Cosmological Helical Hypermagnetic Fields and Baryogenesis

Abstract: Recent gamma-ray observations of TeV blazars exhibits the deficits of the secondary GeV cascade photons. This suggests the existence of the intergalactic magnetic fields, which may have a primordial origin. One of the mechanisms that can produce primordial magnetic fields is so-called the chiral plasma instability, where the (hyper) magnetic fields are destabilized when a large chiral asymmetry exists in the high-temperature plasma in the early Universe. We argue that such a large chiral asymmetry can be produced through the GUT baryogenesis. Note that the chiral asymmetry is a good conserved quantity at high temperature when the Yukawa interaction is weak enough. We also point out that the generated hypermagnetic fields are maximally helical, and hence baryon and lepton asymmetry is inevitably produced through the chiral anomaly in the Standard Model through $U(1)_Y$ gauge interaction at the electroweak symmetry breaking. Consequently, the magnetic fields suggested by the blazar observations over-produce baryon asymmetry. Thus the chiral plasma instability alone cannot be responsible for the intergalactic magnetic fields but can be responsible for the baryon asymmetry of the Universe. In other words, GUT baryogenesis without $B$-$L$ asymmetry generation is revived as a viable baryogenesis scenario, which otherwise has been thought to suffer from $B$+$L$ washout by sphalerons. This presentation is based on the work [1].