Baby universe, third quantization and the cosmological constant

Abstract

A general third-quantized framework for a system of interacting universes is described. The third-quantized fields create and annihilate second-quantized single-universe states, and are equivalent to second-quantized spacetime coupling constants. This implies that the spacetime couplings obey dynamical equations. A direct consequence of this is that the spacetime coupling constants are in general subject to uncertainty relations. A concrete illustration of these facts is given using the semiclassical instanton approximation to a theory of gravity coupled to axions. The field theory action is explicitly constructed and the dynamical equation for the long distance axion potential thereby derived. The equation implies that the potential has a minimum with vanishing effective cosmological constant.