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

Low-energy excitation spectra in the excitonic phase of cobalt oxides