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
摘要：
引力理论从根本上讲是物质与基本时空几何结构之间的关系。因此，一旦我们对时空几何施加了一些额外的限制，引力理论就必然会受到影响，不管它是广义相对论还是修正后的引力理论。在本文中，我们考虑两个基于曲率的约束，即几乎伪Ricci对称和弱Ricci对称条件。作为一个新的结果，这样的时空与非零关联矢量完全分类，然后应用所获得的结果，我们调查这些时空的解决方案的$F(R)$ -引力理论。首先导出了修正的Friedmann方程，并以与模型无关的方式进行了分析。最后，两个$F(R)$重力模型检查最近的观测约束值的减速，加加速度和哈勃参数。我们进一步讨论了能量条件的行为。
英文摘要：
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.
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