The objective of the present paper is to study 4-dimensional almost pseudo Ricci symmetric perfect fluid spacetimes $$(\textit{APRS})_4$$ ( APRS ) 4 . We show that a Robertson–Walker spacetime is $$(\textit{APRS})_4$$ ( APRS ) 4 and vice versa under certain condition imposed on its scale factor. Some popular toy models of F ( R )-gravity are also studied under the current setting and various energy conditions are investigated.

中文翻译：

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F(R)-gravity 中的几乎伪 Ricci 对称时空解

本论文的目的是研究 4 维几乎伪 Ricci 对称完美流体时空 $$(\textit{APRS})_4$$ (APRS) 4 。我们证明了罗伯逊-沃克时空是 $$(\textit{APRS})_4$$ ( APRS ) 4 ，反之亦然，在对其比例因子施加一定条件下。在当前设置下还研究了一些流行的 F ( R ) 重力玩具模型，并研究了各种能量条件。