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# Magnetogenesis in Higgs-Starobinsky inflation

Jul 2022

In the framework of mixed Higgs-Starobinsky inflation, we consider thegeneration of Abelian gauge fields due to their nonminimal coupling to gravity(in two different formulations of gravity -- metric and Palatini). We couplethe gauge-field invariants $F_{\mu\nu}F^{\mu\nu}$ and$F_{\mu\nu}\tilde{F}^{\mu\nu}$ to an integer power of the scalar curvature$R^n$ in Jordan frame and, treating these interactions perturbatively, switchto the Einstein frame where they lead to effective kinetic and axial couplingsbetween gauge fields and inflaton. We determine the power spectra, energydensities, correlation length, and helicality of the generated gauge fields fordifferent values of the nonminimal coupling constants and parameter $n$. Weanalytically estimate the spectral index $n_{B}$ of the magnetic power spectrumand show that for $n>1$ it is possible to get the scale-invariant or evenred-tilted spectrum for a wide range of modes that implies larger correlationlength of the generated fields. On the other hand, the magnitude of thesefields typically decreases in time becoming very small in the end of inflation.Thus, it is difficult to obtain both large magnitude and correlation length ofthe gauge field in the frame of this model.

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