QUANTUM-GRAVITY, THE ORIGIN OF TIME AND TIMES ARROW

The local Lorentz and diffeomorphism symmetries of Einstein's gravitat ional theory are spontaneously broken by a Higgs mechanism by invoking a phase transition in the early universe, at a critical temperature T (c) below which the symmetry is restored The spontaneous breakdown of the vacuum state generates an external time, and the wave function of the universe satisfies a time-dependent Schrodinger equation, which re duces to the Wheeler-de Witt equation in the classical regime for T < T(c) allowing a semiclassical WKB approximation to the wave function. The conservation of energy is spontaneously violated for T > T(c), and matter is created fractions of seconds after the big bang, generating the matter in the Universe. The time direction of the vacuum expectat ion value of the scalar Higgs field generates a time asymmetry, which defines the cosmological arrow of time and the direction of increasing entropy as the Lorentz symmetry is restored at low temperatures.