Perturbations of extended inflation

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Abstract
Perturbing the metric, the inflaton (scalar matter), and the dilaton (Brans-Dicke scalar) of extended inflation, the Lagrangian of quadratic order for the two true, gauge-invariant degrees of freedom of the perturbations is derived. This result should allow a rigorous analysis of the initial spectrum of density fluctuations in all models of extended inflation (i.e., with a self-interacting dilaton field). As an immediate application we show that in the particular case of old extended inflation, where the inflaton is trapped at a false-vacuum local minimum of its potential, its fluctuation does not contribute to the density perturbation, thus confirming earlier approximate calculations.