Dynamical system analysis of FLRW models with Modified Chaplygin gas

Area of Science:

• Cosmology
• Theoretical Physics
• General Relativity

Background:

• The standard cosmological model faces challenges explaining dark energy.
• Modified Chaplygin gas offers an alternative dark energy candidate.
• Cosmological constant remains a key component in understanding cosmic acceleration.

Purpose of the Study:

• To investigate Friedmann-Lemaître-Robertson-Walker (FLRW) models incorporating modified Chaplygin gas and a cosmological constant.
• To analyze the stability and evolution of these cosmological models using dynamical system methods.
• To determine the long-term fate of the universe under these conditions.

Main Methods:

• Application of dynamical system analysis to FLRW cosmological models.
• Investigation of the equation of state for modified Chaplygin gas: p = (α - 1)ρ/α.
• Analysis of state spaces to understand model singularities and future evolution.

Main Results:

• The study maps the state spaces for various parameter values.
• It identifies conditions for stable and unstable solutions.
• The analysis reveals the universe's potential future evolution, including possible singularities.

Conclusions:

• Certain configurations of modified Chaplygin gas and cosmological constant allow for stable cosmic evolution.
• The presence of a singularity at the beginning of the universe is confirmed in some scenarios.
• The long-term fate of the universe depends critically on the chosen parameters.