Observational constraints on early time non-phantom behaviour of dynamical dark energy

TL;DR

This work investigates a broad class of non-phantom dynamical dark energy models that combine an early-time scaling scalar field with various late-time behaviors (ΛCDM, $w$CDM, CPL, and thawing). The authors implement a double-exponential potential to realize early-time scaling and explore how additional late-time components affect cosmological observables, using a joint data set and MCMC with model selection criteria. They find that standard background parameters are remarkably stable across models, while early-time scaling requires a steep potential with $\\lambda_2\\gtrsim 20$–$30$, keeping the early dark energy fraction well below 1% around matter–radiation equality and failing to alleviate the Hubble tension. Although late-time evolving DE (notably CPL) shows a mild preference for deviation from $w=-1$, the inclusion of early-time scaling is strongly penalised by AIC/BIC, disfavouring models that combine early-time scaling with late-time dynamical DE. The results suggest that viable extensions of $\\Lambda$CDM must go beyond straightforward scaling solutions or invoke additional physics to address both early and late-time DE phenomena.

Abstract

We study dynamical dark energy models that allow for general late time behaviour while admitting non-phantom dynamics at early times, including thawing, scaling$+$thawing, and effective fluid extensions. Using current cosmological data, we find that the standard background parameters remain tightly constrained and stable across all models, indicating no significant impact of these dynamics on the late time expansion history. At low redshift, parametrizations with a time-dependent equation of state, particularly CPL, show a $\sim2σ$ preference for evolution away from $w=-1$, driven by phantom-like behaviour. We then examine the observational consequences of allowing non-phantom dark energy at early times through scaling type dynamics. The data impose strong lower bounds on the steepness of the exponential potential $\gtrsim 20-30$, forcing the dark energy density to remain below the percent level around matter-radiation equality. Consequently, early dark energy is tightly constrained, and neither scaling nor tracker-type dynamics can produce a sufficiently large early dark energy component to alleviate the Hubble tension. While late time dynamical dark energy can improve the goodness of fit, the inclusion of early time scaling does not provide additional improvement and is strongly penalised by model selection criteria, leading to a disfavouring of such scenarios.

Figures (2)

• Figure 1: Evolution of the energy densities of matter (long-dashed green), radiation (short-dashed red), and the scalar field (solid blue) normalised by the present critical density $\rho_{\rm c0}$ for the potential \ref{['eq:V_double_exp']} with $\lambda_1=0.1$ and $\lambda_2=20$.
• Figure 2: The 1$\sigma$ and 2$\sigma$ confidence regions for the cosmological and dark energy parameters. The top panels show the six-parameter constraints (left) and the cases with additional scaling parameters together with the dark energy parameters for three models, while the bottom panels display the two-dimensional contours in the $(\Omega_{\rm m0},\lambda_1)$ plane for the thawing model (left) and in the $(\lambda_1,\lambda_2)$ plane for the scaling–thawing model (right).