Perturbations in k-inflation

Abstract

We extend the theory of cosmological perturbations to the case when the "matter" Lagrangian is an arbitrary function of the scalar 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 perfect fluid. In addition, it applies to the recently proposed k-inflation, which 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 tensor perturbations is modified. Thus, at least in principle, k-inflation is phenomenologically distinguishable from standard inflation.Introduction. The quantum theory of cosmological perturbations is one of the most interesting examples of quantum field theory in an external classical field. Indeed, the spectrum of metric perturbations generated during inflation is probably the only prediction of quantum field theory in external fields (besides the Casimir effect) which can be tested "experimentally" in the near future. The quantum theory of linearized cosmological perturbations is well developed in the case of a usual scalar field with the standard kinetic

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