In this paper, we investigate the cosmological implications and constraints of Weyl-type gravity. This theory introduces a coupling between the non-metricity and the trace of the energy–momentum tensor, using the principles of proper Weyl geometry. In this geometry, the scalar non-metricity , which characterizes the deviations from Riemannian geometry, is expressed in its standard Weyl form and is determined by a vector field . To study the implications of this theory, we propose a deceleration parameter with a single unknown parameter , which we constrain by using the latest cosmological data. By solving the field equations derived from Weyl-type gravity, we aim to understand the behavior of the energy conditions within this framework. In the present work, we consider two well-motivated forms of the function : (i) the linear model represented by , and (ii) the coupling model represented by , where , , and are free parameters. Here, represents the gravitational coupling constant. In both of the models considered, the strong energy condition is violated, indicating consistency with the present accelerated expansion. However, the null, weak, and dominant energy conditions are satisfied in these models.

中文翻译：

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探索韦尔型[公式省略]引力：宇宙学含义和约束

在本文中，我们研究了外尔型引力的宇宙学含义和约束。该理论利用适当的外尔几何原理，引入了非度量性与能量动量张量的迹之间的耦合。在此几何中，标量非度量 表征与黎曼几何的偏差，以其标准 Weyl 形式表示，并由向量场 确定。为了研究该理论的含义，我们提出了一个具有单个未知参数 的减速参数，我们通过使用最新的宇宙学数据对其进行约束。通过求解由外尔型引力导出的场方程，我们的目标是了解该框架内能量条件的行为。在目前的工作中，我们考虑函数 的两种动机良好的形式：(i) 由 表示的线性模型，以及 (ii) 由 表示的耦合模型，其中 、 和 是自由参数。这里， 表示引力耦合常数。在所考虑的两个模型中，强能量条件都被违反，表明与当前的加速膨胀一致。然而，这些模型满足零能量、弱能量和主导能量条件。