Can we ever distinguish between quintessence and a cosmological constant?

TL;DR

This paper explores whether future precise measurements of dark energy's equation of state can distinguish between a cosmological constant and dynamical models, finding that some models with high-redshift effects remain observationally viable.

Contribution

It provides a model-independent analysis of quintessence trajectories, identifying classes of acceptable models and discussing their observational constraints across different redshifts.

Findings

Models with flat potentials mimic a cosmological constant.

Models with potential kinks can have high-redshift effects.

High-redshift observations can constrain certain dynamical dark energy models.

Abstract

Many ambitious experiments have been proposed to constrain dark energy and detect its evolution. At present, observational constraints are consistent with a cosmological constant and there is no firm evidence for any evolution in the dark energy equation of state w. In this paper, we pose the following question: suppose that future dark energy surveys constrain w at low redshift to be consistent with -1 to a percent level accuracy, what are the implications for models of dynamical dark energy? We investigate this problem in a model-independent way by following quintessence field trajectories in `energy' phase-space. Attractor dynamics in this phase-space leads to two classes of acceptable models: 1) models with flat potentials, i.e. an effective cosmological constant, and 2) models with potentials that suddenly flatten with a characteristic kink. The prospect of further constraining the second class of models from distance measurements and fluctuation growth rates at low redshift (z<3) seems poor. However, in some models of this second class, the dark energy makes a significant contribution to the total energy density at high redshift. Such models can be further constrained from observation of the cosmic microwave background anisotropies and from primordial nucleosynthesis. It is possible, therefore, to construct models in which the dark energy at high redshift causes observable effects, even if future dark energy surveys constrain w at low redshift to be consistent with -1 to high precision.