We consider a non-minimally coupled curvature-matter gravity model (NMC) with a Weyl connection, a theory referred to as non-minimally coupled Weyl connection gravity (NMCWCG). The Weyl connection is an affine connection that is not compatible with the metric, and involves a vector field. Assuming a vacuum expectation value for the vector field and a matter Lagrangian that only contains the contributions of the vacuum energy, we show that the model admits solutions in the space-form with a reference curvature that can be fine-tuned to much smaller values than the contribution of the matter fields. This shows that, at least in principle, the model admits a workable cosmological description.

中文翻译：

---

非最小耦合外尔连接引力理论的宇宙学解

我们考虑具有 Weyl 连接的非最小耦合曲率-物质引力模型 (NMC)，该理论被称为非最小耦合 Weyl 连接引力 (NMCWCG)。Weyl 连接是与度量不兼容的仿射连接，并且涉及向量场。假设向量场的真空期望值和仅包含真空能量贡献的物质拉格朗日量，我们表明该模型承认空间形式的解，其参考曲率可以微调到比比值小得多的值物质场的贡献。这表明，至少在原则上，该模型承认可行的宇宙学描述。