Inflaton and metric fluctuations in the early universe from a 5D vacuum state

In this Letter we complete a previously introduced formalism to study the gauge-invariant metric fluctuations from a noncompact Kaluza-Klein theory of gravity, to study the evolution of the early universe. The evolution of both, metric and inflaton field fluctuations are reciprocally related. We obtain that 〈δρ〉/ρb depends on the coupling of Φ with δφ and the spectral index of its spectrum is 0.9483