Abstract

Using the Noether symmetry approach, we investigate \(f( \mathcal{R} , \varphi ,\chi)\) theories of gravity, where \( \mathcal{R} \) is the scalar curvature, \( \varphi \) is the scalar field, and \(\chi\) is the kinetic term of \( \varphi \). Based on the Lagrangian for \(f( \mathcal{R} , \varphi ,\chi)\) gravity, we obtain the determining equations. We consider \(f( \mathcal{R} , \varphi ,\chi)\) models of a flat Friedmann–Robertson–Walker universe. Using the obtained solutions, we find conserved quantities. In the framework of this scenario, the continuity equation is extremely important for analyzing the energy density and pressure. Using the first integral of motion, we present a graphical analysis of the energy density, pressure component, and parameter of the equation of state. The negativity of the pressure observed in the considered cases in fact suggests that this theory can describe a Noether universe with dark matter.

中文翻译：

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具有Noether对称性的Dark $$ f（\ mathcal {R}，\ varphi，\ chi）$$宇宙

摘要

使用Noether对称方法，我们研究了\（f（\ mathcal {R}，\ varphi，\ chi）\）的引力理论，其中\（\ mathcal {R} \）是标量曲率\（\ varphi \ ）是标量场，\（\ chi \）是\（\ varphi \）的动力学项。基于\（f（\（mathcal {R}，\ varphi，\ chi）\）引力的拉格朗日方程，我们获得确定方程。我们考虑\（f（\ mathcal {R}，\ varphi，\ chi）\）弗里德曼–罗伯逊–沃克宇宙的平面模型。使用获得的解决方案，我们找到了保守的数量。在这种情况下，连续性方程对于分析能量密度和压力非常重要。使用运动的第一积分，我们给出了能量密度，压力分量和状态方程参数的图形分析。实际上，在考虑的情况下所观察到的压力的负性表明该理论可以描述带有暗物质的Noether宇宙。