AI 中文总结
本研究在度规仿射引力中构建含类Nieh-Yan项的单场慢滚暴胀模型，推导其爱因斯坦框架等价表述，通过数值计算验证中等正耦合可提升模型与CMB观测的兼容性，为暴胀理论研究提供新方向。
AI 中文摘要
我们研究了度规仿射引力中的单场慢滚暴胀模型，其中标量场与非黎曼里奇标量、挠率矢量的散度以及非度规性矢量的散度存在非最小耦合，该结构推广了著名的Nieh-Yan项。通过施加物质部分的投影相干性并求解联络场方程，我们积掉挠率和非度规性，得到了等价的爱因斯坦框架表述，其中度规仿射耦合被编码在修正的动力学函数和势中。对于非黎曼里奇标量的耦合函数取$\u27e8(ϕ) = M_P^2 + ξϕ^2$、类Nieh-Yan项的耦合函数取$\u27e7_i(ϕ) = ξ_i ϕ$、约旦框架势取单项式$\ud835\udc9b ∝ ϕ^k$的情况，我们证明在大的正有效类Nieh-Yan耦合$\barξ$极限下，正则场满足$χ\tilde{} ϕ^2$，暴胀期间的约旦框架场值变为亚普朗克尺度，且爱因斯坦框架势简化为$U \tilde{} χ^{k/2}$。我们通过数值计算了四次和二次约旦框架势下的慢滚预言，并将其与来自Planck、BICEP/Keck、ACT和SPT的当前宇宙微波背景（CMB）约束进行了比较。我们发现，中等大小的$\barξ$可以恢复非最小耦合Palatini暴胀与观测的兼容性：在四次势情形下，当$\barξ\tilde{}<10^4$时，模型预言的张标比处于下一代CMB实验的可探测范围内；而在二次势情形下，该耦合解决了$ξ\tilde{}> 10^{-2}$时出现的$η$问题，且在$10^{-2}\tilde{}<\barξ\tilde{}< 10^2$范围内给出了可行的预言。在负$\barξ$区域，该模型并未优于标准Palatini暴胀，不过它仍能产生独特的、可检验的预言。
英文摘要
We study single-field slow-roll inflation in metric-affine gravity with a scalar field non-minimally coupled to the non-Riemannian Ricci scalar and to the divergences of the torsion and nonmetricity vectors, a structure that generalizes the well-known Nieh-Yan term. By imposing projective coherence of the matter sector and solving the connection field equations, we integrate out torsion and nonmetricity and obtain an equivalent Einstein-frame formulation in which the metric-affine couplings are encoded in a modified kinetic function and potential. For the choice of coupling functions $\mathcal{A}(ϕ) = M_P^2 + ξϕ^2$ to the non-Riemannian Ricci scalar, $\mathcal{C}_i(ϕ) = ξ_i ϕ$ to the Nieh-Yan-like terms and a monomial Jordan-frame potential $\mathcal{V} \propto ϕ^k$, we show that in the limit of a large positive effective Nieh-Yan-like coupling $\barξ$ the canonical field satisfies $χ\sim ϕ^2$, the Jordan-frame field values during inflation become sub-Planckian, and the Einstein-frame potential reduces to $U \sim χ^{k/2}$. We compute the slow-roll predictions numerically for quartic and quadratic Jordan-frame potentials and compare them with the current CMB constraints from Planck, BICEP/Keck, ACT, and SPT. We find that intermediate values of $\barξ$ can restore the compatibility of non-minimally coupled Palatini inflation with observations: in the quartic case, the model predicts a tensor-to-scalar ratio within reach of next-generation CMB experiments for $\barξ\lesssim10^4$, while in the quadratic case the coupling cures the $η$-problem arising for $ξ\gtrsim 10^{-2}$ and yields viable predictions for $10^{-2}\lesssim\barξ\lesssim 10^2$. In the negative $\barξ$ regime, the model does not improve upon standard Palatini inflation, though it can still produce distinct, testable predictions.
Comments16 pages, 4 figures
