Halo Counts-in-cells for Cosmological Models with Different Dark Energy

We examine the counts-in-cells probability distribution functions that describe dark matter halos in the Dark Energy Universe Simulations (DEUS). We describe the measurements between redshifts $z=0$ to $z=4$ on both linear and non-linear scales. The best-fits of the gravitational quasi-equilibrium distribution (GQED), the negative binomial distribution (NBD), the Poisson-Lognormal distribution (PLN), and the Poisson-Lognormal distribution with a bias parameter (PLNB) are compared to simulations. The fits agree reasonably consistently over a range of redshifts and scales. To distinguish quintessence (RPCDM) and phantom ($w$CDM) dark energy from $\Lambda$ dark energy, we present a new method that compares the model parameters of the counts-in-cells probability distribution functions. We find that the mean and variance of the halo counts-in-cells on $2-25h^{-1}$Mpc scales between redshifts $0.65<z<4$ show significant percentage differences for different dark energy cosmologies. On $15-25h^{-1}$Mpc scales, the $g$ parameter in NBD, $\omega$ parameter in PLN, $b$ and $C_b$ parameters in PLNB show larger percentage differences for different dark energy cosmologies than on smaller scales. On $2-6h^{-1}$Mpc scales, kurtosis and the $b$ parameter in the GQED show larger percentage differences for different dark energy cosmologies than on larger scales. For cosmologies explored in the DEUS simulations, the percentage differences between these statistics for the RPCDM and $w$CDM dark energy cosmologies relative to $\Lambda$CDM generally increases with redshift from a few percent to significantly larger percentages at $z=4$. Applying our method to simulations and galaxy surveys can provide a useful way to distinguish among dark energy models and cosmologies in general.