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

Baryon Asymmetry and Gravitational Waves from Pseudoscalar Inflation