dashed curves in the plot $S_{3b}$ are the fit (17); the dotted curves the approximation (16). The light rectangle marks the astrophysical bounds on ${\Omega }_m$, the darker one adds the CMB constraint assuming constant $\beta$.