Non-linear matter power spectrum without screening dynamics modelling in f(R) gravity

Abstract

Halo model is a physically intuitive method for modelling the non-linear power spectrum, especially for the alternatives to the standard ΛCDM models. In this paper, we examine the Sheth–Tormen barrier formula adopted in the previous CHAM method. As an example, we model the ellipsoidal collapse of top-hat dark matter haloes in f(R) gravity. A good agreement between Sheth–Tormen formula and our result is achieved. The relative difference in the ellipsoidal collapse barrier is less than or equal to 1.6 per cent⁠. Furthermore, we verify that, for F4 and F5 cases of Hu–Sawicki f(R) gravity, the screening mechanism does not play a crucial role in the non-linear power spectrum modelling up to k ∼ 1 h Mpc−1. We compare two versions of modified gravity modelling, namely with/without screening. We find that by treating the effective Newton constant as constant number, Geff = 4/3GN is acceptable. The scale dependence of the gravitational coupling is subrelevant. The resulting spectra in F4 and F5, are in 0.1 per cent agreement with the previous CHAM results. The published code is accelerated significantly. Finally, we compare our halo model prediction with N-body simulation. We find that the general spectrum profile agrees, qualitatively. However, via the halo model approach, there exists a systematic underestimation of the matter power spectrum in the comoving wavenumber range between 0.3 and 3 h Mpc−1. These scales are overlapping with the transition scales from two-halo term dominated regimes to those of one-halo term dominated regimes.