Tying Knots in Particle Physics

Knots emerge in various fields of mathematics and physics today. We show that knots indeed appear as stable solitons in a realistic extension of the standard model of particle physics that provides the QCD axion and right-handed neutrinos. This result suggests that, during the early Universe, a "knot dominated era" may have existed, where knots were a dominant component of the Universe, and this scenario can be tested through gravitational wave observations. Furthermore, we propose that the end of this era involves the collapse of the knots via quantum tunneling, leading to the generation of matter-antimatter asymmetry in the Universe.