k-Inflation

TL;DR

The paper demonstrates that a broad class of non-quadratic kinetic terms $p(\varphi,X)$ can drive inflation without a potential, starting from generic initial conditions and evolving toward lower curvature with a natural exit to radiation. It develops slow-roll and power-law kinetically driven inflation (k-inflation), derives stability criteria via the sound speed $c_s^2 = p_X/\varepsilon_X$, and shows how the $\\varphi$-dependence of the kinetic terms enables graceful exit. It further shows how power-law inflation can arise in generalized kinetic models and discusses exit dynamics, reheating implications, and potential connections to string theory and dilaton/moduli cosmology. The findings broaden inflationary model-building beyond potential-dominated scenarios and suggest new routes to couple string-theoretic moduli to early-universe dynamics, while outlining future work on perturbations and observable signatures.

Abstract

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.

Figures (3)

• Figure 1: Graph of the equation of state linking $p$ to $\varepsilon$ for an hypothetical general kinetic Lagrangian $p(\dot{\varphi})$. The evolution for expanding, flat cosmologies proceeds along the indicated arrows. The shaded region ($\varepsilon<0$) is excluded. Except for the origin and the point above it on the vertical axis, the attractors of the evolution are inflationary fixed points with $p=-\varepsilon$.
• Figure 2: Change of form of the equation of state $p=f(\varepsilon, \varphi)$ in the model (\ref{['eq:simplest-p-expansion']}) as $\varphi$ varies from the weak-coupling region ($K(\varphi)>0$) to the strong-coupling one ($K(\varphi)<0$).
• Figure 3: Schematic phase diagram of "slow-roll" $k$-inflation. Trajectories approach the attractor but do not reach the line $\epsilon+p=0$ where the speed of sound vanishes. Around the point where the slow-roll condition is violated, the solutions leave the inflationary stage and approach then smoothly the vacuum $\dot{\varphi}=0$.