Why is TeV-scale a geometric mean of neutrino mass and GUT-scale?

Among three typical energy scales, a neutrino mass scale ($m_\nu\sim$ 0.1 eV), a GUT scale ($M_{GUT}\sim 10^{16}$ GeV), and a TeV-scale ($M_{NP}\sim 1$ TeV), there is a fascinating relation of $M_{NP}\simeq \sqrt{m_\nu\cdot M_{GUT}}$. The TeV-scale, $M_{NP}$, is a new physics scale beyond the standard model which is regarded as supersymmetry in this letter. We suggest a simple supersymmetric neutrinophilic Higgs doublet model, which realizes the above relation dynamically as well as the suitable $m_\nu$ through a tiny vacuum expectation value of neutrinophilic Higgs without additional scales other than $M_{NP}$ and $M_{GUT}$. A gauge coupling unification, which is an excellent feature in the supersymmetric standard model, is preserved automatically in this setup.Comment: 7 page

Dark Energy from Mass Varying Neutrinos

We show that mass varying neutrinos (MaVaNs) can behave as a negative pressure fluid which could be the origin of the cosmic acceleration. We derive a model independent relation between the neutrino mass and the equation of state parameter of the neutrino dark energy, which is applicable for general theories of mass varying particles. The neutrino mass depends on the local neutrino density and the observed neutrino mass can exceed the cosmological bound on a constant neutrino mass. We discuss microscopic realizations of the MaVaN acceleration scenario, which involve a sterile neutrino. We consider naturalness constraints for mass varying particles, and find that both ev cutoffs and ev mass particles are needed to avoid fine-tuning. These considerations give a (current) mass of order an eV for the sterile neutrino in microscopic realizations, which could be detectable at MiniBooNE. Because the sterile neutrino was much heavier at earlier times, constraints from big bang nucleosynthesis on additional states are not problematic. We consider regions of high neutrino density and find that the most likely place today to find neutrino masses which are significantly different from the neutrino masses in our solar system is in a supernova. The possibility of different neutrino mass in different regions of the galaxy and the local group could be significant for Z-burst models of ultra-high energy cosmic rays. We also consider the cosmology of and the constraints on the ``acceleron'', the scalar field which is responsible for the varying neutrino mass, and briefly discuss neutrino density dependent variations in other constants, such as the fine structure constant.Comment: 26 pages, 3 figures, refs added, typos corrected, comment added about possible matter effect