Recent advances in the three flavor Larkin-Ovchinnikov-Fulde-Ferrel phase of QCD

We present a summary of the recent advances achieved in the study of three flavor Larkin-Ovchinnikov-Fulde-Ferrell (LOFF)phase of QCD. We have explored, using a Ginzburg-Landau expansion of the free energy, the LOFF phase with three flavors, in the simplest single plane wave structure, using the NJL four-fermion coupling. We have found that this phase does not suffer the chromo-magnetic instability problem. A preliminary study of astrophysical effects of quark matter in the aforementioned phase has been done and we have evaluated self-consistently the strange quark mass extending the pairing ansatz to the CubeX and 2Cube45z structure. Finally we have investigated the possibility of Goldstone bosons condensation in the favored cubic structures of LOFF phase.