Sen, SrimoyeeThis dissertation explores the properties of neutron matter for baryon chemi- cal potential of the order of a hundred MeV in the context of neutron star interior. Neutron stars are known to be cold (< 10^9 K) dense objects composed mostly of neutrons with densities of the outer core reaching 1013 g/cc to 1014 g/cc. For such densities neutron matter is speculated to form a superfluid condensate in the triplet channel of angular momentum. The implication of this superfluidity for the transport properties of the core of a neutron star is dramatic as the neutrons get gapped leading to a Boltzmann suppression in most observables at low temperature and the low energy properties of the system is dictated by ungapped low energy modes. The first part of the thesis discusses the effective theory of the low energy modes of triplet neutron matter. We also derive the masses of the slightly high lying massive modes as a function of temperature. This is followed by a calculation of neutrino emissivity of the Goldstone modes in the presence of realistic magnetic fields in magnetars.enDissertationTheoretical physicsFInite densityNeutron star