A revisited Correction to the Halo Mass Function for local-type Primordial non-Gaussianity

The theory of inflation predicts that the early Universe underwent a phase of rapid expansion, generating the initial density fluctuations that led to the formation of cosmic structures. A key observational signature of inflation are primordial non-Gaussianities (PNG), which quantify deviations from a Gaussian distribution of the primordial perturbations. Local-type PNG is particularly relevant, as its detection with a large amplitude would challenge standard inflationary models, such as single-field slow-roll inflation. In this work, we investigate the impact of local-type PNG on the halo mass function using a large set of cosmological N-body simulations. We find that existing theoretical models do not accurately describe the non-Gaussian halo mass function, with discrepancies becoming more pronounced for halos identified using higher density thresholds. These deviations are linked to changes in the internal density profile of dark matter halos, which we show is by the PNG parameter. To address these discrepancies, we introduce a correction to the linear density threshold for collapse, which depends on the halo identification threshold and is calibrated through Bayesian analysis. Finally, we show that this correction factor is independent of the PNG amplitude, the resolution of the simulations, and helps avoid systematic biases in parameter constraints. Our results provide an improved framework for extracting cosmological information from the halo mass function, which is particularly relevant for upcoming data from surveys such as Euclid and the Dark Energy Spectroscopic Instrument.