Nieh–Yan Endpoint Structure in Palatini Inflation: FRW Analogue, Observational Constraints, and Axion Dark Matter

This preprint develops the cosmological part of a two-paper sequence on Nieh–Yan structures in Palatini gravity.

The first paper established the geometric endpoint-localization mechanism in cylindrical Riemann–Cartan backgrounds and clarified how the Nieh–Yan structure reduces to endpoint data. The present paper studies the corresponding Friedmann–Robertson–Walker realization and shows that, in Palatini gravity, the Nieh–Yan endpoint contribution is exponentially dominated by the end of inflation, while the initial contribution is erased by FRW volume dilution.

Within Palatini Higgs inflation, the torsion sector remains algebraic rather than dynamical, so the Nieh–Yan contribution does not introduce an independent propagating degree of freedom. Its main effects are instead encoded in endpoint data. The paper derives the FRW endpoint difference explicitly, separates the trace and axial torsion channels, and shows that the induced corrections to standard inflationary observables such as the scalar spectral index and tensor-to-scalar ratio remain small for representative parameter choices.

The paper also analyzes the coupling of the endpoint-localized Nieh–Yan structure to an axion-like field. In this setting, the endpoint term can generate an axion velocity kick, which may be interpreted as a geometric contribution to axion initial conditions. For standard QCD-axion parameters, the redshift-corrected effect is practically negligible, but the mechanism can become more relevant for heavier axion-like particles and for non-standard post-inflationary reheating histories. The reheating equation of state strongly affects the size of the effect, so the mechanism may also be viewed, in principle, as a probe of otherwise inaccessible post-inflationary dynamics.

This work is intended as the cosmological companion to the first paper:
“The Nieh–Yan Term on Cylindrical Riemann–Cartan Backgrounds: Endpoint Localization and Bulk-Boundary Structure”
(DOI: 10.5281/zenodo.19040497).

V2: Revised the FRW analysis and corrected the effective kinetic coefficient \Keff(h)\Keff(h)\Keff(h), now written consistently as \Keff=F−1+23(Y′)2/F2\Keff=F^{-1}+\frac{2}{3}(Y')^2/F^2\Keff=F−1+32(Y′)2/F2. The text was also clarified to distinguish the axial channel relevant to the Nieh--Yan endpoint term from the trace torsion induced by the scalar background, and to state the inflationary effect in terms of Jacobian suppression of the initial-slice contribution rather than suppression of τ\tauτ itself. Numerical estimates and phenomenological remarks were updated accordingly.