Quadratic Dark Energy Phase-Space Dynamics and Analysis

TL;DR

This paper analyzes a quadratic dark energy model using phase-space methods, revealing stable phantom attractors and distinctive late-time acceleration behaviors consistent with recent observational constraints.

Contribution

It introduces a nonlinear quadratic term in dark energy pressure, providing a novel dynamical framework that explains late-time acceleration without crossing the phantom divide.

Findings

Stable phantom attractors lead to increased Hubble expansion rates.

The model approaches the phantom divide asymptotically from both sides.

Results align with recent DESI observations of evolving dark energy.

Abstract

We present a comprehensive phase-space analysis of a quadratic dark energy model where the pressure includes a nonlinear term proportional to the square of the energy density. This minimal extension beyond the $\Lambda$CDM framework introduces a dynamical parameter $\eta(z)$ that governs transitions between different cosmological regimes. Through dynamical systems theory, we identify critical points and their stability properties, revealing that negative $\eta$ values drive the system toward stable phantom attractors (sinks), while positive values correspond to unstable repellers (sources). The model exhibits a distinctive asymptotic approach to the phantom divide ($w_{\rm eff}=-1$) from both quintessence and phantom sides without actual crossing, providing a non-crossing alternative to the phantom-crossing behavior preferred by recent DESI DR2 constraints. Our analysis shows that stable phantom attractors produce enhanced Hubble expansion rates and more pronounced late-time acceleration, features that can be compared with recent DESI observations suggesting evolving dark energy.