e^+e^- annihilation on the stochastic background of primordial gravitational waves with BKP18

The evolution of inflationary primordial gravitational waves with the expansion of the universe is studied while taking into account the $e^+e^-$ annihilation which leads to step correction in the spectrum of primordial gravitational waves which is $\sim 10\%$ in the amplitude and $\sim 25\%$ in the energy density. The amplitudes and energy densities are studied for the $\alpha$-attractor inflation models which are in agreement with the recent BICEP/Keck and Planck 2018 joint result. The energy densities are well within the big bang nucleosynthesis bound, but the spectra for these models are very much below the detection range of the currently operating and upcoming detectors.