Baby universes in 2d and 4d theories of quantum gravity

TL;DR

This paper investigates the Coleman mechanism in quantum gravity, showing it is ineffective in 2D models but potentially effective in 4D Lorentzian gravity, leading to a near-zero cosmological constant.

Contribution

It provides a detailed analysis of baby universe contributions in 2D quantum gravity and introduces a non-Hermitian Hamiltonian model in 4D Lorentzian gravity supporting the Coleman mechanism.

Findings

Baby universes are too small to realize the Coleman mechanism in 2D.

The 4D Lorentzian gravity model supports the Coleman mechanism.

The cosmological constant is tuned to nearly zero in the 4D model.

Abstract

The validity of the Coleman mechanism, which automatically tunes the fundamental constants, is examined in two-dimensional and four-dimensional quantum gravity theories. First, we consider two-dimensional Euclidean quantum gravity on orientable closed manifolds coupled to conformal matter of central charge $c \leq1$. The proper time Hamiltonian of this system is known to be written as a field theory of noncritical strings, which can also be viewed as a third quantization in two dimensions. By directly counting the number of random surfaces with various topologies, we find that the contribution of the baby universes is too small to realize the Coleman mechanism. Next, we consider four-dimensional Lorentzian gravity. Based on the difference between the creation of the mother universe from nothing and the annihilation of the mother universe into nothing, we introduce a non-Hermitian effective Hamiltonian for the multiverse. We show that Coleman's idea is satisfied in this model and that the cosmological constant is tuned to be nearly zero. Potential implications for phenomenology are also discussed.