Potential for a transition from standard to phantom dark energy in the FLRW cosmology: A dynamical systems analysis

Modern cosmology is based on the ΛCDM model, in which the Universe’s accelerated expansion is driven by dark energy with equation of state w = –1. While ΛCDM agrees well with observational data — from CMB anisotropies to large-scale structure — both theoretical considerations and emerging observations suggest that dark energy may be dynamical, with w(z) that evolves over time. A scenario of particular interest is a potential transition from standard dark energy (w ≥ –1) to phantom energy (w < –1), which violates the strong energy condition and may lead to a ‘Big Rip’. Planck data (Aghanim et al. 2020) confirm that, as of today, dark energy dominates (ΩDE ≈ 0.685) and w is consistent with –1; however, combined analyses (Planck + BAO + supernovae) permit slight deviations into the phantom regime (w ≈ –1.03 ± 0.03). Though marginal, this possibility motivates the study of models where w(z) crosses the w = –1 barrier. Moreover, recent JWST observations reveal unexpectedly massive galaxies at z > 10, challenging ΛCDM predictions of structure formation and hinting at modified expansion histories that may involve evolving — or phantom — dark energy. This work investigates whether phantom energy can act as a future attractor in a flat FLRW cosmology. Using autonomous dynamical systems, we analyse the evolution of density parameters Ωi(z) and w(z) in a model that permits crossing the w = –1 divide.