we shall call, from now on, N1 and N5, respectively.

### N-body Simulations {#sim}

Accurate realizations of structure formation in the nonlinear regime can only be achieved by performing N-body simulations. In this paper, we test our results against two groups of state-of-the-art N-body simulations, that serve complementary purposes to each other, as explained below.

The first group of simulations, to which we shall refer as Group I from now on, are the [ELEPHANT]{} simulations, presented in [@Cautun:2017tkc]. These span the parameter space of both MG models we study: the F4, F5 and F6 $f(R)$ models and N1 and N5 $n$DGP models. The $f(R)$ simulations were performed using the [ECOSMOG]{} code [@1475-7516-2012-01-051; @Bose:2016wms], while the $n$DGP ones [@Hellwing:2017pmj] using the [ECOSMOG-V]{} version [@Li:2013nua; @Barreira:2015xvp], both of which were based on the GR code [RAMSES]{} [@Teyssier:2001cp] and where suitably extended to integrate the scalar field KG equation for the corresponding models using adaptive-mesh-refinement techniques. The parameters describing the background $\Lambda$CDM cosmology are the best-fit ones given by the 9-year WMAP release [@0067-0049-208-2-19] and have the following values: $\Omega_b=0.046$, $\Omega_{cdm}=0.235$, $\Omega_m=0.281$, $\Omega_L=0.719$, $h=0.7$, $n_s=0.971$ and $\sigma_8=0.82$. $N_p=1024^3$ equal mass particles were placed in a simulation box with a side $L_{box}=1024$ Mpc/h and 