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Effects of Chameleon Scalar Field on Rotation Curves of the Galaxies

We investigate the effects of chameleon scalar field to the effective density and pressure of a dark matter halo. The pressure is generated from the chameleonic fifth force on the matter. We demonstrate that the thick-shell non-singular boundary condition which forbids singular point leads to extremely stringent constraint on the matter-chameleon coupling when applied to galaxy. We argue that chameleon profile with central singularity is more likely to develop in general physical situation. The chameleonic fifth force from the chameleon profile with central singularity experienced by the dark matter could significantly modify the rotation curve of galaxies. The chameleonic fifth force could generate steeper cusp to the rotation curves in any dark matter profiles starting from the Navarro-Frenk-White (NFW) to the pseudo-isothermal (ISO) profile. Upper limits on the coupling constant between the chameleon and the dark matter are estimated from observational data of the late-type Low-Surface-Brightness galaxies (LSB). It is in the order of $β< 10^{-3}$.