Hierarchical clustering in chameleon f(R) gravity

We use a suite of high-resolution state-of-the-art N-body dark matter simulations of chameleon f(R) gravity to study the higher order volume-averaged correlation functions ξ n ¯ ¯ ¯ together with the hierarchical nth-order correlation amplitudes S n =ξ ¯ n /ξ ¯ n−1 2 and density distribution functions (PDF). We show that under the non-linear modifications of gravity the hierarchical scaling of the reduced cumulants is preserved. This is however characterized by significant changes in the values of both ξ n ¯ ¯ ¯ and Sn and their scale dependence with respect to General Relativity gravity (GR). In addition, we measure a significant increase of the non-linear σ8 parameter reaching 14, 5 and 0.5 per cent in excess of the GR value for the three flavours of our f(R) models. We further note that the values of the reduced cumulants up to order n = 9 are significantly increased in f(R) gravity for all our models at small scales R ≲ 30 h−1 Mpc. In contrast, the values of the hierarchical amplitudes, Sn, are smaller in f(R) indicating that the modified gravity density distribution functions are deviating from the GR case. Furthermore, we find that the redshift evolution of relative deviations of the f(R) hierarchical correlation amplitudes is fastest at high and moderate redshifts 1 ≤ z ≤ 4. The growth of these deviations significantly slows down in the low-redshift universe. We also compute the PDFs and show that for scales below ∼20 h−1 Mpc, they are significantly shifted in f(R) gravity towards the low densities. Finally, we discuss the implications of our theoretical predictions for measurements of the hierarchical clustering in galaxy redshift surveys, including the important problems of the galaxy biasing and redshift space distortions.