# Hyperbolic vacuum decay

## TL;DR

This paper investigates hyperbolically expanding wormholes, deriving their equations of motion and analyzing their properties within de Sitter space, revealing a Planck-scale cosmological constant hidden at tiny scales.

## Contribution

It introduces a specific equation of state for wormhole throats leading to constant surface energy density and connects the wormhole dynamics to a relativistic free particle Hamiltonian.

## Key findings

- The surface energy density of the wormhole remains constant.
- The cosmological constant is of Planck order but hidden at small scales.
- The wormhole's dynamics relate to a relativistic free particle Hamiltonian.

## Abstract

The properties of an hyperbolically-expanding wormhole are studied. Using a particular equation of state for the fluid on the wormhole throat, we reached an equation of motion for the throat that leads to a constant surface energy density $\sigma$. The Lagrangean leading to the above equation of motion contains the "rest mass" of the expanding particle as a potential energy. The associated Hamiltonian corresponds to a relativistic free particle of a total Planck energy $E_{P}$. When the wormhole is embedded in de Sitter space, we found that the cosmological constant is of Planck order of magnitude but hidden at very tiny scales, in accordance with Carlip's recipe.