Universality of the halo mass function in screened gravity theories

We investigate the efficacy of the halo mass function (HMF) as a probe of f(R), symmetron and Dvali-Gabadadze-Porrati (DGP) gravity. In this regard, we develop an excursion-set method to generalise a range of popular HMF fitting functions from General Relativity (GR) to screened Modified Gravity (MG), considering the HMF dependence on the critical density parameter delta(c). In particular, we propose a variety of new methods to account for the environmental dependence of chameleon screening and compare their accuracy to existing ones by submitting them to N-body simulation acid tests. Using the nested sampling routine MultiNest, we then examine two propositions: can the MG N-body results be accurately described by a Lambda CDM GR HMF, and do MG HMFs display universality. More specifically, the values of the free parameters defining a given HMF can always be determined by fitting N-body simulation data, but the question arises as to the dependency of these values on cosmological parameters and halo finding algorithm in the GR case, and indeed on the gravitational force itself when considering MG theories. We find that haloes extracted from any one of the MG N-body simulations can plausibly be fit by a Lambda CDM GR HMF, albeit with unusual best fit parameter values. In other words, despite the MG N-body data failing to support a clear deviation in the functional form of the HMF, it indicates that one needs to carefully establish Lambda CDM-expected credible regions for the values of the best fit parameters before attributing any difference in these values to MG. Alternatively, one can ask whether the MG N-body data is compatible with the existence of a truly universal (as in completely independent of the gravity model) HMF. Although we find that some HMFs display more universality than others - in the sense that they exhibit better overlap of their best fit parameters posterior probability distribution functions (PDFs) for different screening models -, the general trend, regardless of the HMF considered, is for DGP HMF parameter PDFs to overlap with those of Lambda CDM, symmetron HMF parameter PDFs to overlap with those of vertical bar f(R0)vertical bar = 10(-6), and vertical bar f(R0)vertical bar = 10(-5) HMF parameter PDFs to remain somewhat distinct from all the others. These results strongly suggest that a truly universal HMF will remain elusive.