In this work we consider a scale-tensor theory in which the space-time is endowed with a Weyl integrable geometrical structure due to the Palatini variational method. Since the scalar field has a geometrical nature (related to non-metricity), the theory is known as \textit{Geometrical Scalar-Tensor}. On the framework of Weyl transformations, a non-minimally coupled scalar-tensor theory on the Jordan frame corresponds to a minimally coupled Einstein-Hilbert action on the Einstein frame. The scalar potential is selected by the Noether symmetry approach in order to obtain conserved quantities for the FRW cosmological model. Exact solutions are obtained and analyzed in the context of the cosmological scenarios consistent with an expanding universe. A particular case is matched in each frame and the role of scalar field as a dark energy component is discussed.

中文翻译：

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具有由诺特对称方法确定的势的几何标量张量的宇宙学解

在这项工作中，我们考虑了一种尺度张量理论，其中由于帕拉蒂尼变分方法，时空被赋予了 Weyl 可积几何结构。由于标量场具有几何性质（与非度量相关），因此该理论被称为 \textit{Geometrical Scalar-Tensor}。在外尔变换的框架上，乔丹框架上的非最小耦合标量张量理论对应于爱因斯坦框架上的最小耦合爱因斯坦-希尔伯特作用。标量势由 Noether 对称方法选择，以获得 FRW 宇宙学模型的守恒量。在与膨胀的宇宙一致的宇宙学情景的背景下获得和分析精确解。