Baryon Asymmetry and Gravitational Waves from Pseudoscalar Inflation

Abstract: In models of inflation driven by an axion-like pseudoscalar field, the inflaton, a, may couple to the standard model hypercharge via a Chern-Simons-type interaction, $L \subset a/(4\Lambda) F\tilde{F}$. This coupling results in explosive gauge field production during inflation, especially at its last stage, which has interesting phenomenological consequences: For one thing, the primordial hypermagnetic field is maximally helical. It is thus capable of sourcing the generation of nonzero baryon number, via the standard model chiral anomaly, around the time of electroweak symmetry breaking. For another thing, the gauge field production during inflation feeds back into the primordial tensor power spectrum, leaving an imprint in the stochastic background of gravitational waves (GWs). In this paper, we focus on the correlation between these two phenomena. Working in the approximation of instant reheating, we (1) update the investigation of baryogenesis via hypermagnetic fields from pseudoscalar inflation and (2) examine the corresponding implications for the GW spectrum. We find that successful baryogenesis requires a suppression scale Lambda of around Lambda ~ 3 x 10^17 GeV, which corresponds to a relatively weakly coupled axion. The gauge field production at the end of inflation is then typically accompanied by a peak in the GW spectrum at frequencies in the MHz range or above. The detection of such a peak is out of reach of present-day technology; but in the future, it may serve as a smoking-gun signal for baryogenesis from pseudoscalar inflation. Conversely, models that do yield an observable GW signal suffer from the overproduction of baryon number, unless the reheating temperature is lower than the electroweak scale.