Future asymptotics of tilted Bianchi type II cosmologies

TL;DR

This paper analyzes the long-term behavior of tilted Bianchi type II cosmological models using Hamiltonian methods, establishing a comprehensive description of their future asymptotic states and introducing new monotone functions.

Contribution

It introduces a novel set of monotone functions for tilted Bianchi type II models and proves a complete characterization of their future asymptotics.

Findings

Complete description of future asymptotic states for tilted Bianchi type II models

Development of new monotone functions for analyzing cosmological models

Methodology applicable to other tilted perfect fluid cosmologies

Abstract

In this paper we study the future asymptotics of spatially homogeneous Bianchi type II cosmologies with a tilted perfect fluid with a linear equation of state. By means of Hamiltonian methods we first find a monotone function for a special tilted case, which subsequently allows us to construct a new set of monotone functions for the general tilted type II cosmologies. In the context of a new partially gauge invariant dynamical system, this then leads to a proof for a theorem that for the first time gives a complete description of the future asymptotic states of the general tilted Bianchi type II models. The generality of our arguments suggests how one can produce monotone functions that are useful for determining the asymptotics of other tilted perfect fluid cosmologies, as well as for other sources.