Gravity's Rainbow induces Topology Change

TL;DR

This paper investigates how quantum fluctuations within Gravity's Rainbow framework can induce topology change, potentially leading to a Planck-scale wormhole through a semi-classical analysis involving graviton one-loop contributions.

Contribution

It introduces a novel semi-classical approach to demonstrate that quantum fluctuations can cause topology change, resulting in a Planckian wormhole in Gravity's Rainbow.

Findings

Quantum fluctuations induce a natural UV cutoff.

The cutoff prevents an interior spacetime region, suggesting topology change.

A multipy-connected spacetime or wormhole may form at Planck scale.

Abstract

In this work, we explore the possibility that quantum fluctuations induce a topology change, in the context of Gravity's Rainbow. A semi-classical approach is adopted, where the graviton one-loop contribution to a classical energy in a background spacetime is computed through a variational approach with Gaussian trial wave functionals. The energy density of the graviton one-loop contribution, or equivalently the background spacetime, is then let to evolve, and consequently the classical energy is determined. More specifically, the background metric is fixed to be Minkowskian in the equation governing the quantum fluctuations, which behaves essentially as a backreaction equation, and the quantum fluctuations are let to evolve; the classical energy, which depends on the evolved metric functions, is then evaluated. Analysing this procedure, a natural ultraviolet (UV) cutoff is obtained, which forbids the presence of an interior spacetime region, and may result in a multipy-connected spacetime. Thus, in the context of Gravity's Rainbow, this process may be interpreted as a change in topology, and in principle results in the presence of a Planckian wormhole.