One of the alternative theories to Einstein’s general theory, a divergence-free theory was proposed by J. Nash with Lagrangian density given by [Formula: see text]. Although it was proved that the Nash theory does not have classical Einstein limits, it has been proven to be formally divergent free and considered to be of interest in constructing theories of quantum gravity. The original Nash gravity without matter contents cannot explain the current acceleration expansion of the Universe. A possible extension of theory is by adding some matter contents to the model. In this work, we generalize Nash theory of gravity by adding the matter fields. In order to examine the effects of this generalization, we first derive the equations of motion in the flat FLRW space–time and examine the behaviors of the solutions by invoking specific forms of the Hubble parameter. We also classify the physical behaviors of the solutions by employing the stability analysis and check the consistency of the model by considering particular cosmological parameters.

中文翻译：

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论含物质含量的纳什万有引力理论

作为爱因斯坦一般理论的替代理论之一，J. Nash 提出了一种无散理论，其拉格朗日密度由 [公式：见正文] 给出。尽管证明纳什理论没有经典的爱因斯坦极限，但它已被证明是形式上无发散的，并且被认为对构建量子引力理论很感兴趣。没有物质含量的原始纳什引力无法解释当前宇宙的加速膨胀。一个可能的理论扩展是在模型中添加一些物质内容。在这项工作中，我们通过添加物质场来推广纳什引力理论。为了检验这种概括的效果，我们首先推导出平面 FLRW 时空中的运动方程，并通过调用特定形式的哈勃参数来检查解的行为。我们还通过稳定性分析对解的物理行为进行分类，并通过考虑特定的宇宙学参数来检查模型的一致性。