Early time perturbations behaviour in scalar field cosmologies

We consider the problem of the initial conditions and behaviour of the perturbations in scalar field cosmology with general potential. We use the general definition of adiabatic and isocurvature conditions to set the appropriate initial values for the perturbation in the scalar field and in the ordinary matter and radiation components. In both the cases of initial adiabaticity and isocurvature, we solve the Einstein and fluid equation at early times and on superhorizon scales to find the initial behaviour of the relevant quantities. In particular, in the isocurvature case, we consider models in which the initial perturbation arises from the matter as well as from the scalar field itself, provided that the initial value of the gauge invariant curvature is zero. We extend the standard code to include all these cases, and we show some results concerning the power spectrum of the cosmic microwave background temperature and polarization anisotropies. In particular, it turns out that the acoustic peaks follow opposite behaviours in the adiabatic and isocurvature regimes: in the first case their amplitude is higher than in the corresponding pure cold dark matter model, while they make the opposite thing for pure isocurvature initial perturbations.