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 \left < \delta \rho \right > / \rho _ { b } depends on the coupling of \Phi with \delta \varphi and the spectral index of its spectrum is 0.9483 < n _ { 1 } < 1 .