In this study, we investigated scalar field in [Formula: see text]-gravity by using LRS Bianchi type-I universe. Massless and massive scalar field models are separately constructed in [Formula: see text]-gravity. Massless scalar field models are examined in the cases of constant and exponential potential fields. For all models, solutions of field equations are obtained under the consideration of [Formula: see text]. [Formula: see text] functions for each model are separately attained in theory. It is shown that constructed models in the presence of massless scalar field permit quintessence scalar field. Also, it is observed that each model indicates expanding universe with deceleration. Also, kinematical quantities are analyzed in the light of obtained solutions. All models are concluded with a geometric and physical perspective.

中文翻译：

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f(G) 引力中的标量场

在这项研究中，我们使用 LRS Bianchi I 型宇宙研究了 [公式：见文本]-重力中的标量场。无质量和有质量的标量场模型分别在[公式：见正文]-gravity中构建。在恒定和指数势场的情况下检查无质量标量场模型。对于所有模型，场方程的解都是在考虑[公式：见正文]的情况下获得的。【公式：见正文】 理论上各模型的功能分别得到。结果表明，在存在无质量标量场的情况下构建的模型允许典型标量场。此外，观察到每个模型都表明宇宙在减速膨胀。此外，根据获得的解决方案分析运动学量。所有模型都以几何和物理视角结束。