Cosmological Helical Hypermagnetic Fields and Baryogenesis
  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].
