From neutron stars to quark stars in mimetic gravity

Realistic models of neutron and quark stars in the framework of mimetic gravity with Lagrange multiplier constraint are presented. We discuss the effect of mimetic scalar aiming to describe dark matter on mass-radius relation and the moment of inertia for slowly rotating relativistic stars. The mass-radius relation and moment of inertia depend on the value of mimetic scalar in the center of star. This fact leads to the ambiguity in the mass-radius relation for a given equation of state. {Such ambiguity allows to explain some observational facts better than in standard General Relativity}. The case of two mimetic potentials namely $V(\phi)\sim A\phi^{-2}$ and $V(\phi)\sim Ae^{B\phi^{2}}$ is considered in detail. The relative deviation of maximal moment of inertia is approximately twice larger than the relative deviation of maximal stellar mass. We also briefly discuss the mimetic $f(R)$ gravity. In the case of $f(R)=R+aR^2$ mimetic gravity it is expected that increase of maximal mass and maximal moment of inertia due to mimetic scalar becomes much stronger with bigger parameter $a$. The contribution of scalar field in mimetic gravity can lead to possible existence of extreme neutron stars with large masses.