From neutron stars to quark stars in mimetic gravity

Realistic models of neutron and quark stars in the framework of mimetic gravity with a Lagrange multiplier constraint are presented. We discuss the effect of a mimetic scalar aiming to describe dark matter on the 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 the mimetic scalar in the center of the star. This fact leads to the ambiguity in the mass-radius relation for a given equation of state. Such ambiguity allows us to explain some observational facts better than in standard general relativity. The case of mimetic potential V(phi) similar to Ae(C phi 2) is considered in detail. The relative deviation of the maximal moment of inertia is approximately twice as large as the relative deviation of the 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 the increase of maximal mass and maximal moment of inertia due to the mimetic scalar becomes much stronger with bigger parameter a. The influence of the scalar field in mimetic gravity can lead to the possible existence of extreme neutron stars with large masses.