This paper presents a novel mechanism for inflation called "k-inflation," which relies on non-standard kinetic terms for a scalar field rather than a potential energy term. The authors show that a large class of higher-order scalar kinetic terms can drive inflation from generic initial conditions without the need for a potential. In many models, this kinetically driven inflation rolls slowly from a high-curvature phase to a low-curvature phase, ending in a radiation-dominated universe in a natural way. The authors suggest that this mechanism could help reconcile the string dilaton with inflation. They consider a general model with a scalar field interacting with gravity through non-standard kinetic terms, and show that the energy density and pressure of the field can be expressed in terms of the kinetic term. The authors analyze the evolution of the universe in this model and find that it can exhibit slow-roll inflation, with a natural exit mechanism. They also discuss the stability of the model under scalar perturbations and the possibility of a graceful exit from inflation. The paper concludes that k-inflation is a viable alternative to traditional inflationary models and could provide new insights into the compatibility of string theory with inflation.This paper presents a novel mechanism for inflation called "k-inflation," which relies on non-standard kinetic terms for a scalar field rather than a potential energy term. The authors show that a large class of higher-order scalar kinetic terms can drive inflation from generic initial conditions without the need for a potential. In many models, this kinetically driven inflation rolls slowly from a high-curvature phase to a low-curvature phase, ending in a radiation-dominated universe in a natural way. The authors suggest that this mechanism could help reconcile the string dilaton with inflation. They consider a general model with a scalar field interacting with gravity through non-standard kinetic terms, and show that the energy density and pressure of the field can be expressed in terms of the kinetic term. The authors analyze the evolution of the universe in this model and find that it can exhibit slow-roll inflation, with a natural exit mechanism. They also discuss the stability of the model under scalar perturbations and the possibility of a graceful exit from inflation. The paper concludes that k-inflation is a viable alternative to traditional inflationary models and could provide new insights into the compatibility of string theory with inflation.