in a periodic box of $300\mpc$ on a side. The cosmological parameters used in the simulations are $\Omega_{\rm m}=
\Omega_{\rm  dm}+\Omega_{\rm b}  =0.276$, $\Omega_{\rm b}=0.046$, $h=0.703$, $\Omega_\Lambda=0.724$, $n=1$, and $\sigma_8=0.811$. The particle mass and softening length are $1.541\times10^{10}   \msun$ and $12.89   \kpc$, respectively. Glass-like cosmological initial conditions were generated at redshift $z=100$ using the Zel’dovich approximation.

In this paper as in Paper [slowromancap1@]{}, the modified gravity model is characterized by a single parameter $\zeta$, which determines the enhancement of particle acceleration with respect to GR, given the identical mass distribution ($\zeta=1$ in GR). All the simulations for different $\zeta$ values have the same linear power spectrum, such that $$P_L(k;z_S, \zeta=1) = P_L(k;z_\zeta, \zeta),$$ where $P_L$ is linear matter power spectrum, $z_S$ and $z_\zeta$ denote the redshifts in the standard $\Lambda$CDM and the MG cosmology, respectively. Since all the simulations begin with the identical initial condition, the above relation means that $$\label{eqn:D_z}
D(z_S, \zeta=1) = D(z_\zeta, \zeta),$$ where $D(z,\zeta)$ is the linear density growth factor. Given redshifts $z_S$ in the $\Lambda$CDM, through Eq. (\[eqn:D\_z\]) we can calculate the corresponding redshifts $z_\zeta$, which are shown in Table [slowromancap1@]{} of Paper [slowromancap1@]{}. In this paper, we mainly focus on the redshift $z_S  = 