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 Σ, as |Σ(Tf)| < or approx. 0.4, where Tf 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.