Cosmological Volumes

Cosmological voumes are relatively simple: they are cubic regions, with a uniform mass resolution, seeded with slight density perturbations by shifting an initially uniform grid of particles. The particle mass in a cosmological volume is set purely by the cosmology. The key quantity here will be the critical density, where $h=H/100km/s/Mpc$:

${\rho }_{crit}\equiv \frac{3H^2}{8\pi G}\approx 2.775\times 10^{11}{h}^2{\mathrm{cMpc}}^{-3}$

For a collisionless run with $N^3$ particles in box with side length $L\mathrm{cMpc}$, this gives a particle mass of

$m_p=\frac{{\Omega }_{m}3H^2}{8\pi G}{\left(\frac{L}{N}\right)}^3$