Inflationary Dynamics and CMB Constraints in $f(T,L_m)$ gravity

Abstract

We investigate slow-roll inflation in a modified teleparallel framework with a non-minimal coupling between torsion and the matter sector. Focusing on Starobinsky-type plateau inflation, we derive the modified background dynamics and the corresponding slow-roll observables, and examine how the gravitational couplings affect the scalar spectral index, tensor-to-scalar ratio, and running of the spectral index. The model continuously recovers the standard Starobinsky scenario in the appropriate weak-coupling limit, while the matter--geometry coupling produces a non-monotonic modification of the inflationary predictions. We find that weak couplings leave the standard predictions essentially unchanged, whereas stronger couplings can significantly shift the scalar spectral index and eventually become incompatible with current cosmic microwave background constraints. The quadratic torsion correction has a comparatively mild impact within the controlled low-energy regime, primarily affecting the tensor amplitude. We confront the resulting predictions with the Planck and BICEP/Keck constraints and find that the model remains viable over a broad range of the inflationary parameter space. Our results demonstrate that the matter--geometry coupling can leave a potentially testable imprint on primordial observables while retaining the successful plateau-inflation phenomenology of the Starobinsky scenario.