After the recent GW170817 event of the two neutron stars merging, many string corrected cosmological theories confronted the non-viability peril. This was due to the fact that most of these theories produce massive gravitons primordially. Among these theories were the ones containing a non-minimal kinetic coupling correction term in the Lagrangian, which belong to a subclass of Horndeski theories. In this work we demonstrate how these theories may be revived and we show how these theories can produce primordial gravitational waves with speed $c_T^2=1$ in natural units, thus complying with the GW170817 event. As we show, if the gravitational action of an Einstein-Gauss-Bonnet theory also contains a kinetic coupling of the form $\sim \xi(\phi) G^{\mu\nu}\partial_\mu\phi\partial_\nu\phi$, the condition of having primordial massless gravitons, or equivalently primordial gravitational waves with speed $c_T^2=1$ in natural units, results to certain conditions on the scalar field dependent coupling function of the Gauss-Bonnet term, which is also the non-minimal coupling of the kinetic coupling. We extensively study the phenomenological implications of such a theory focusing on the inflationary era, by only assuming slow-roll dynamics for the scalar field. Accordingly, we briefly study the case that the scalar field evolves in a constant-roll way. By using some illustrative examples, we demonstrate that the viability of the theoretical framework at hand may easily be achieved. Also, theories containing terms of the form $\sim \xi(\phi)\Box\phi g^{\mu\nu}\partial_\mu\phi\partial_\nu\phi$ and $\sim \xi(\phi)\left(g^{\mu\nu}\partial_\mu\phi\partial_\nu\phi\right)^2$ also lead to the same gravitational wave speed as the theory we shall study in this paper, so this covers a larger class of Horndeski theories.

中文翻译：

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在 GW170817 之后复兴类似 Horndeski 的非最小理论：动力学耦合修正了爱因斯坦-高斯-博内膨胀

在最近两颗中子星合并的 GW170817 事件之后，许多弦校正的宇宙学理论面临着不存在的危险。这是因为这些理论中的大多数最初都会产生巨大的引力子。在这些理论中，包含拉格朗日函数中的非最小动力学耦合校正项的理论，属于 Horndeski 理论的一个子类。在这项工作中，我们展示了这些理论如何被复兴，并展示了这些理论如何以自然单位产生速度为 $c_T^2=1$ 的原始引力波，从而符合 GW170817 事件。正如我们所展示的，如果爱因斯坦-高斯-博内理论的引力作用也包含形式为 $\sim \xi(\phi) G^{\mu\nu}\partial_\mu\phi\partial_\ nu\phi$，具有原始无质量引力子的条件，或等效于自然单位速度 $c_T^2=1$ 的原始引力波，导致高斯-博内项的标量场相关耦合函数的某些条件，这也是动力学耦合的非最小耦合。我们通过仅假设标量场的慢滚动力学，广泛研究了这种关注暴胀时代的理论的现象学含义。因此，我们简要研究了标量场以恒定滚动方式演化的情况。通过使用一些说明性的例子，我们证明手头理论框架的可行性很容易实现。还，