With the increasing number of precise observation of neutron stars and their collisions their understanding requires accurate determination of the equation of state of the high density strongly interacting matter which is constrained by heavy ion collisions, too. We would like to use effective field theory using loop expansion and/or functional renormalization group method to determine the equation of state. The effective field theory should fulfill the symmetry requirements like chiral symmetry, and  the low-energy nuclear physics constraints like the binding energy and normal nuclear matter density. During the PhD the candidate should derive the equation of state of the strongly interacting matter and determine the structure of neutron stars, fulfilling the available astrophyisical data like tidal deformability, and radius mass constraints by the NICER analysis.