  One possibility to explain the current accelerated expansion of the universe
may be related with the presence of cosmologically evolving scalar whose mass
depends on the local matter density (chameleon cosmology). We point out that
matter quantum effects in such scalar-tensor theory produce the chameleon
scalar field dependent conformal anomaly. Such conformal anomaly adds higher
derivative terms to chameleon field equation of motion. As a result, the
principal possibility for instabilities appears. These instabilities seem to be
irrelevant at small curvature but may become dangerous in the regions where
gravitational field is strong.
