  We present a systematic theory of acoustic-phonon-mediated superconductivity,
which incorporates Coulomb repulsion, explaining the recent experiment in
Bernal bilayer graphene under a large displacement field. The acoustic-phonon
mechanism predicts that $s$-wave spin-singlet and $f$-wave spin-triplet
pairings are degenerate and dominant. Assuming a spin-polarized
valley-unpolarized normal state, we obtain $f$-wave spin-triplet
superconductivity with a $T_c\sim 20$ mK near $n_e=-0.6\times 10^{12}$
cm$^{-2}$ for hole doping, in approximate agreement with the experiment. We
further predict the existence of superconductivity for larger doping in both
electron-doped and hole-doped regimes. Our results indicate that the observed
spin-triplet superconductivity in Bernal bilayer graphene arises from acoustic
phonons.
