Electrocardiogram of the Mixmaster Universe

TL;DR

This paper introduces a novel gauge-invariant scalar measure called the speciality index to analyze Mixmaster universe dynamics, revealing a pattern akin to an electrocardiogram that captures curvature transitions and spike solutions in inhomogeneous cosmology.

Contribution

It presents the speciality index as a new gauge-invariant tool to study Mixmaster universe dynamics and inhomogeneous cosmological features, providing a clearer understanding of curvature transitions.

Findings

Speciality index graph shows pulse patterns corresponding to curvature wall collisions.

Pulse pairs in the index serve as invariant markers of spike solutions.

The approach offers a gauge-invariant perspective on complex cosmological dynamics.

Abstract

The Mixmaster dynamics is revisited in a new light as revealing a series of transitions in the complex scale invariant scalar invariant of the Weyl curvature tensor best represented by the speciality index $\mathcal{S}$, which gives a 4-dimensional measure of the evolution of the spacetime independent of all the 3-dimensional gauge-dependent variables except for the time used to parametrize it. Its graph versus time characterized by correlated isolated pulses in its real and imaginary parts corresponding to curvature wall collisions serves as a sort of electrocardiogram of the Mixmaster universe, with each such pulse pair arising from a single circuit or ``complex pulse'' around the origin in the complex plane. These pulses in the speciality index and their limiting points on the real axis seem to invariantly characterize some of the so called spike solutions in inhomogeneous cosmology and should play an important role as a gauge invariant lens through which to view current investigations of inhomogeneous Mixmaster dynamics.