  The primordial spectra are calculated using dispersion relations which
deviate from the relativistic one above a certain energy scale Lambda. We
determine the properties of the leading modifications with respect to the
standard spectra when Lambda is much greater than H, the Hubble scale during
inflation. To be generic, we parameterize the lowest order deviation from the
relativistic law by alpha, the power of P/Lambda where P is the proper
momentum. When working in the asymptotic vacuum, the leading modification
scales as (H/Lambda)^alpha for all alpha, except for a discrete set where the
power is higher. Moreover, this modification is robust against introducing
higher order terms in the dispersion relation. We then algebraically deduce the
modifications of scalar and tensor power spectra in slow roll inflation from
modifications calculated in de Sitter space. The modifications do not exhibit
oscillations unless the dispersion relation induces some non-adiabaticity near
a given scale. Finally, we explore the much less studied regime where H and
Lambda are comparable. Our results indicate that the project of reconstructing
the inflaton potential cannot be pursued without making some hypothesis about
the dispersion relation of the fluctuation modes.
