Universality of the halo mass function in modified gravity cosmologies

TL;DR

This paper demonstrates that the halo mass function in modified gravity models can be universally characterized using a dimensionless multiplicity function, leading to accurate, simple fits that outperform traditional analytic models.

Contribution

It introduces universal, empirically derived fits for the halo mass function in MG models, improving accuracy over previous analytic approaches and confirming a universal shape of deviations across models.

Findings

HMF in MG models is approximately universal when expressed as a multiplicity function.

Proposed fits accurately describe the HMF within a few percent for the models studied.

The deviation of HMF in MG models exhibits a Gaussian-like shape peaking at a characteristic mass scale.

Abstract

We study the halo mass function (HMF) in modified gravity (MG) models using a set of large $N$-body simulations -- the ELEPHANT suite. We consider two popular beyond-general relativity scenarios: the Hu-Sawicki chameleon $f(R)$ model and the normal branch of the Dvali-Gabadadze-Porrati braneworld (nDGP). We show that in MG, analytic formulation based on the Press-Schechter framework offers a grossly inaccurate description of the HMF. We find, however, that once the HMF is expressed in terms of the dimensionless multiplicity function, it approximately assumes a redshift-independent universal character for all the models. Exploiting this property, we propose universal fits for the MG HMF in terms of their fractional departures from the $\mathrm{\Lambda \text{CDM}}$ case. We find two enclosed formulas, one for $f(R)$ and another for nDGP, that provide a reliable description of the HMF over the mass range covered by the simulations. These are accurate to a few percent with respect to the $N$-body data. We test the extrapolation potential of our fits against separate simulations with a different cosmological background and mass resolution, and find very good accuracy, within $\sim 10\%$. A particularly interesting finding from our analysis is a Gaussian-like shape of the HMF deviation that seems to appear universally across the whole $f(R)$ family, peaking at a mass variance scale characteristic for each $f(R)$ variant. We attribute this behavior to the specific physics of the environmentally-dependent chameleon screening models.