Gas density profile in dark matter halo in chameleon cosmology
  We investigate the gas density, temperature, and pressure profiles in a dark
matter halo under the influence of the chameleon force. We solve the
hydrostatic equilibrium equation for the gas coupled with the chameleon field
in an analytic manner, using an approximate solution for the chameleon field
equation with the source term, with a generalized Navarro-Frenk-White universal
density profile. We find that the gas distribution becomes compact because a
larger pressure gradient is necessary due to the additional chameleon force. By
confronting the theoretical prediction with the data of the temperature profile
of the Hydra A cluster according to Suzaku x-ray observations out to the virial
radius, we demonstrate that a useful constraint on a model parameter can be
obtained depending on the value of the coupling constant. For example, the
upper bound of the background value of chameleon field,
$\phi_\infty<10^{-4}\mpl$, is obtained in the case $\beta=1$, where $\beta$ is
the coupling constant between the chameleon field and the matter, and $\mpl$ is
the Planck mass. However, the error of the present data is not so small that we
obtain a useful constraint in the case $\beta=1/\sqrt{6}$, which corresponds to
an $f(R)$ model.
