Maximal neutron star mass and the resolution of the hyperon puzzle in modified gravity

The so-called ``hyperon puzzle'' in the theory of neutron stars is considered in the framework of modified $f(R)$ gravity. We show that for simple hyperon equations of state, it is possible to obtain the maximal neutron star mass which satisfies the recent observational data for PSR J1614-2230, in higher-derivative models with power-law terms as $f(R)=R+\ensuremath{\gamma}{R}^{2}+\ensuremath{\beta}{R}^{3}$. The soft hyperon equation of state under consideration is usually treated as unrealistic in the standard general relativity. The numerical analysis of the mass-radius relation for massive neutron stars with a hyperon equation of state in modified gravity turns out to be consistent with observations. Thus, we show that the same modified gravity can solve at once three problems: a consistent description of the maximal mass of a neutron star, a realistic mass-radius relation, and a method to account for hyperons in the equation of state.