Macroscopic effect of quantum gravity: graviton, ghost and instanton condensation on horizon scale of the Universe

Abstract

We discuss a special class of quantum gravity phenomena that occur on the scale of the Universe as a whole at any stage of its evolution. These phenomena are a direct consequence of the zero rest mass of gravitons, conformal non-invariance of the graviton field, and one-loop finiteness of quantum gravity. The effects are due to graviton-ghost condensates arising from the interference of quantum coherent states. Each of coherent states is a state of gravitons and ghosts of a wavelength of the order of the horizon scale and of different occupation numbers. The state vector of the Universe is a coherent superposition of vectors of different occupation numbers. To substantiate the reliability of macroscopic quantum effects, the formalism of one-loop quantum gravity is discussed in detail. The theory is constructed as follows: Faddeev-Popov path integral in Hamilton gauge -> factorization of classical and quantum variables, allowing the existence of a self-consistent system of equations for gravitons, ghosts and macroscopic geometry -> transition to the one-loop approximation. The ghost sector corresponding to the Hamilton gauge ensures of one-loop finiteness of the theory off the mass shell. The Bogolyubov-Born-Green-Kirckwood-Yvon (BBGKY) chain for the spectral function of gravitons renormalized by ghosts is used to build a self-consistent theory of gravitons in the isotropic Universe. We found three exact solutions of the equations, consisting of BBGKY chain and macroscopic Einstein's equations. The solutions describe virtual graviton, ghost, and instanton condensates and are reproduced at the level of exact solutions for field operators and state vectors. Each exact solution corresponds to a certain phase state of graviton-ghost substratum. We establish conditions under which a continuous quantum-gravity phase transitions occur between different phases of the graviton-ghost condensate.