We discuss physics of exotic high baryon density QCD phases which are believed to exist in the core of a neutron star. This can provide a laboratory for exploring exotic physics such as axion emission, KK graviton production etc.Much of the physics of these high-density phases is model-dependent and not very well understood, especially the densities expected to occur inside neutron stars. We follow a different approach and use primarily universal aspects of the physics of different high-density phases and associated phase transitions. We study effectsof density fluctuations during transitions with and without topological defect production and study the effect on pulsar timings due to changing moment of inertia of the star. We also discuss gravitational wave production due to rapidly changing quadrupole moment of the star due to these fluctuations.