Geometric Langlands duality in Einstein-Cartan cosmology

Independent Researcher - India

Received: 5 March 2026
Accepted: 11 May 2026

Abstract

A geometric correspondence between Einstein-Cartan cosmology and the geometric Langlands program is established. Spin-torsion interactions generate a non-singular cosmological bounce, while a well-posed variational principle on the resulting manifold with boundary induces residual geometric data on the bounce hypersurface, organising as a Higgs-type pair satisfying a torsion-deformed Hitchin system. The boundary projection of axial torsion —fixed algebraically by the primordial fermionic spin density— serves as the Higgs field, whose spectral structure selects a constrained sector of the Hitchin moduli space and, via the non-Abelian Hodge correspondence, determines flat connections for the Langlands dual group, governing stability of the post-bounce configuration and imposing non-perturbative constraints on the inflaton sector. The resulting Hitchin data shift the scalar spectral index and its running in a manner bounded by current CMB observations and within the projected sensitivity of next-generation experiments, establishing a direct and falsifiable link between torsion-induced boundary geometry and primordial perturbations.