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

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