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<img src='content_image/393020.jpg'>

ΛCDM but the potential is not significantly deeper, so that particles tend to get far away from the centre of the halo, producing a lower inner density profile. As for the model with γ = 0 . 5 , µ = 10 − $^{5}$, the situation is just the opposite: the fifth force is saturated and of the same order as gravity due to the weak chameleon effect, so that the total potential is greatly deeper than its ΛCDM counter- part, while at the same time the particles are not as fast as those in γ = 1 . 0 , µ = 10 − $^{5}$: the consequence is that the halo accretes more particles towards its centre. 

One might also have interests in how the CDM part and the baryonic part of the halo profile differ from each other, and this is given in Fig. 11, in which we compare the CDM and baryon density profiles of halos I and II. Obviously the CDM density is higher than baryons ev- erywhere, again thanks to the boost from the fifth force. For smaller µ and larger γ (which help strengthen the chameleon effect and suppress the fifth force), the differ- ence between the two is smaller (compare the halo I in the models γ = 0 . 5 , µ = 10 − 5 and γ = 1 . 0 , µ = 10 − $^{5}$). However, in the situations where the fifth force is already saturated or unsuppressed (such as in halo II), increasing γ increases the saturated value of the fifth force, and thus can instead magnify the difference (compare the halo II in the models γ = 0 . 5 , µ = 10 − 5 and γ = 1 . 0 , µ = 10 − $^{5}$). 

The above results again show the complexity of the chameleon scalar field model as compared to other cou- pled scalar field models. We will study the environment and epoch dependence of the halo density profiles in a upcoming work. 

## IV. DISCUSSION AND CONCLUSION 

To summarize, in this paper we have investigated into a model where CDM and baryons couple differently to a chameleon-like scalar field, and performed full N -body simulations, by directly solving the spatial distribution of the scalar field, to study the nonlinear structure for- mation under this setup. The new complexity introduced here compared to [23] is that we must distinguish between baryons and CDM so that we know how to calculate the force upon each particle. We do this by tagging the initial almost homogeneously distributed particle randomly so that 80% of all particles are tagged as CDM. We then only use CDM particles to calculate the scalar field and only applies the fifth scalar force on CDM particles. 

The coupling function (characterized by the coupling strength γ ) and bare potential (characterized by the pa- rameter µ which controls its steepness) of the scalar field 

