the modified gravity can significantly affect the structure formation on small scale and the internal properties of the dark matter halos. For $\zeta=0.8$, the deviation of halo concentration even differ by larger than $50\%$ compared to that of $\zeta=1.0$. Here again, with similar difference in $\zeta$, the concentration difference of $\zeta< 1$ is much larger than that of $\zeta>1$.

The discrepancy between the different $\zeta$ values is mainly due to the different background density although they have the same linear matter perturbation. Since structure grows faster in $\zeta>1$ cosmology ($z_\zeta >
z_S$), halos in this universe form in a background with higher mean density ($\propto(1+z)^3$). We then expect them to have a smaller concentration[@Zhao2009]. For the same reason, we expect halos with $\zeta<1$ have a larger concentration. The behavior of the concentrations for different $\zeta$ values is roughly similar to the trend of the concentrations corresponding to the redshift $z_\zeta$ in $\Lambda$CDM models. Large values of the ratio of the concentration parameters from unity implies that the halo concentration is a valuable property to detect different modified gravity models.

Halo bias
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![Measured halo bias from N-body simulations for different $\zeta$ values at the baseline redshift $z_S=1.2$. The lower panel 