The Diffusion Coefficient of the Splashback Mass Function as a Probe of Cosmology

We present an analytic model for the splashback mass function of dark matter halos, which is parameterized by a single coefficient and constructed in the framework of the generalized excursion set theory and the self-similar spherical infall model. The value of the single coefficient that quantifies the diffusive nature of the splashback boundary is determined at various redshifts by comparing the model with the numerical results from the Erebos N-body simulations for the Planck and the WMAP7 cosmologies. Showing that the analytic model with the best-fit coefficient provides excellent matches to the numerical results in the mass range of $5\le M/(10^{12}h^{-1}\,M_{\odot})< 10^{3}$, we employ the Bayesian and Akaike Information Criterion tests to confirm that our model is most preferred by the numerical results to the previous models at redshifts of $0.3\le z\le 3$ for both of the cosmologies. It is also found that the diffusion coefficient decreases almost linearly with redshifts, converging to zero at a certain threshold redshift, $z_{c}$, whose value significantly differs between the Planck and WMAP7 cosmologies. Our result implies that the splashback mass function of dark matter halos at $z\ge z_{c}$ is well described by a parameter-free analytic formula and that $z_{c}$ may have a potential to independently constrain the initial conditions of the universe.