Geometric suppression of CMB isocurvature and a blue-tilted spectrum

CMB limits on cold-dark-matter isocurvature are often interpreted as excluding the simultaneous realization of high-scale inflation and large QCD axion decay constants in preinflationary Peccei-Quinn (PQ) scenarios. This conclusion can be evaded by exploiting . For a minimal complex PQ scalar with a U ( 1 ) -symmetric potential and a nonlinear sigma-model kinetic term d σ 2 = d R 2 + f 2 ( R ) d θ 2 , the observable axion fluctuation is δ θ ∼ H inf / f ( R ) , so an enhanced effective decay constant f ( R ) suppresses isocurvature without explicit PQ breaking, extreme radial displacements, or additional couplings. We specialize to a hyperbolic metric f ( R ) ∝ sinh ( R / L ) with curvature scale L . The same geometry also induces a time-dependent O ( H inf ) effective mass for the canonical axial mode during radial slow-roll, and fixing the tilt and running of isocurvature. Thus, CMB-scale isocurvature is suppressed while a characteristic blue-tilted spectrum is generated. As a result, inflationary Hubble scales as large as H inf ∼ 10 13 GeV can be compatible with f a ∼ 10 14 – 10 16 GeV , reopening parameter space usually regarded as excluded. We present observable benchmarks and a semianalytic template that relates the scale-dependence of isocurvature to the geometric lever arm R / L , providing a direct phenomenological probe on PQ field-space geometry.