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.