A note on the vacuum structure of lattice Euclidean quantum gravity: ‘birth’ of macroscopic space-time and <i>PT</i> -symmetry breaking
S. N. Vergeles
Abstract
Abstract It is shown that the ground state or vacuum of the lattice quantum gravity is significantly different from the ground states of the well-known vacua in QED, QCD, et cetera. In the case of the lattice quantum gravity, the long-wavelength scale vacuum structure is similar to that in QED, moreover the quantum fluctuations of gravitational degrees of freedom are very reduced in comparison with the situation in QED. But the small scale (of the order of the lattice scale) vacuum structure in gravity is significantly different from that in the long-wavelength scales: the fluctuation values of geometrical degrees of freedom (tetrads) are commensurable with theirs most probable values. It is also shown that the macroscopic Universe can exist only in the presence of fermion fields. In this case, spontaneous breaking of the PT symmetry occurs.