  We study the excitonic phase and low-energy excitation spectra of perovskite
cobalt oxides. Constructing the five-orbital Hubbard model defined on the
three-dimensional cubic lattice for the $3d$ bands of
Pr$_{0.5}$Ca$_{0.5}$CoO$_3$, we calculate the excitonic susceptibility in the
normal state in the random-phase approximation (RPA) to show the presence of
the instability toward excitonic condensation. Based on the excitonic ground
state with a magnetic multipole obtained in the mean-field approximation, we
calculate the dynamical susceptibility of the excitonic phase in the RPA and
find that there appear the gapless collective excitation in the spin-transverse
mode (Goldstone mode) and the gapful collective excitation in the
spin-longitudinal mode (Higgs mode). Experimental relevance is discussed.
