Primordial Magnetic Helicity from Stochastic Electric Currents
  We study the possibility that primordial magnetic fields generated in the
transition between inflation and reheating posses magnetic helicity, $H_M$. The
fields are induced by stochastic currents of scalar charged particles created
during the mentioned transition. We estimate the rms value of the induced
magnetic helicity by computing different four-point SQED Feynman diagrams. For
any considered volume, the magnetic flux across its boundaries is in principle
non null, which means that the magnetic helicity in those regions is gauge
dependent. We use the prescription given by Berger and Field and interpret our
result as the difference between two magnetic configurations that coincide in
the exterior volume. In this case the magnetic helicity gives only the number
of magnetic links inside the considered volume. We calculate a concrete value
of $H_M$ for large scales and analyze the distribution of magnetic defects as a
function of the scale. Those defects correspond to regular as well as random
fields in the considered volume. We find that the fractal dimension of the
distribution of topological defects is $D = 1/2$. We also study if the regular
fields induced on large scales are helical, finding that they are and that the
associated number of magnetic defects is independent of the scale. In this case
the fractal dimension is $D=0$. We finally estimate the intensity of fields
induced at the horizon scale of reheating, and evolve them until the decoupling
of matter and radiation under the hypothesis of inverse cascade of magnetic
helicity. The resulting intensity is high enough and the coherence length long
enough to have an impact on the subsequent process of structure formation.
