  As first noted by Robert Wagoner in the 1970s, if a scalar field is
nonminimally coupled to the Ricci scalar and propagates at subluminal speeds,
then there exists the possibility of scalar $\check{\hbox{C}}$erenkov radiation
from a moving particle. The mere observation of high-energy cosmic rays could
in principle rule out the existence of such scalar fields since any particle
moving faster than scalar perturbations would lose energy in the form of scalar
waves until it moves slower than those. We compute in detail the energy loss to
scalar waves and find that it scales with the square of the ultra-violet (UV)
cutoff frequency of the effective field theory (EFT) of gravity. For
dark-energy-motivated EFTs, the UV cutoff can be low, in which case that energy
loss could always be negligible. In contrast, if viewed as a covariant theory
valid at all scales or as an EFT valid at higher energies, perhaps even all the
way up to the Planck scale, as may be the case if motivated by quantum-gravity
perspectives, then the energy loss to scalar waves may diverge or become
dramatically large. In this case, high-energy cosmic rays of extragalactic
origin stringently constrain any conformally coupled scalar fields with
non-canonical kinetic terms, although a minimum scalar phase velocity is
required to trust the EFT.
