Adiabatic and Isocurvature Perturbations from Inflation: Power Spectra and Consistency Relation

We study adiabatic and isocurvature perturbations produced during a period of cosmological inflation. We compute the power spectra and cross spectra of the curvature and isocurvature modes, as well as the tensor perturbation spectrum in terms of the slow-roll parameters. We provide two consistency relations for the amplitudes and spectral indices of the corresponding power spectra. These relations represent a definite prediction and a test of inflationary models which should be adopted when studying cosmological perturbations through the cosmic microwave background in forthcoming satellite experiments.