Some remarks on neutrino oscillation and masses

We discuss an Ansatz for the neutrino mixing matrix and speculate on the form and origin of the neutrino mass matrix.Comment: Latex 9 pages, Talk presented at the neutrino conference held in Palm Cove, Australia, June 200

Dark Energy and the Nature of the Graviton

Does the existence of dark energy suggest that there is more to the graviton than we think we know?Comment: 4 page

Message in the Sky

We argue that the cosmic microwave background (CMB) provides a stupendous opportunity for the Creator of universe our (assuming one exists) to have sent a message to its occupants, using known physics. Our work does not support the Intelligent Design movement in any way whatsoever, but asks, and attempts to answer, the entirely scientific question of what the medium and message might be IF there was actually a message. The medium for the message is unique. We elaborate on this observation, noting that it requires only careful adjustment of the fundamental Lagrangian, but no direct intervention in the subsequent evolution of the universe.Comment: 3 pages, revtex; to appear in Mod.Phys.Lett.

Generalized Supersymmetric Quantum Mechanics and Reflectionless Fermion Bags in 1+1 Dimensions

We study static fermion bags in the 1+1 dimensional Gross-Neveu and Nambu-Jona-Lasinio models. It has been known, from the work of Dashen, Hasslacher and Neveu (DHN), followed by Shei's work, in the 1970's, that the self-consistent static fermion bags in these models are reflectionless. The works of DHN and of Shei were based on inverse scattering theory. Several years ago, we offered an alternative argument to establish the reflectionless nature of these fermion bags, which was based on analysis of the spatial asymptotic behavior of the resolvent of the Dirac operator in the background of a static bag, subjected to the appropriate boundary conditions. We also calculated the masses of fermion bags based on the resolvent and the Gelfand-Dikii identity. Based on arguments taken from a certain generalized one dimensional supersymmetric quantum mechanics, which underlies the spectral theory of these Dirac operators, we now realize that our analysis of the asymptotic behavior of the resolvent was incomplete. We offer here a critique of our asymptotic argument.Comment: 33 pages, 2 figure

A speculative relation between the cosmological constant and the Planck mass

We propose the relation $M_\Lambda \sim (M_{Pl} M_U)^{1/2}$ where $M_\Lambda$, $M_{Pl},$ and $M_U$ denote the mass scale associated with the cosmological constant, the gravitational interaction, and the size of the universe respectively.Comment: 3 page

The quantization of unimodular gravity and the cosmological constant problem

A quantization of unimodular gravity is described, which results in a quantum effective action which is also unimodular, ie a function of a metric with fixed determinant. A consequence is that contributions to the energy momentum tensor of the form of the metric times a spacetime constant, whether classical or quantum, are not sources of curvature in the equations of motion derived from the quantum effective action. This solves the first cosmological constant problem, which is suppressing the enormous contributions to the cosmological constant coming from quantum corrections. We discuss several forms of uniodular gravity and put two of them, including one proposed by Henneaux and Teitelboim, in constrained Hamiltonian form. The path integral is constructed from the latter. Furthermore, the second cosmological constant problem, which is why the measured value is so small, is also addressed by this theory. We argue that a mechanism first proposed by Ng and van Dam for suppressing the cosmological constant by quantum effects obtains at the semiclassical level.Comment: 22 pages, no figure