Is Phantom Barrier Crossing Inevitable? A Cosmographic Analysis

TL;DR

This paper uses a model-independent cosmographic approach to analyze dark energy evolution, constraining its behavior with recent observational data and showing that phantom barrier crossing is unlikely due to the nature of the dynamical system.

Contribution

It introduces an analytical, single-parameter model for dark energy EoS and demonstrates, through a dynamical systems analysis, that crossing the phantom barrier is prevented.

Findings

Deviations from a cosmological constant at late times.

No evidence of phantom barrier crossing in the data.

Dark energy's EoS behaves as a bifurcation point preventing crossing.

Abstract

Recent findings from the Dark Energy Spectroscopic Instrument (DESI), analyzed together with supernova observations and CMB measurements, provide statistically significant indications (at the 2-5$\sigma$ level) of a time-varying dark energy component alongwith a possible phantom-to-quintessence transition in the recent past. In this letter, we investigate the evolution of dark energy using a model-independent cosmographic approach and explore the possibility of phantom barrier crossing. By mapping the differential equation defining jerk parameter into an anharmonic oscillator, we derive an analytical expression for the dark energy equation of state (EoS), which, remarkably, depends on a single parameter. Using DESI-DR2 BAO data, supernova data, and a compressed Planck likelihood, we constrain the cosmological parameters and find deviations from a cosmological constant at late times. Unlike the CPL parametrization, our results show no phantom barrier crossing, highlighting the power of kinematic reconstructions in probing the nature of dark energy. Furthermore, using a dynamical system approach, we demonstrate that $w_{DE}=-1$ acts as a bifurcation point with degenerate stable fixed points and therefore prevents solutions from crossing this barrier from either side.