adopted parameters. In one word, by comparing the results shown in Fig. \[fig:concentration\] and Fig. \[fig:concen\_vir\], we can see that there exists a significant difference of the halo concentration for different $\zeta$ values, which illustrates that deviations from general relativity can strongly affect the mass distribution in the nonlinear regime, although the large-scale structures are remarkably similar (see Fig. \[fig:slice\]) [^3].

Fig. \[fig:bias\_vir\] shows that the bias of halos defined with virial mass still shows weak dependence on gravity, for all the $\zeta\ne1$ considered ($0.8\leq \zeta\leq
1.5$). This confirmes previous finding that the halo bias may not be a sensitive probe of gravity. This conclusion would be robust for halos of mass less than $10^{13}\msun$. Neverthless, our simulations do not have sufficiently large box size to robustly measure the bias of halos with mass larger than $10^{13}\msun$ and evaluate its dependence on gravity. In th above results $\Delta_{\rm vir}$ is evaluated assuming GR. It is known that $\Delta_{\rm vir}$ is changed in MG models [@Schmidt2009a; @Schmidt2010]. To what extent it can account for the found difference in the mass function [@Schmidt2009a; @Schmidt2010] is an issue for further investigation.

Our results have robustly demonstrated that the halo mass function is not 