arXiv2026
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.