Magnetic reheating
  We provide a new bound on the amplitude of primordial magnetic fields (PMFs)
by using a novel mechanism, named {\it magnetic reheating}. Before the epoch of
recombination, PMFs induce the fluid motions in a photon-baryon plasma through
the Lorentz force. Due to the viscosity in the plasma, such induced fluid
motions would be damped and this means the dissipation of PMFs. In the early
Universe with $z \gtrsim 2 \times 10^6$, cosmic microwave background (CMB)
photons are quickly thermalized with the dissipated energy and shift to a
different Planck distribution with a new temperature. In other words, the
energy injection due to the dissipation of PMFs changes the baryon-photon
number ratio during this era and we name such a process {\it magnetic
reheating}. By using the current results of the baryon-photon number ratio
obtained from the Big Bang nucleosynthesis and CMB observations, we put a
strongest constraint on the amplitude of PMFs on small scales which we can not
access through CMB anisotropy and CMB distortions, $B_{0} \lesssim 1.0 \;
\mu{\rm G}$ at the scales $10^{4} \; h{\rm Mpc}^{-1} < k < 10^{8} \; h{\rm
Mpc}^{-1}$. Moreover, when the spectrum of PMFs is given by the power-law, the
magnetic reheating puts a quite strong constraint in the case of the
blue-tilted spectrum, for example, $B_0 \lesssim 10^{-17} \;{\rm nG}$,
$10^{-23} \;{\rm nG}$, and $10^{-29} \;{\rm nG}$ at 1~comoving Mpc for
$n_{B}=1.0$, $2.0$, and $3.0$, respectively. This constraint would give an
impact on generation mechanisms of PMFs in the early Universe.
