  In chameleon gravity, there exists a light scalar field that couples to the
trace of the stress-energy tensor in such a way that its mass depends on the
ambient matter density, and the field is screened in local, high-density
environments. Recently it was shown that, for the runaway potentials commonly
considered in chameleon theories, the field's coupling to matter and the
hierarchy of scales between Standard Model particles and the energy scale of
such potentials result in catastrophic effects in the early Universe when these
particles become nonrelativistic. Perturbations with trans-Planckian energies
are excited, and the theory suffers a breakdown in calculability at the
relatively low temperatures of Big Bang Nucleosynthesis. We consider a
chameleon field in a quartic potential and show that the scale-free nature of
this potential allows the chameleon to avoid many of the problems encountered
by runaway potentials. Following inflation, the chameleon field oscillates
around the minimum of its effective potential, and rapid changes in its
effective mass excite perturbations via quantum particle production. The
quartic model, however, only generates high-energy perturbations at comparably
high temperatures and is able remain a well-behaved effective field theory at
nucleosynthesis.
