The description of the abundance and clustering of haloes for non‐Gaussian initial conditions has recently received renewed interest, motivated by the forthcoming large galaxy and cluster surveys, which can potentially yield constraints of the order of unity on the non‐Gaussianity parameter fNL. We present tests on N‐body simulations of analytical formulae describing the halo abundance and clustering for non‐Gaussian initial conditions. We calibrate the analytic non‐Gaussian mass function of Matarrese, Verde & Jimenez and LoVerde et al. and the analytic description of clustering of haloes for non‐Gaussian initial conditions on N‐body simulations. We find an excellent agreement between the simulations and the analytic predictions if we make the corrections and , where q≃ 0.75, in the density threshold for gravitational collapse and in the non‐Gaussian fractional correction to the halo bias, respectively. We discuss the implications of this correction on present and forecasted primordial non‐Gaussianity constraints. We confirm that the non‐Gaussian halo bias offers a robust and highly competitive test of primordial non‐Gaussianity.

We have performed high-resolution cosmological N-body simulations of a concordance ΛCDM model to study the evolution of virialized, dark matter haloes in the presence of primordial non-Gaussianity. Following a standard procedure, departures from Gaussianity are modelled through a quadratic Gaussian term in the primordial gravitational potential, characterized by a dimensionless non-linearity strength parameter fNL. We find that the halo mass function and its redshift evolution closely follow the analytic predictions of Matarrese, Verde & Jimenez. The existence of precise analytic predictions makes the observation of rare, massive objects at large redshift an even more attractive test to detect primordial non-Gaussian features in the large-scale structure of the Universe

We study non‐linear structure formation in high‐resolution simulations of early dark energy (EDE) cosmologies and compare their evolution with the standard Λ cold dark matter (ΛCDM) model. In EDE models, the impact on structure formation is expected to be particularly strong because of the presence of a non‐negligible dark energy component even at very high redshift, unlike in standard models that behave like matter‐dominated universes at early times. In fact, extensions of the spherical top‐hat collapse model predict that the virial overdensity and linear threshold density for collapse should be modified in EDE model, yielding significant modifications in the expected halo mass function. Here, we present numerical simulations that directly test these expectations. Interestingly, we find that the Sheth & Tormen formalism for estimating the abundance of dark matter haloes continues to work very well in its standard form for the EDE cosmologies, contrary to analytic predictions. The residuals are even slightly smaller than for ΛCDM. We also study the virial relationship between mass and dark matter velocity dispersion in different dark energy cosmologies, finding excellent agreement with the normalization for ΛCDM as calibrated by Evrard et al. The earlier growth of structure in EDE models relative to ΛCDM produces large differences in the mass functions at high redshift. This could be measured directly by counting groups as a function of the line‐of‐sight velocity dispersion, skirting the ambiguous problem of assigning a mass to the halo. Using dark matter substructures as a proxy for member galaxies, we demonstrate that even with three to five members sufficiently accurate measurements of the halo velocity dispersion function are possible. Finally, we determine the concentration–mass relationship for our EDE cosmologies. Consistent with the earlier formation time, the EDE haloes show higher concentrations at a given halo mass. We find that the magnitude of the difference in concentration is well described by the prescription of Eke, Navarro & Steinmetz for estimating halo concentrations.

n this work, we study the properties of the mass density field in the non-Gaussian world models simulated by Grossi et al. In particular, we focus on the one-point density probability distribution function of the mass density field in non-Gaussian models with quadratic non-linearities quantified by the usual parameter fNL. We find that the imprints of primordial non-Gaussianity are well preserved in the negative tail of the probability function during the evolution of the density perturbation. The effect is already notable at redshifts as large as 4 and can be detected out to the present epoch. At z = 0, we find that the fraction of the volume occupied by regions with underdensity δ < -0.9, typical of voids, is about 1.3 per cent in the Gaussian case and increases to ~2.2 per cent if fNL = -1000 while decreases to ~0.5 per cent if fNL = +1000. This result suggests that void-based statistics may provide a powerful method to detect non-Gaussianity even at low redshifts, which is complementary to the measurements of the higher order moments of the probability distribution function like the skewness or the kurtosis for which deviations from the Gaussian case are detected at the 25-50 per cent level