Local duality for equitable partitions of a Hamming space

AbstractThe Hamming space Qn is the set of binary words of length n. A partition (C1,C2,…,Cr) of Qn with quotient matrix B=[bij]r×r is equitable if for all i and j, any word in the cell Ci has exactly bij neighbors in the cell Cj. In this paper, we provide an explicit formula relating the local spectrum of cells in the face to that in the orthogonal face

Inflaton Dark Matter

Publisher Copyright: © Copyright owned by the author(s) under the terms of the Creative Commons.We discuss a minimal extension of the Standard Model (SM) where a single real scalar field serves as both inflaton and dark matter. The corresponding Lagrangian contains the renormalizable interactions of the inflaton field. Quantum effects generally induce a non-minimal coupling to gravity which facilitates inflation consistent with the PLANCK constraints. A large fraction of the inflaton quanta produced after inflation must be converted into the SM radiation reheating the Universe and the rest remains dark matter today. We consider thermal and non-thermal production of inflaton dark matter. In the non-thermal case, we take into account collective effects with the help of lattice simulations. Combining analytic and numerical results with the unitarity consideration, we find that the inflaton dark matter model is viable only in the thermal case where the inflaton mass is near half the Higgs mass.Peer reviewe