  We present a new isocurvature mode present in scalar-tensor theories of
gravity that corresponds to a regular growing solution in which the energy of
the relativistic degrees of freedom and the scalar field that regulates the
gravitational strength compensate during the radiation dominated epoch on
scales much larger than the Hubble radius. We study this isocurvature mode and
its impact on anisotropies of the cosmic microwave background for the simplest
scalar-tensor theory, i.e. the extended Jordan-Brans-Dicke gravity, in which
the scalar field also drives the acceleration of the Universe. We use Planck
data to constrain the amplitude of this isocurvature mode in the case of fixed
correlation with the adiabatic mode and we show how this mode could be
generated in a simple two field inflation model.
