In this paper, we have discussed string cosmological model within the framework of [Formula: see text] theory of gravity in homogeneous but anisotropic Bianchi Type-II space-time. We have considered cosmic string as a source of energy–momentum tensor. We get the solution of the corresponding field equations by assuming deceleration parameter [Formula: see text], which is time-dependent (here, [Formula: see text] and [Formula: see text] are arbitrary constants). This particular form of scale factor enables us to explain the two scenarios, (i) By using recent constraints ([Formula: see text], [Formula: see text]) from supernovae type Ia union data (Cunha, Kinematic constraints to the transition redshift from supernovae type Ia union data, Phys. Rev. D 79 (2009) 047301), we find the values of arbitrary constants [Formula: see text] and [Formula: see text] for which we have derived a cosmological model showing accelerating expansion universe ([Formula: see text]) only throughout the evolution and (ii) By using the recent constraints ([Formula: see text], and [Formula: see text]) from SNIa data in combination with BAO and CMB observations (Giostri et al. From cosmic deceleration to acceleration: new constraints from SN Ia and BAO/CMB, J. Cosmol. Astrophys. 3 (2012) 27), we find the values of arbitrary constants for which we have derived a cosmological model with phase transition from early decelerating ([Formula: see text]) to the present accelerating ([Formula: see text]) universe. Also, for the model, we have evaluated and discussed the various physical and kinematic parameters. We have also shown the variation of these cosmological parameters graphically for specific values of the constants. The stability and physical viability are also discussed for the derived models using some recently developed diagnostic tools.

中文翻译：

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f(R,T)-引力理论中 Bianchi II 型弦宇宙减速到加速场景

在本文中，我们在[公式：见正文]均匀但各向异性的Bianchi Type-II时空引力理论的框架内讨论了弦宇宙学模型。我们已经将宇宙弦视为能量-动量张量的来源。我们通过假设减速参数[公式：见文本]得到相应场方程的解，该参数是时间相关的（这里，[公式：见文本]和[公式：见文本]是任意常数）。这种特殊形式的比例因子使我们能够解释这两种情况，（i）通过使用来自超新星 Ia 型联合数据（Cunha，Kinematic constraints to the transition）的最新约束（[公式：见文本]，[公式：见文本]）从超新星 Ia 型联合数据的红移，Phys. Rev. D 79 (2009) 047301)，我们找到任意常数的值 [公式：见正文] 和 [公式：见文本]，为此我们推导出了一个宇宙模型，显示宇宙加速膨胀（[公式：见文本]）仅在整个演化过程中，以及 (ii) 通过使用最近的约束（[公式：见文本]和 [公式：见文本] ]）从 SNIa 数据结合 BAO 和 CMB 观测（Giostri 等人。从宇宙减速到加速：来自 SN Ia 和 BAO/CMB 的新约束，J. Cosmol. Astrophys. 3 (2012) 27），我们找到了值我们推导出了一个宇宙学模型，该模型具有从早期减速（[公式：参见文本]）到当前加速（[公式：参见文本]）宇宙的相变。此外，对于模型，我们已经评估和讨论了各种物理和运动学参数。我们还以图形方式显示了这些宇宙学参数对于常数的特定值的变化。还使用一些最近开发的诊断工具讨论了衍生模型的稳定性和物理可行性。