Horizon crossing causes baryogenesis, magnetogenesis and dark-matter acoustic wave

Sapcetime ${mathcal S}$ produces massive particle-antiparticle pairs $bar F F$ that in turn annihilate to spacetime. Such back and forth gravitational process ${mathcal S}Leftrightarrow bar F F$ is described by Boltzmann-type cosmic rate equation of pair-number conservation. This cosmic rate equation, Einstein equation, and the reheating equation of pairs decay to relativistic particles completely determine the horizon $H$, cosmological energy density, massive pair and radiation energy densities in reheating epoch. Moreover, oscillating ${mathcal S}Leftrightarrow bar F F$ process leads to the acoustic perturbations of massive particle-antiparticle symmetric and asymmetric densities. We derive wave equations for these perturbations and find frequencies of lowest lying modes. Comparing their wavelengths with horizon variation, we show their subhorion crossing at preheating, and superhorizon crossing at reheating. The superhorizon crossing of particle-antiparticle asymmetric perturbations accounts for the baryogenesis of net baryon numbers, whose electric currents lead to magnetogenesis. The baryon number-to-entropy ratio, upper and lower limits of primeval magnetic fields are computed in accordance with observations. Given a pivot comoving wavelength, it is shown that these perturbations, as dark-matter acoustic waves, originate in pre-inflation and return back to the horizon after the recombination, possibly leaving imprints on the matter power spectrum at large length scales. Due to the Jeans instability, tiny pair-density acoustic perturbations in superhorizon can be amplified to the order of unity. Thus their amplitudes at reentry horizon become non-linear and maintain approximately constant physical sizes, and have physical influences on the formation of large scale structure and galaxies.