Ji-Hoon Ha

We investigate whether stochastic acceleration associated with pressure-anisotropy-driven magnetogenesis can generate a dynamically significant population of cosmic rays (CRs) prior to nonlinear structure formation. As magnetic fields amplify in the early Universe, the associated increase in gyrofrequency enhances pitch-angle scattering, potentially shortening the stochastic acceleration time. We derive an analytic criterion for efficient cosmological acceleration by comparing the acceleration timescale with the Hubble time, which defines a critical magnetic field and a corresponding CR turn-on redshift $z_{\rm on}$. For representative parameters, we find $z_{\rm on}\sim1.7$. To quantify the resulting particle population, we solve a Fokker-Planck equation for the isotropic proton distribution in the redshift interval $z=10\rightarrow z_{\rm on}$. Throughout most of this epoch, adiabatic expansion dominates over stochastic energization and the distribution remains close to a cooling Maxwellian. However, as the system approaches the turn-on epoch, the stochastic acceleration time decreases, allowing a mild suprathermal tail to develop. Even under optimistic assumptions corresponding to the strong-scattering limit, the maximum attainable proton energy reaches at most $\mathcal{O}(10^2)\,\mathrm{GeV}$. These results indicate that efficient CR production in the intergalactic medium is intrinsically tied to the onset of structure-formation shocks, while earlier microinstability-driven stochastic processes can provide at most a modest pre-acceleration.