Double Higgs mechanisms, supermassive stable particles and the vacuum energy

In the present work it is shown that some specific double Higgs like mechanisms may have interesting cosmological applications. A hidden scenario which cast long lived super heavy particles together with an extremely light particle $a$ with mass $m_a\sim 10^{-32}-10^{-33}$eV is presented. The potential energy of this particle models the vacuum energy density of the universe $\rho_c\simeq 10^{-47}\;\hbox{GeV}^4$. The construction of such scenario is non trivial since the presence of light particles may spoil the stability of the heavy particles. However, double Higgs mechanisms may be helpful for overcoming this problem. The hidden sector we propose include fermions with masses near the neutrino mass $m_\nu\sim 10^{-2}$eV which arise in terms of a see saw mechanism. Besides, the super heavy particles acquire a mass due to a double Higgs like mechanism of the order of the GUT scale. The gauge group of the model is $\hbox{SU(2)}_L$ and the scalars of the double Higgs mechanism are not charged under these interactions. The light particle $a$ is the Goldstone boson associated to a Peccei-Quinn like symmetry in the double Higgs model. In addition, the double Higgs mechanism posses another CP odd scalar $A^0$, which acquire a mass of the order of the GUT scale. We show that if there is no direct coupling between $A^0$ and $a$, even in presence of indirect couplings, the $A^0$ particle is long lived an may appear in events above the GKZ bound in present times.