  Electron-phonon interaction in copper oxide superconductors is still
enigmatic. Strong coupling for certain optic phonons is now well established
experimentally, but theoretical understanding is challenging. Scattering of
electrons near the Fermi surface by the longitudinal acoustic (LA) phonons is
expected from basic theory because these phonons modulate electron density. We
used inelastic neutron scattering on a large single crystal sample of
optimally-doped Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$ to show that low-energy LA
phonons could couple to electronic density fluctuations only at small phonon
wavevectors, which naturally limits any interaction to forward scattering. Such
scattering should not be pairbreaking in the case of the d-wave gap. We also
found that previously the reported low energy phonon spectral weight half-way
to the zone boundary is consistent with conventional lattice dynamics and does
not reflect an incipient charge density wave.
