论文标题
基于曲率的几何约束对$ f（r）$理论的影响
Impact of curvature based geometric constraints on $F(R)$ theory
论文作者
论文摘要
重力理论从根本上是物质与基础时空的几何结构之间的关系。因此，一旦我们对时空的几何形状提出了一些额外的限制，重力理论必定会产生影响，而不论是一般相对论还是重力理论。在本文中，我们考虑了两个基于曲率的约束，即几乎是伪-RICCI对称和弱RICCI对称条件。作为一个新的结果，这种具有非无效相关矢量的空间被完全分类，然后应用所获得的结果，我们将这些空间作为$ f（r）$重力理论的解决方案进行了研究。首先以模型无关的方式得出和分析了修改的Friedmann方程。最后，检查了两个$ f（r）$重力模型，以了解减速，混蛋和哈勃参数的最新观察性约束值。我们进一步讨论能量条件的行为。
Theories of gravity are fundamentally a relation between matter and the geometric structure of the underlying spacetime. So once we put some additional restrictions on the spacetime geometry, the theory of gravity is bound to get the impact, irrespective of whether it is general relativity or the modified theories of gravity. In the present article, we consider two curvature-based constraints, namely the almost pseudo-Ricci symmetric and weakly Ricci symmetric condition. As a novel result, such spacetimes with non-null associated vectors are entirely classified, and then applying the obtained results, we investigate these spacetimes as solutions of the $F(R)$-gravity theory. The modified Friedmann equations are derived and analysed in a model-independent way first. Finally, two $F(R)$ gravity models are examined for recent observational constrained values of the deceleration, jerk, and Hubble parameters. We further discuss the behavior of energy conditions.
