Modern cosmology has been remarkably successful in describing the Universe from a second after the Big Bang until today. However, its physics before that time is still much less certain. It profoundly involves particle theory beyond the Standard Model to explain long-standing puzzles: the origin of the observed matter asymmetry, nature of dark matter, and cosmic inflation. In this talk, I will explain that fractions of a second after the Big Bang, relic SU(2)_R gauge field with its axion can possibly relate and explain these seemingly unrelated pillars of modern cosmology. Moreover, these relics provides a new window into the early Universe in the form of primordial chiral gravitational waves. This mechanism can possibly lead to a new paradigm for particle cosmology, and its smoking gun signature is testable by future CMB missions and laser interferometers.