Perturbation initial conditions for a couple of dark energy scalar field potentials

We present perturbation initial conditions for two types of scalar field potential often used in the dark energy study: one inverse power-law and the other exponential. The solutions are presented in the presence of the $w =$ constant fluid ($w = 1/3$ for radiation fluid), a minimally coupled scalar field and a sub-dominating zero-pressure fluid (cold dark matter and baryon dust). We consider two gauge conditions, the $w$-fluid comoving gauge and the cold-dark-matter comoving gauge; solutions in the latter gauge are derived by the gauge transformation and this method can be applied to derive solutions in any other gauge condition.