hope is that, by choose appropriate spatial and time dependence in $\zeta$, one can effectively take the environmental dependence into account [^1].

In the current paper, we will examine the halo properties in these simplified MG simulations, including the halo abundance, concentration and bias as a function of mass and redshift. In the standard framework of structure formation in GR, these properties, in particular the halo abundance and bias, are largely fixed by the linear matter power spectrum at the corresponding epoch. We utilize this property to better isolate the impact of MG. We will compare the above properties not at the same redshift, but at redshifts of identical linear matter power spectrum. The same method is also adopted in paper I. It has extra benefit of reducing cosmic variance and numerical artifact, since we focus on the differences between different MG simulations with identical initial condition.

This paper is organized as follows. We briefly describe our simulations in §\[sec\_data\] and present results in §\[sec\_imethod\]. We discuss and summarize in §\[sec:conclusion\].

N-body Simulation {#sec_data}
=================

We run a set of simulations with the TreePM parallel code GADGET-2 [@Springel2005] at Shanghai Astronomical Observatory. All the simulations evolved $512^3$ dark matter particles 