  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.
