Isocurvature fluctuations in the effective Newton's constant

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.