Perturbations in k-inflation

We extend the theory of cosmological perturbations to the case when the "ma tter" Lagrangian is an arbitrary function of the scaler field and its first derivatives. In particular, this extension provides a unified description of known cases such as the usual scalar field and the hydrodynamical perfec t fluid. In addition, it applies to the recently proposed k-inflation, whic h is driven by non-minimal kinetic terms in the Lagrangian. The spectrum of quantum fluctuations for slow-roll and power law k-inflation is calculated . We find, for instance, that the usual "consistency relation" between the tensor spectral index and the relative amplitude of scalar and tenser pertu rbations is modified. Thus, at least in principle, k-inflation is phenomeno logically distinguishable from standard inflation. (C) 1999 Published by El sevier Science B.V. All rights reserved.