论文标题
$ f（\ Mathcal {r}，φ，χ）$宇宙学与Noether对称性
$f(\mathcal{R},φ,χ)$ Cosmology with Noether Symmetry
论文作者
论文摘要
本文致力于使用Noether对称方法探索修改后的$ F（\ Mathcal {r}）$重力理论。为此，选择了弗里德曼·罗伯逊（Friedmann-Robertson）步行者的时空来研究宇宙的进化。这项研究主要分为两个部分：首先，对度量$ f（\ MATHCAL {r}）$重新度进行了noe对称性，并报告了一些新的解决方案，并在保守数量的帮助下进行了新的解决方案。结果表明，可以使用Noether对称性讨论宇宙进化的不同情况，其中一种情况表明了存在大裂口奇异性的机会。其次，已经详细讨论了$ f（\ Mathcal {r}）$理论与标量字段。据报道，弗里德曼·罗伯逊 - 沃克宇宙的三个子速率据报道了修饰的重力方程。可以得出结论，在宇宙学环境中找到一些重要的精确解决方案非常有帮助。此外，在宇宙进化中涉及的标量场在宇宙进化中起着至关重要的作用，并且可以观察到$ f（\ Mathcal {r}，φ，χ）$重力模型的某些合适选择的加速膨胀阶段。
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 $f(\mathcal{R},φ,χ)$ gravity models.
