  Axions are candidates for dark matter in the universe.We develop an accurate
Boltzmann code to calculate the linear growth of the plasma. As an interesting
example, we investigate a mixed dark matter model consisting of cold dark
matter (CDM) and two-axion dark matter. We analyze the growth of the structure
numerically and analytically. We find that an effective single axion with an
effective mass and an effective abundance is useful to characterize the
two-axion cosmology. Moreover, we generalize the effective single axion
description to multi-axion dark matter cosmology. We also compare the results
with those of warm dark matter (WDM) model. Moreover, we calculate halo mass
functions for the mixed model by using the Press-Schechter model and linear
perturbations and then determine the mass function as a function of masses and
axion abundance.
