Primordial magnetic fields and formation of molecular hydrogen

We study the implications of primordial magnetic fields for the thermal and ionization history of the post-recombination era. In particular we compute the effects of dissipation of primordial magnetic fields owing to ambipolar diffusion and decaying turbulence in the intergalactic medium (IGM) and the collapsing halos and compute the effects of the altered thermal and ionization history on the formation of molecular hydrogen. We show that, for magnetic field strengths in the range $2 \times 10^{-10} {\rm G} \la B_0 \la 2 \times 10^{-9} {\rm G}$, the molecular hydrogen fraction in IGM and collapsing halo can increase by a factor 5 to 1000 over the case with no magnetic fields. We discuss the implication of the increased molecular hydrogen fraction on the radiative transfer of UV photons and the formation of first structures in the universe.