New Einstein-Hilbert type action of space-time and matter -Nonlinear-supersymmetric general relativity theory-

Abstract

The geometric argument of the general relativity principle can be carried out on (unstable) Riemann space-time just inspired by nonlinear representation of supersymmetry(NLSUSY), where tangent space is specified by Grassmann degrees of freedom $\psi$ for SL(2,C) besides the ordinary Minkowski one $x^{a}$ for SO(1,3) and gives straightforwardly new Einstein-Hilbert(EH)-type action with global NLSUSY invariance(NLSUSYGR)) equipped with the cosmological term. Due to the NLSUSY nature of space-time NLSUSYGR would collapse(Big Collapse) spontaneously to ordinary E-H action of graviton, NLSUSY action of Nambu-Goldstone fermion $\psi$ and their gravitational interaction. Simultaneously the universal attractive gravitational force would constitute the NG fermion-composites corresponding to the eigenstates of liner-SUSY(LSUSY) super-Poincar\'{e}(sP) symmetry of space-time, which gives a new paradigm for the unification of space-time and matter, which can . bridge naturally the cosmology and the low energy particle physics and provides new insights into unsolved problems of cosmology, SM and mysterious relations between them, e.g. the space-time dimension {\it four}, the origin of SUSY breaking, the dark energy and dark matter, the dark energy density$\sim$( neutrino mass$)^{4}$, the tiny neutrino mass, the three-generations structure of quarks and leptons, the rapid expansion of space-time, the magnitude of bare gauge coupling constant, etc..