In the present paper, we study the inflationary phenomenology of a k-inflation corrected Einstein-Gauss-Bonnet theory. Non-canonical kinetic terms are known for producing Jean instabilities or superluminal sound wave velocities in the aforementioned era, but we demonstrate in this work that by adding Gauss-Bonnet string corrections and assuming that the non-canonical kinetic term $\omega X^{\gamma }$ is in quadratic, one can obtain a ghost free description. Demanding compatibility with the recent GW170817 event forces one to accept that the relation $\ddot{\xi }=H\dot{\xi }$ for the scalar coupling function $\xi (\varphi )$. As a result, the scalar functions of the theory are revealed to be interconnected and by assuming a specific form for one of them, specifies immediately the other. Here, we shall assume that the scalar potential is directly derivable from the equations of motion, once the Gauss-Bonnet coupling is appropriately chosen, but obviously the opposite is feasible as well. As a result, each term entering the equations of motion, can be written in terms of the scalar field and a relatively tractable phenomenology is produced. For quadratic kinetic terms, the resulting scalar potential is quite elegant functionally. Different exponents, which lead to either a more perplexed solution for the scalar potential, are still a possibility which was not further studied. We also discuss in brief the non-Gaussianities issue under the slow-roll and constant-roll conditions holding true, and we demonstrate that the predicted amount of non-Gaussianities is significantly enhanced in comparison to the k-inflation free Einstein-Gauss-Bonnet theory.

在本文中，我们研究了由k通胀修正的爱因斯坦-高斯-邦尼理论的通胀现象。非规范动力学术语在上述时代会产生吉恩不稳定性或超光速声波速度，但我们在这项工作中证明了通过添加高斯-贝纳特弦校正并​​假设非规范动力学术语$\omega X^{\gamma }$是二次方的，可以得到无重影的描述。与最近的GW170817事件的苛刻兼容性迫使人们不得不接受这种关系$\ddot{\xi }=H\dot{\xi }$ 标量耦合功能 $\xi （\varphi ）$。结果，该理论的标量函数被显示为相互联系的，并且通过假设其中一个的特定形式，立即指定另一个。在这里，我们假设一旦适当地选择了高斯-邦尼特耦合，标量势就可以直接从运动方程式推导出，但是显然相反也是可行的。结果，每个进入运动方程的项都可以用标量场来表示，并产生相对易处理的现象学。对于二次动力学项，所得到的标量势在功能上非常出色。导致指数标量势更复杂的解决方案的不同指数仍然是一种可能性，因此未作进一步研究。无k通胀的爱因斯坦-高斯-邦尼理论。