An LRS Bianchi-I space-time model is studied with constant Hubble parameter in $f(R,T)=R+2\lambda T$ gravity. Although a single (primary) matter source is considered, an additional matter appears due to the coupling between matter and $f(R,T)$ gravity. The constraints are obtained for a realistic cosmological scenario, i.e., one obeying the null and weak energy conditions. The solutions are also extended to the case of a scalar field (normal or phantom) model, and it is found that the model is consistent with a phantom scalar field only. The coupled matter also acts as phantom matter. The study shows that if one expects an accelerating universe from an anisotropic model, then the solutions become physically relevant only at late times when the universe enters into an accelerated phase. Placing some observational bounds on the present equation of state of dark energy, $\omega_0$, the behavior of $\omega(z)$ is depicted, which shows that the phantom field has started dominating very recently, somewhere between $0.2\lesssim z\lesssim0.5$.

中文翻译：

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LRS Bianchi I 模型在 $f(R,T)$ 重力下具有恒定膨胀率

在$f(R,T)=R+2\lambda T$引力下研究了一个LRS Bianchi-I时空模型，该模型具有恒定的哈勃参数。尽管考虑了单一（主要）物质来源，但由于物质与 $f(R,T)$ 引力之间的耦合，会出现额外的物质。这些约束是针对现实的宇宙学场景获得的，即遵守零能量和弱能量条件的场景。解决方案还扩展到标量场（正常或幻影）模型的情况，发现该模型仅与幻影标量场一致。耦合的物质也作为幻象物质。该研究表明，如果人们从各向异性模型中预测宇宙会加速，那么这些解只有在宇宙进入加速阶段的后期才会变得物理相关。