$\zeta$ values. Although the shape of Cosmic Web (the pattern on clusters, filaments, sheets, and voids) is more or less preserved in the $\zeta\ne1$ runs when compared to the $\Lambda$CDM case, we can depict arising differences when looking into the internal properties of dark matter halos.

Numerical Results {#sec_imethod}
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In this section we show the halo mass function, concentration and bias as a function of $M_{200}$. Structure grows more slowly in $\zeta<1$ models than that in GR. So for too low $z_S$ in $\Lambda$CDM, structure growth in a $\zeta<1$ universe may not be able to catch up with that of $\Lambda$CDM even at $z_\zeta=0$ (table I, paper I). For this reason, we only compare the results corresponding to $z_S=1.2$ in $\Lambda$CDM, for which we can compare the halo statistics for all $\zeta$.

The halo mass function
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![Measured halo mass functions from N-body simulations for different $\zeta$ values at redshift $z_\zeta$ where the linear matter power spectrum is identical to that in $\Lambda$CDM ($\zeta=1$) at the baseline redshift $z_S=1.2$. Since all simulations begin with the identical condition, the measured halo mass function has similar Poisson error. Hence we only show the Poisson error bars of $\Lambda$CDM to demonstrate the 