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We study the classic hybrid inflation model in its original and modified forms and show the shape of the inflationary potentials and analyze the amount of primordial gravitational waves each model predicts. We compare the resulting EE-mode and BB-mode power spectrum with the data from the joint BICEP2/Keck and Planck collaboration to check the viability of each model.

The evolution of inflationary primordial gravitational waves with the expansion of the universe is studied while taking into account the $$e^+e^-$$ e + e - annihilation which leads to step correction in the spectrum of primordial gravitational waves which is $$\sim 10\%$$ ∼ 10 % in the amplitude and $$\sim 25\%$$ ∼ 25 % in the energy density. The amplitudes and energy densities are studied for the $$\alpha $$ α -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.

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