In this paper, evolution of a Friedmann–Robertson–Walker universe is studied in a higher derivative theory of gravity. The relativistic solutions admitting hybrid expansion law of the universe are explored here. Hybrid expansion law is a general form of scale factor from which one can recover both the power-law expansion and exponential expansion as a special case. The hybrid expansion law is interesting as it addresses the early deceleration phase and presents accelerating phase satisfactorily. It is found that an inflationary scenario with hybrid expansion law is permitted in the R2 gravity fairly well. We consider universe filled with cosmic fluid that describes by an equation of state (EoS) parameter which varies with time. Consequently, we analyze the time variation of energy density parameter, cosmic pressure, equation of state parameter, deceleration parameter and jerk parameter in the cosmological model. The constraints of the model parameters imposed by the cosmological observational data set are determined. The present value of the deceleration parameter (q), EoS parameter and the epoch at which the transition of decelerated phase to accelerated phase are estimated. In the higher derivative theory, we obtain some new and interesting cosmological solutions relevant for building cosmological models.

中文翻译：

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具有混合膨胀定律的 R2 引力宇宙学模型

在本文中，弗里德曼-罗伯逊-沃克宇宙的演化是在更高的引力导数理论中研究的。这里探讨了承认宇宙混合膨胀定律的相对论解决方案。混合展开律是比例因子的一种一般形式，可以从中恢复幂律展开和指数展开作为特例。混合膨胀定律很有趣，因为它解决了早期的减速阶段并令人满意地呈现了加速阶段。研究发现，混合膨胀法的通货膨胀情景是允许的R2重力相当好。我们考虑充满宇宙流体的宇宙，该流体由随时间变化的状态方程 (EoS) 参数描述。因此，我们分析了宇宙学模型中能量密度参数、宇宙压力、状态方程参数、减速参数和加加速度参数的时间变化。确定了由宇宙学观测数据集施加的模型参数的约束。减速参数的当前值(q), EoS 参数和估计减速阶段到加速阶段过渡的时期。在高阶导数理论中，我们获得了一些与构建宇宙学模型相关的新的有趣的宇宙学解。