Helium-4 Synthesis in an Anisotropic Universe
  We calculate the 4He abundance in a universe of Bianchi type I whose cosmic
anisotropy is dynamically generated by a fluid with anisotropic equation of
state. Requiring that the relative variation of mass fraction of 4He is less
than 4% with respect to the standard isotropic case to be consistent with
astrophysical data, we constrain the parameter of cosmic anisotropy, the shear
\Sigma, as |\Sigma(T_f)| < 0.4, where T_f is the freeze-out temperature of the
weak interactions that interconvert neutrons and protons. Anisotropic fluids,
whose energy density is subdominant with respect to the energy content of the
Universe during inflation and radiation era, generate much smaller shears at
the time of freeze-out and then do not appreciably affect the standard 4He
production. This is the case of anisotropic dark energy, and of a uniform
magnetic field with energy density much smaller than about 1.25 times the
energy density of neutrinos.
