16 FIG. 8: The mass functions for the 4 models under consideration at a = 1 . 0 (solid curves). The dashed curve is the mass function for the ΛCDM simulation. The (solid) curves and error bars denote respectively the mean and standard deviation for 5 sample results. tion gets suppressed and in particular decreases towards small scales, showing the desirable property of chameleon models that they evade constraints on small scales. The bias between CDM and baryons power spectra follows the same trend. are chosen to be the same as in [23]. As discussed there, the coupling of the scalar field to CDM particles acts on the latter a fifth force. When µ is small and γ is large, the chameleon effect becomes stronger, which gives the scalar field a heavy mass, making the fifth force short- ranged and the scalar field dependent only on the local matter density. Other ways to strengthen the chameleon effect includes increasing the density and decreasing the background value of the scalar field, which itself is equiv- alent to increasing the background CDM energy density. We have displayed in Figs. 2, 4 how changing the deter- mining factors change the scalar field configuration and the strength of the fifth force. We have also measured the nonlinear matter power spectrum from the simulation results and compared them with the ΛCDM prediction. Depending on the values of γ, µ as well as the background CDM density, the former can be up to ∼ 80% larger than the latter. Nonetheless, when the chameleon effect is set to be strong, the devia- Finally, we have analyzed the internal profiles of (the same) two halos selected from each simulation. We find To identify virialized halos from the simulations, we have modified MHF, MLAPM’s default halo finder, so that the calculation of the escape velocity includes the effect of the scalar field. We find that such a modifica- tion leads to up to a-few-percent enhancement on the mass function compared with what is obtained using the default MHF code, because in the latter case the escape velocity is underestimated and some particles are incor- rectly removed from the virialized halos. We find that the mass function in the coupled scalar field models is sig- nificantly larger than the ΛCDM result, because of the enhanced structure growth induced by the fifth force.