In the present communication, we investigated flat Friedmann-Lemaitre-Robertson-Walker mathematical model of universe in $f (R,T )$ theory of gravity with bulk viscous fluid as a source of energy. A system of modified field equations with cosmological constant has been solved by considering time-dependent deceleration parameter (DP) (Mishra et al. in Eur. Phys. J. Plus 127:137, 2012). Suitable assumption yields the scale factor as $a(t)=(\sinh (\eta t))^{\frac{1}{m}}$ , where, $\eta $ and $m>0$ are arbitrary constants. The authors have also observed the nature of various energy conditions graphically. In addition, we constrained the model using recent Hubble and Pantheon Type 1a supernova observational data and obtained best fit curves of Hubble parameter $H(z)$ and apparent magnitude $m_{B}(z)$ from $\chi ^{2}$ statistical test. The findings of a constructed model are in good agreement with the recently reported data.

中文翻译：

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宇宙学模型的相变与统计技术

在目前的通讯中，我们在 $f (R,T )$ 引力理论中研究了扁平的 Friedmann-Lemaitre-Robertson-Walker 宇宙数学模型，以大量粘性流体作为能量来源。通过考虑与时间相关的减速参数 (DP)，已经解决了具有宇宙学常数的修正场方程系统（Mishra 等人在 Eur. Phys. J. Plus 127:137, 2012 中）。合适的假设产生的比例因子为 $a(t)=(\sinh (\eta t))^{\frac{1}{m}}$ ，其中 $\eta $ 和 $m>0$ 是任意常数. 作者还以图形方式观察了各种能量条件的性质。此外，我们使用最近的哈勃和万神殿 1a 型超新星观测数据约束模型，并从 $\chi ^{2 获得哈勃参数 $H(z)$ 和视星等 $m_{B}(z)$ 的最佳拟合曲线}$ 统计测试。