# The evolution of the FRW universe with decaying metastable dark energy --- a dynamical system analysis

## TL;DR

This paper explores a cosmological model where dark energy decays from a metastable vacuum into a true vacuum, analyzing its dynamics, thermodynamics, and implications for the universe's evolution using quantum decay theory and dynamical systems methods.

## Contribution

It introduces a novel model of decaying metastable dark energy with quantum decay characteristics and analyzes its cosmological implications through dynamical system techniques.

## Key findings

- Quantum effects modify early Universe temperature evolution.
- Late-time energy behaves as holographic dark energy.
- Multiple evolution scenarios are possible from initial conditions.

## Abstract

We investigate a cosmological model in which dark energy identified with the vacuum energy which is running and decaying. In this model vacuum is metastable and decays into a bare (true) vacuum. This decaying process has a quantum nature and is described by tools of the quantum decay theory of unstable systems. We have found formulas for an asymptotic behavior of the energy density of dark energy in the form of a series of inverse powers of the cosmological time. We investigate the dynamics of FRW models using dynamical system methods as well as searching for exact solutions. From dynamical analysis we obtain different evolutional scenarios admissible for all initial conditions. For the interpretation of the dynamical evolution caused by the decay of the quantum vacuum we study the thermodynamics of the apparent horizon of the model as well as the evolution of the temperature. For the early Universe, we found that the quantum effects modified the evolution of the temperature of the Universe. In our model the adiabatic approximation is valid and the quantum vacuum decay occurs with an adequate unknown particle which constitutes quantum vacuum. We argue that the late-time evolution of metastable energy is the holographic dark energy.