K -inflation I Introduction

It is shown that a large class of higher-order (i.e. non-quadratic) scalar kinetic terms can, without the help of potential terms, drive an inflationary evolution starting from rather generic initial conditions. In many models, this kinetically driven inflation (or " k-inflation " for short) rolls slowly from a high-curvature initial phase, down to a low-curvature phase and can exit inflation to end up being radiation-dominated, in a naturally graceful manner. We hope that this novel inflation mechanism might be useful in suggesting new ways of reconciling the string dilaton with inflation. The inflationary paradigm [1] offers the attractive possibility of resolving many of the puzzles of standard hot big bang cosmology. The crucial ingredient of most successful inflationary scenarios is a period of " slow-roll " evolution of a scalar field ϕ (the " inflaton "), during which the potential energy V (ϕ) stored in ϕ dominates its kinetic energy ˙ ϕ 2 /2 and drives a quasi-exponential expansion of the Universe. At present there exists no preferred concrete inflationary scenario based on a convincing realistic particle physics model. In particular, though string theory provides one with several very weakly coupled scalar fields (the moduli), which could be natural inflaton candidates, their non-perturbative potentials V (ϕ) do not seem fit to sustain slow-roll inflation because, for large values of ϕ, they tend either to grow, or to tend to zero, too fast. It is therefore important to explore novel possibilities for implementing an inflationary evolution of the early Universe.