标题： 非最小耦合标量$k$-暴胀动力学 显示英文标题

标题： Non-minimally Coupled Scalar $k$-Inflation Dynamics

摘要： 在本工作中，我们将研究具有标量场与引力非最小耦合的$k$-膨胀理论，在仅存在形式为$\sim \mathrm{const}\times X^{\mu}$的高阶动能项的情况下，带有$X=\frac{1}{2}\partial_{\mu}\phi\partial^{\mu}\phi$。 研究将集中在包含或不包含标量势的情况，标量场的演化将假设满足慢滚或常滚条件。 在包含标量势的慢滚模型情况下，我们将计算慢滚指数和该理论的相应观测指数，并证明所得理论与最新的普朗克数据相容。 在常滚情况下，至少在存在标量势的情况下，得到相同的结果。 在考虑无势模型的情况下，结果不太吸引人，因为这些结果强烈依赖于模型，至少对于非最小耦合的幂律选择，该理论不可行。 最后，由于标量和张量功率谱是共形不变量，我们认为具有标量势的非最小$k$-膨胀模型的爱因斯坦框架对应物，由于观测指数的共形不变性，可以是一个可行的理论。 爱因斯坦框架理论更为复杂，因此更难以进行解析处理，因此我们工作的含义之一是，我们提供了另一个类别的$k$-膨胀模型可行性的证据。 显示英文摘要

摘要： In this work we shall study $k$-inflation theories with non-minimal coupling of the scalar field to gravity, in the presence of only a higher order kinetic term of the form $\sim \mathrm{const}\times X^{\mu}$, with $X=\frac{1}{2}\partial_{\mu}\phi\partial^{\mu}\phi$. The study will be focused in the cases where a scalar potential is included or is absent, and the evolution of the scalar field will be assumed to satisfy the slow-roll or the constant-roll condition. In the case of the slow-roll models with scalar potential, we shall calculate the slow-roll indices, and the corresponding observational indices of the theory, and we demonstrate that the resulting theory is compatible with the latest Planck data. The same results are obtained in the constant-roll case, at least in the presence of a scalar potential. In the case that models without potential are considered, the results are less appealing since these are strongly model dependent, and at least for a power-law choice of the non-minimal coupling, the theory is non-viable. Finally, due to the fact that the scalar and tensor power spectra are conformal invariant quantities, we argue that the Einstein frame counterpart of the non-minimal $k$-inflation models with scalar potential, can be a viable theory, due to the conformal invariance of the observational indices. The Einstein frame theory is more involved and thus more difficult to work with it analytically, so one implication of our work is that we provide evidence for the viability of another class of $k$-inflation models.