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 <\delta\rho/\rho_b$dependsonthecouplingof$\Phi$with$\delta\phi$ and the spectral index of its spectrum is: $0.9483<n_1<1$.