Evolution of the chameleon scalar field in the early universe

In order to satisfy limits on the allowed variation of particle masses from big bang nucleosynthesis until today, the chameleon scalar field is required to reach its attractor solution early on in its cosmological evolution. Brax et al. [Phys. Rev. D 70, 123518 (2004)] have shown this to be possible for certain specific initial conditions on the chameleon field at the end of inflation. However the extreme fine-tuning necessary to achieve this poses a problem if the chameleon is to be viewed a natural candidate for dark energy. In this paper we revisit the behavior of the chameleon in the early universe, including the additional coupling to electromagnetism proposed by Brax et al. [Phys. Lett. B 699, 5 (2011)]. Solving the chameleon evolution equations in the presence of a primordial magnetic field, we find that the strict initial conditions on the chameleon field at the end of inflation can be relaxed, and we determine the associated lower bound on the strength of the primordial magnetic field.