Extreme neutron stars from Extended Theories of Gravity

We discuss neutron stars with strong magnetic mean fields in the framework of Extended Theories of Gravity. In particular, we take into account models derived from $f(R)$ and $f(\cal G)$ extensions of General Relativity where functions of the Ricci curvature invariant $R$ and the Gauss-Bonnet invariant ${\cal G}$ are respectively considered. Dense matter in magnetic mean field, generated by magnetic properties of particles, is described by assuming a model with three meson fields and baryons octet. As result, the considerable increasing of maximal mass of neutron stars can be achieved by cubic corrections in $f(R)$ gravity. In principle, massive stars with $M> 4 M_{\odot}$ can be obtained. On the other hand, stable stars with high strangeness fraction (with central densities $\rho_{c}\sim 1.5-2.0$ GeV/fm$^{3}$) are possible considering quadratic corrections of $f(\cal {G})$ gravity. The magnetic field strength in the star center is of order $6-8\times 10^{18}$ G. In general, we can say that other branches of massive neutron stars are possible considering the extra pressure contributions coming from gravity extensions. Such a feature can constitute both a probe for alternative theories and a way out to address anomalous self-gravitating compact systems.