Properties of potential modelling three benchmarks: the cosmological constant, inflation and three generations

Abstract

We argue for a model of low-energy correction to the inflationary potential as caused by the gauge-mediated breaking down the supersymmetry at the scale of $\mu_\textsc{x}\sim 10^4$ GeV, that provides us with the seesaw mechanism of thin domain wall fluctuations in the flat vacuum. The fluctuations are responsible for the vacuum with the cosmological constant at the scale of $\mu_\Lambda\sim 10^{-2}$ eV suppressed by the Planckian mass $m_\mathtt{Pl}$ via $\mu_\Lambda\sim\mu_\textsc{x}^2/m_\mathtt{Pl}$. The appropriate vacuum state is occupied after the inflation with quartic coupling constant $\lambda\sim\mu_\textsc{x}/m_\mathtt{Pl}\sim 10^{-14}$ inherently related with the bare mass scale of $\widetilde m\sim\sqrt{\mu_\textsc{x}m_\mathtt{Pl}}\sim 10^{12}$ GeV determining the thickness of domain walls $\delta r\sim1/\widetilde m$. Such the parameters of potential are still marginally consistent with the observed inhomogeneity of matter density in the Universe. The inflationary evolution suggests the vacuum structure compatible with three fermionic generations of matter as well as with observed hierarchies of masses and mixing in the Standard Model.