发表机构
Universidad de La Frontera; Durban University of Technology; North-West University; Universidad Católica de Temuco; National Institute for Theoretical and Computational Sciences（拉弗龙特拉大学; 德班理工大学; 西北大学; 特木科天主教大学; 国家理论与计算科学研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文在平坦 FLRW 背景下对 $k$-essence 模型进行对称性分类，通过拉格朗日乘子引入动能项并保留 lapse 为动力学变量，发现两类非平凡对称性，并利用 Noether 守恒律导出精确宇宙学解及尺度因子的幂律形式。
AI 中文摘要
在空间平坦的 FLRW 背景下，我们对拉格朗日密度形如 $f_1(\phi)R+f_2(\phi,X)$ 的 $k$-essence 模型进行了对称性分类。动能项 $X$ 通过拉格朗日乘子作为独立自由度引入，并且 lapse 函数被视为动力学变量。对称性分析应用于约束系统，且在任何规范固定之前进行。这种方法揭示了在作用量层面固定 lapse 时会丢失的对称性。所推导出的允许非平凡对称性的 $k$-essence 模型族分为两大类：与引力最小耦合的理论和与引力非最小耦合的理论。我们利用相应的 Noether 守恒律来推导精确的宇宙学解。我们发现，当守恒荷的数值为零时，场方程简化为代数关系。随后，我们推导出尺度因子的幂律表达式，其指数由特定的 $k$-essence 函数决定。
英文摘要
In the context of a spatially flat FLRW background, we perform a symmetry classification of $k$-essence models with Lagrangian densities of the form $f_1(ϕ)R+f_2(ϕ,X)$. The kinetic term $X$ is introduced as an independent degree of freedom via a Lagrange multiplier, and the lapse function is treated as a dynamical variable. The symmetry analysis is applied to the constrained system prior to any gauge fixing. This approach reveals symmetries which otherwise are lost when the lapse is fixed at the level of the action. The derived families of $k$-essence models admitting nontrivial symmetries fall to two general classes: minimally coupled and nonminimally coupled theories to gravity. We use the corresponding Noetherian conservation laws to derive exact cosmological solutions. We find that, when the numerical value of the conserved charges is zero, the field equations reduce to an algebraic relation. We subsequently derive power-law expressions for the scale factor with exponents determined by the particular $k$-essence function.
Comments13 pages, no figures
