Separate Universe

In standard N-body simulations, the mean matter matter density in the box is \(\Omega_{\rm m}\rho_{\rm crit}(1+z)^3\), where \(\rho_{\rm crit}(z)\) is the critical density at redshift 0. In other words, the mean matter overdensity (with respect to the global one), \(\delta_b\), is zero. However, in the real Universe, regions of finite volume will exhibit fluctuations around \(\delta_b=0\) due to perturbation on scales larger than the considered regions. Separate Universe simulations will follow the evolution of dark matter particles under the influence of an overdensity different to zero; or equivalently under the impact of a fluctuation that is larger than the size of the box. These simulations will thus have one extra parameter, \(\delta_b\) that represents the mean overdensity over the entire box.

The way to incorporate the global overdensity is to change the cosmology of it, introducing curvature. Thus, in these simulations \(\Omega_K \neq 1\). Currently, the only Quijote simulations with \(\delta_b\neq 0\) are DC_p and DC_m that are designed to compute partial derivatives to quantify supersample covariance effects. See section 2.3 of the Quijote paper.

These simulation are designed to explore and quatify the impact of super-sample covariance on cosmological ohservables. Many thanks to Yin Li for setting up the initial conditions and cosmology of these simulations.