  The disorder and interaction effects on Bogoliubov-Fermi surfaces with
preserved inversion symmetry are studied for a low-energy effective model
coupled to bosonic degrees of freedom. It is shown that the non-ideal
Bogoliubov quasiparticles (bogolons) generically induce the odd-frequency pair
amplitude which reflects a Cooper pairing at different time. The self-energy of
bogolons is mainly contributed by the disorder effects in the low frequency
limit as in the usual electron liquid. Depending on the choice of the
parameters, there are two kinds of solutions: one is frequency-independent (but
with sign function of frequency) and the other is proportional to the inverse
of the frequency, which exist in both the normal and anomalous parts of the
self-energy. These characteristic self-energy structures are clearly reflected
in the single-particle spectrum. Since the bogolons are originally composed of
electrons, the connection between the two is also sought using the concrete
$j=3/2$ fermion model, which reveals that the odd-frequency pairing of bogolons
is mainly made of the electrons' odd-frequency pairing.
