Vacuum density fluctuations in extended chaotic inflation

An inflation (scalar field) with the potential ${c\sigma }^{2n}$ is coupled to gravity within the Jordan-Brans-Dicke theory. The corresponding inflationary model (that is, a flat Friedmann-Robertson-Walker solution with a slowly varying inflation) is constructed for all values of the coupling $\beta$ of the inflaton to the dilaton (Brans-Dicke scalar field). The linearized perturbations of the metric, the dilaton, and the inflaton are then quantized within a gauge-invariant formalism. The power spectrum of the vacuum density fluctuations is calculated as a function of $c$, $n$, and $\beta$. It is the juxtaposition of two powers of the wave number corresponding, respectively, to the contribution of the inflaton and the dilaton. We find the value of $\beta$ for which the dilaton contribution dominates on observable cosmological scales.