Generating Seed magnetic field \`a la Chiral Biermann battery
  Cosmological and astrophysical observations indicate the presence of magnetic
field over all scales. In order to explain these magnetic fields, it is assumed
that there exists a seed magnetic field that gets amplified by dynamos. These
seed fields may have been produced during inflation, at phase transitions, or
some turbulent phase of the early universe. One well-known mechanism to get the
seed field is the Biermann battery, which was originally discussed in the
context of generation in an astrophysical object. Requirements for this
mechanism to work are (i) non-zero gradient of the electron number density and
pressure, (ii) they are non-parallel to each other. In the present article, we
propose a similar mechanism to generate the seed field but in inhomogeneous
chiral plasma. Our mechanism works, in presence of chiral anomaly, by the
virtue of inhomogeneity in the chiral chemical potential and temperature. We
will discuss various scenarios where inhomogeneities in the chemical potential
and temperature can arise. We found that, depending on the epoch of generation,
the strength of the seed magnetic fields varies from a few nano-Gauss (nG) to a
few hundred nG.
