Cluster abundance in chameleon $f(R)$ gravity I: toward an accurate halo mass function prediction

TL;DR

This paper develops a refined model for predicting the halo mass function in chameleon $f(R)$ gravity, achieving high accuracy and enabling competitive constraints on the theory from galaxy cluster surveys.

Contribution

It introduces a calibrated correction to the spherical collapse model for chameleon $f(R)$ gravity, improving halo mass function predictions and enabling forecasts of observational constraints.

Findings

Achieves <5% accuracy in $f(R)$ halo abundance predictions.

Provides fitting formulas for fractional enhancement over GR.

Forecasts competitive constraints on scalar degree of freedom from cluster surveys.

Abstract

We refine the mass and environment dependent spherical collapse model of chameleon $f(R)$ gravity by calibrating a phenomenological correction inspired by the parameterized post-Friedmann framework against high-resolution $N$-body simulations. We employ our method to predict the corresponding modified halo mass function, and provide fitting formulas to calculate the fractional enhancement of the $f(R)$ halo abundance with respect to that of General Relativity (GR) within a precision of $\lesssim 5\%$ from the results obtained in the simulations. Similar accuracy can be achieved for the full $f(R)$ mass function on the condition that the modeling of the reference GR abundance of halos is accurate at the percent level. We use our fits to forecast constraints on the additional scalar degree of freedom of the theory, finding that upper bounds competitive with current Solar System tests are within reach of cluster number count analyses from ongoing and upcoming surveys at much larger scales. Importantly, the flexibility of our method allows also for this to be applied to other scalar-tensor theories characterized by a mass and environment dependent spherical collapse.