Effects of the Axion Through the Higgs Portal on Primordial Gravitational Waves During the Electroweak Breaking

We investigate the effects of short axion kination eras on the energy spectrum of the primordial gravitational waves corresponding to modes that re-enter the Hubble horizon at the post-electroweak symmetry breaking epoch, well within the radiation domination era. Our main assumption is the existence of an extremely weakly coupled hidden sector between the Higgs and the axion, materialized by higher order non-renormalizable dimension six and dimension eight operators, active at a scale M of the order 20-100TeV. This new physics scale M which is way higher than the electroweak scale, is motivated by the lack of new particle observations in the large hadron collider to date, beyond the electroweak scale. Once the electroweak symmetry breaking occurs at T\sim 100 GeV, the axion potential acquires a new minimum due to the new terms generated by the electroweak breaking, and the axion oscillations at the origin are destabilized. In effect after some considerable amount of time, the axion rolls swiftly to its new minimum, experiencing a short kination epoch, where its energy density redshifts as $\rho_a\sim a^{-6}$. After it reaches the new minimum, since the latter is energetically less favorable that the Higgs minimum, it decays to the Higgs minimum and the Universe is described again by the Higgs minimum. The axion returns to the origin and commences again oscillations initiated by quantum fluctuations, redshifts as dark matter, and the same procedure is repeated perpetually. These short axion kination eras may disturb the background total equation of state parameter during the radiation domination era. As we show, the energy spectrum of the gravitational waves mainly depends on how many times the short axion kination epochs occur.