Inflation with Nieh-Yan-like terms in metric-affine gravity

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 A(phi) = M P squared + xi phi squared to the non-Riemannian Ricci scalar, C i(phi) = xi i phi to the Nieh-Yan-like terms and a monomial Jordan-frame potential V proportional to phi k, we show that in the limit of a large positive effective Nieh-Yan-like coupling the canonical field satisfies chi about phi squared, the Jordan-frame field values during inflation become sub-Planckian, and the Einstein-frame potential reduces to U about chi 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 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 10 4, while in the quadratic case the coupling cures the eta-problem arising for xi 10-2 and yields viable predictions for 10-2 10 squared. In the negative regime, the model does not improve upon standard Palatini inflation, though it can still produce distinct, testable predictions.