Single Field Baryogenesis and the Scale of Inflation

In the context of inflationary cosmology, we discuss a minimal baryogenesis scenario in which the resulting baryon to entropy ratio is determined by the amplitude of the anisotropies of the cosmic microwave background. The model involves a new $SU(2)_L$ scalar field which generates a Dirac neutrino mass and which is excited by quantum fluctuations during inflation, yielding a CP-violating phase. During the scalar field decay after inflation, an asymmetry in the left-handed neutrino number is generated, which then converts to a net baryon asymmetry via sphalerons. A lower limit on the expected initial value of the scalar field translates to a lower limit on the baryon to entropy ratio (which also depends on the Dirac neutrino Yukawa coupling). Consistency with the limits on baryonic isocurvature perturbations requires that the spectral index of adiabatic perturbations produced during inflation be very close to unity. In a variant of our scenario in which the scalar is a gauge singlet, the connection between the baryon to entropy ratio and the inflationary scale is lost, although the basic mechanism of baryogenesis remains applicable.