标题： 标量场的Eisenhart提升在FLRW宇宙中 显示英文标题

标题： Eisenhart Lift for Scalar Fields in the FLRW Universe

摘要： Eisenhart提升的黎曼类型描述了粒子在更高维黎曼流形中的运动，该流形有一个额外的坐标。 最近，它已被推广到标量场系统，通过引入一个额外的矢量场。 我们将这种方法应用于FLRW（弗里德曼-勒梅特-罗伯逊-沃尔克）宇宙中的标量场系统，并对系统的对称性进行分类。 特别是，我们发现对于由指数函数组合的平方构成的标量场势，存在非平凡的（共形）Killing矢量场和Killing张量场，其特定指数为$e^{\pm\frac{\sqrt{6}}{4}\phi}$。 此外，我们发现对于写成指数函数势组合的指数形式的势，存在非平凡的共形Killing矢量场。 给出了运动方程的完整解。 我们还对多标量场系统的对称性进行了分类。 显示英文摘要

摘要： The Eisenhart lift of Riemannian type describes the motion of a particle as a geodesic in a higher-dimensional Riemannian manifold with one additional coordinate. It has recently been generalized to a scalar field system by introducing one additional vector field. We apply this approach to a scalar field system in the FLRW (Friedmann-Lemaitre-Robertson-Walker) universe and classify the symmetries of the system. In particular, we find nontrivial (conformal) Killing vector field and Killing tensor fields for a scalar field potential consisting of the square of a combination of exponential functions with specific index $e^{\pm\frac{\sqrt{6}}{4}\phi}$. Moreover, we find nontrivial conformal Killing vector fields for a potential which is written as an exponentiation of a combination of exponential potentials with general index. Complete solutions to the equations of motion are given. We also classify the symmetries of multiple scalar field system.