Derivative chameleons

We consider generalized chameleon models where the conformal coupling between matter and gravitational geometries is not only a function of the chameleon field Φ, but also of its derivatives via higher order co-ordinate invariants (such as ∂μφ∂^μφ,squφ,...). Specifically we consider the first such non-trivial conformal factor A(φ,∂μφ∂^μφ). The associated phenomenology is investigated and we show that such theories have a new generic mass-altering mechanism, potentially assisting the generation of a sufficiently large chameleon mass in dense environments. The most general effective potential is derived for such derivative chameleon setups and explicit examples are given. Interestingly this points us to the existence of a purely derivative chameleon protected by a shift symmetry for φ → φ+c. We also discuss potential ghost-like instabilities associated with mass-lifting mechanisms and find another, mass-lowering and instability-free, branch of solutions. This suggests that, barring fine-tuning, stable derivative models are in fact typically anti-chameleons that suppress the field's mass in dense environments. Furthermore we investigate modifications to the thin-shell regime and prove a no-go theorem for chameleon effects in non-conformal geometries of the disformal type.