Non-minimal $\alpha$-attractor magnetogenesis with potential dependent couplings

Abstract

We investigate inflationary magnetogenesis driven by a non conformal coupling in the case of large-field $\alpha$-attractor inspired models. We introduce potential-dependent electromagnetic coupling functions $f(\varphi )$ that reproduce the scaling $f\propto a^p$ during slow roll. Starting from Starobinsky inflation, we analytically derive explicit couplings for $(E)$-model and $(T)$-model potentials. We then study how these functions affect electromagnetic amplification in the regime of non-minimal coupling between the inflaton field and the Ricci scalar ${\varphi }^{2}R$. In particular, we compare different values for the coupling strength $\xi$, accounting for electromagnetic backreaction and Schwinger pair production through the gradient expansion formalism. Our numerical results show that the non-minimal coupling affects the evolution of the electromagnetic sector and the resulting magnetic-field amplitude. We find that, within the analyzed configurations, minimally coupled and $\xi >0$ scenarios are compatible with the adopted CMB constraints, yielding conditional present-day magnetic-field estimates of order $10^{-23}$ G.

arXiv comment12 pages, 3 figures, 3 tables