Antipodal correlation on the meron wormhole and a bang-crunch universe

TL;DR

This paper introduces a covariant Euclidean wormhole solution in Einstein-Yang-Mills theory, analyzes scalar perturbations, and explores the antipodal correlations and their implications in a bang-crunch universe.

Contribution

It provides a novel covariant Euclidean wormhole solution and analyzes its scalar perturbations and antipodal correlations in a bang-crunch universe context.

Findings

Positive definite spectrum of fluctuation operator

Maximal antipodal correlation on the three sphere

Connection between Euclidean and Lorentzian geometries

Abstract

We present a covariant euclidean wormhole solution to Einstein Yang-Mills system and study scalar perturbations analytically. The fluctuation operator has a positive definite spectrum. We compute the Euclidean Green's function, which displays maximal antipodal correlation on the smallest three sphere. Upon analytic continuation, it corresponds to the Feynman propagator on a compact bang-crunch universe. We present the connection matrix that relates past and future modes. We thoroughly discuss the physical implications of the antipodal map in both the Euclidean and Lorentzian geometries.