Role of a "Local" Cosmological Constant in Euclidean Quantum Gravity

TL;DR

This paper investigates how adding a local term to the gravitational action in Euclidean quantum gravity influences the collapse phase and damping of lattice excitations, with implications for coupling to external Bose condensates.

Contribution

It introduces and analyzes a local volume-dependent term in the gravitational action, exploring its effects on the phase structure and excitations in Euclidean quantum gravity.

Findings

Local term induces collapse of certain volumes.

Damps propagating lattice excitations.

Potential coupling to Bose condensates.

Abstract

In 4D non-perturbative Regge calculus a positive value of the effective cosmological constant characterizes the collapsed phase of the system. If a local term of the form $S'=\sum_{h \epsilon \{h_1,h_2,...\} } \lambda_h V_h$ is added to the gravitational action, where $\{h_1,h_2,...\}$ is a subset of the hinges and $\{\lambda_h\}$ are positive constants, one expects that the volumes $V_{h_1}$, $V_{h_2}$, ... tend to collapse and that the excitations of the lattice propagating through the hinges $\{h_1,h_2,...\}$ are damped. We study the continuum analogue of this effect. The additional term $S'$ may represent the coupling of the gravitational field to an external Bose condensate.