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that when chameleon effect is strong and fifth force is suppressed, our result is very close to the ΛCDM predic- tion; this is the case for very large halos (which generally reside in higher density regions) and µ = 10 − $^{6}$. For large halos and µ = 10 − $^{5}$, the situation is more complicated because the competition between two effects of the cou- pled scalar field, namely the speedup of the particles and the deepening of the total attractive potential, has ar- rived a critical point: if the former wins, such as in the model γ = 1 . 0 , µ = 10 − $^{5}$, then the inner density profile can be lower than that in ΛCDM; if the latter wins, such as in the model γ = 1 . 0 , µ = 10 − $^{5}$, then we expect the opposite. For smaller halos which locate in lower den- sity regions, the fifth force is not suppressed that much and causes faster growth of the structure, so the halo is more concentrated and has a higher internal density. Meanwhile, the bias between baryons and CDM density 

profiles also increase as the fifth force becomes less sup- pressed, which is as expected. 

Our results already show that new features can be quantitatively studied with the N -body method and the improving supercomputing techniques, and that the chameleon model has rather different consequences from other coupled scalar field models. The enhancement in the structure formation due to the fifth force is signifi- cant for some of our parameter space, which means other observables, such as weak lensing, could place new con- straints on the model. Also one might be interested in how the halo profiles would be like at different epoch of the cosmological evolution and in different environments. These will be left as future work. 

