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

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 ≤ 1. 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.

Random statistics of OPE coefficients and Euclidean wormholes

“…Similar observations related to connected contribution have been made in JT gravity [32]. Unfortunately, no wormhole solution of AdS 3 gravity exists with torus boundaries, leaving the explanation of this contribution as a puzzle.…”

Is the present acceleration of the Universe caused by merging with other universes?

“…It should be noted that ideas somewhat related to the ones presented here and in[1][2][3][4][5][6][7] have also been advocated in[8].…”

“…We will now include matter in the most simple way, as a matter density ρ m (v) in the Hamiltonian (2.8). 8 In addition we will only consider relatively late times in the evolution of our universe, namely the period after the time of last scattering (t LS ), where matter to a good approximation can be considered as dust that exerts zero pressure. Thus the Hamiltonian has the form…”

Type V singularities in non-standard cosmological backgrounds

“…1 for more works on baby universes [40][41][42][43][44][45][46][47][48][49][50][51] Here, Ĥ(0) describes the quantum Hamiltonian corresponding to the action (1) (with β = 2/3), portraying the propagation of a single universe and note that we are taking g > 0 in our work 2 . The two cubic terms describe the splitting of a universe into two and the merging of two universes into one, respectively.…”