Initial conditions for cosmological perturbations in scalar-tensor dark-energy models

We discuss the evolution and imprints of isocurvature initial conditions for the scalar field in scalar tensor extensions of Einstein gravity. We consider the simplest models of scalar tensor theories, as Induced gravity (IG, which can be recasted in form of Jordan-Brans-Dicke theory by a redefinition of the scalar field) or non-minimally coupled (NMC) scalar fields in which the acceleration of the Universe is connected to a variation of the effective Planck mass. After introducing the fundamental ideas of cosmological perturbation theory and scalar tensor theories of gravity, we give the evolution equations for matter, metric and scalar field fluctuations in synchronous gauge. We use this set of equations for both the IG and the NMC models to find a new isocurvature solution in which the scalar field fluctuations compensate for the relativistic components respectively. We also show how we can generalize the well known isocurvature modes in Einstein GR to these models. We show the different evolution of cosmological fluctuations for these isocurvature initial conditions compared to the standard adiabatic one. After that, we compute the CMB angular power spectrum for these solutions in the IG model, with the help of a modified Einstein-Boltzmann CLASS code. In particular the CMB power spectrum is computed separately for adiabatic and isocurvature initial conditions, i.e. for totally uncorrelated modes, and with arbitrary correlations leading to an interesting explanation of the lack of power in the low multipoles region of the CMB temperature power spectrum. Finally we show how a simple model of double inflation in IG could explain the generation of the new isocurvature mode.