Nelson-Barr Inflation

Abstract

The Nelson-Barr mechanism solves the strong CP problem through spontaneous CP violation, but the resulting CP-conjugate vacua generically lead to stable domain walls. We propose that the Nelson-Barr scalar itself drives hilltop inflation. A CP-symmetric double-well potential for its imaginary component forms two CP-breaking valleys, with inflation proceeding along one of them. Since the lowest CP-invariant ridge is generically much higher than the energy available after inflation, transitions between the two branches are energetically inaccessible, and the domain walls cannot be regenerated after inflation. A small CP-preserving linear deformation raises the scalar spectral index of quartic hilltop inflation and yields CMB-compatible parameter regions. The Nelson-Barr sector necessarily provides a portal to visible-sector reheating. When coupled to right-handed neutrinos, it can also transmit the spontaneous CP phase to the lepton sector and, in an extension that allows a higher CP-breaking scale, even realize nonthermal leptogenesis. This establishes a unified cosmological realization of the Nelson--Barr mechanism in which the same CP-breaking dynamics solves the strong CP problem, can generate quark and lepton CP violation, drives inflation and reheating, and enables baryogenesis, while simultaneously eliminating the associated domain-wall problem.