# Interacting vacuum at infinity

## TL;DR

This paper investigates the dynamics of a pressureless matter and vacuum mixture near a finite-time singularity, revealing that the only stable solution at infinity is a model with vanishing matter and vacuum at early times.

## Contribution

It applies the Poincare central extension technique to analyze the asymptotic behavior of matter-vacuum interactions near singularities, identifying the attractor solution.

## Key findings

- The attractor corresponds to a vanishing matter-vacuum model at early times.
- The analysis uses the Poincare central extension method.
- The solution describes the dynamics near a finite-time singularity.

## Abstract

We apply the central extension technique of Poincare to dynamics involving an interacting mixture of pressureless matter and vacuum near a finite-time singularity. We show that the only attractor solution on the circle of infinity is the one describing a vanishing matter-vacuum model at early times