Gauge-invariant metric fluctuations from NKK theory of gravity: de Sitter expansion

In this Letter we study gauge-invariant metric fluctuations from a noncompact Kaluza-Klein (NKK) theory of gravity in de Sitter expansion. We recover the well-known result δρ/ρ≃2Φ, obtained from the standard 4D semiclassical approach to inflation. The spectrum for these fluctuations should be dependent of the fifth (spatial-like) coordinate.