Hypermagnetogenesis from axion inflation: Model-independent estimates

Axion inflation coupled to the Standard Model (SM) hypercharge gauge sector represents an attractive scenario for generation of primordial hypermagnetic fields. The description this is, however, complicated by Schwinger effect, which gives rise highly nonlinear dynamics. Hypermagnetogenesis during axion in absence effects is well studied and known result a energy density that scales like $H^4\,e^{2\pi\xi}/\xi^5$, where $\xi$ proportional time derivative axion-vector coupling units Hubble rate $H$. In paper, we generalize full SM case consistently taking into account pair production all fermions. To end, employ novel gradient-expansion formalism recently developed [2109.01651], based on set vacuum expectation values bilinear hyperelectromagnetic functions position space. We parametrize numerical output our terms three parameters ($\xi$, $H$, $\Delta$, latter accounts damping subhorizon gauge-field modes because finite conductivity medium) work out semianalytical fit describe results with high accuracy. Finally, validate comparing them existing estimates literature as explicit specific inflationary model, leads good overall agreement. conclude systematic uncertainties hypermagnetogenesis inflation, previously spanned up several orders magnitude, are now reduced typically less than 1 order paves way further phenomenological studies.