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This work is devoted to the construction of slowly rotating neutron stars inthe framework of the nonminimal derivative coupling sector of Horndeski theory.We match the large radius expansion of spherically symmetric solutions withcosmological solutions and we find that the most viable model has only one freeparameter. Then, by using several tabulated and realistic equations of state,we establish numerically the upper bound for this parameter in order toconstruct neutron stars in the slow rotation approximation with the maximalmass observed today. We finally study the surface redshift and the inertia ofthese objects and compare them with known data.

Slowly rotating neutron stars in the nonminimal derivative coupling sector of Horndeski gravity