标题： $f(\mathcal{R},\varphi,χ)$宇宙学中的Noether对称性 显示英文标题

标题： $f(\mathcal{R},\varphi,χ)$ Cosmology with Noether Symmetry

摘要： 本文致力于利用诺特定理方法探索修改的$f(\mathcal{R})$引力理论。 为此，选择了弗里德曼-罗伯逊-沃尔克时空来研究宇宙演化。 研究主要分为两部分：首先重新考察了度规$f(\mathcal{R})$引力的诺特定理，并借助守恒量报告了一些新的解类。 结果表明，可以利用诺特定理讨论不同的宇宙演化情景，其中一个情况表明存在大撕裂奇点的可能性。 其次，详细讨论了与标量场耦合的$f(\mathcal{R})$理论。 报告了修改引力的诺特方程，并针对平坦弗里德曼-罗伯逊-沃尔克宇宙给出了三个子情况。 结论认为，守恒量在宇宙学背景下寻找一些重要的精确解非常有帮助。 此外，参与修改引力的标量场在宇宙演化中起着关键作用，对于某些合适的$f(\mathcal{R},\varphi,\chi)$引力模型可以选择出加速膨胀阶段。 显示英文摘要

摘要： This paper is devoted to explore modified $f(\mathcal{R})$ theories of gravity using Noether symmetry approach. For this purpose, Friedmann-Robertson-Walker spacetime is chosen to investigate the cosmic evolution. The study is mainly divided into two parts: Firstly Noether symmetries of metric $f(\mathcal{R})$ gravity are revisited and some new class of solutions with the help of conserved quantities are reported. It is shown that different scenarios of cosmic evolution can be discussed using Noether symmetries and one of the case indicates the chances for the existence of Big Rip singularity. Secondly, $f(\mathcal{R})$ theory coupled with scalar field has been discussed in detail. The Noether equations of modified gravity are reported with three subcases for flat Friedmann-Robertson-Walker universe. It is concluded that conserved quantities are quite helpful to find some important exact solutions in the cosmological contexts. Moreover, the scalar field involved in the modified gravity plays a vital role in the cosmic evolution and an accelerated expansion phase can be observed for some suitable choices of $f(\mathcal{R},\varphi,\chi)$ gravity models.