The paper discusses a novel inflationary mechanism, referred to as "k-inflation," driven by higher-order scalar kinetic terms. This mechanism can initiate inflation from generic initial conditions without the need for a potential term. The authors show that a class of non-standard kinetic terms can lead to an inflationary evolution characterized by slow-roll behavior, starting from a high-curvature phase and transitioning to a low-curvature phase. This evolution can end gracefully, transitioning to a radiation-dominated phase. The paper explores the conditions under which this inflationary behavior occurs, including the requirement that the kinetic term depends on the scalar field in a specific way. It also discusses the stability of the model under scalar perturbations and the exit mechanisms from inflation. The authors suggest that this mechanism could be useful in reconciling string theory with inflation, particularly in the context of string dilaton fields.The paper discusses a novel inflationary mechanism, referred to as "k-inflation," driven by higher-order scalar kinetic terms. This mechanism can initiate inflation from generic initial conditions without the need for a potential term. The authors show that a class of non-standard kinetic terms can lead to an inflationary evolution characterized by slow-roll behavior, starting from a high-curvature phase and transitioning to a low-curvature phase. This evolution can end gracefully, transitioning to a radiation-dominated phase. The paper explores the conditions under which this inflationary behavior occurs, including the requirement that the kinetic term depends on the scalar field in a specific way. It also discusses the stability of the model under scalar perturbations and the exit mechanisms from inflation. The authors suggest that this mechanism could be useful in reconciling string theory with inflation, particularly in the context of string dilaton fields.