A model independent approach to the dark energy equation of state

TL;DR

The paper addresses determining the dark energy equation of state without committing to a specific quintessence potential. It introduces a model-independent parametrization of $w_Q(a)$, built from two logistic transitions, to capture tracker behavior and rapid late-time evolution, and shows how to fix the transition parameters from boundary values, reducing to a four-parameter (or five-parameter) description. Across representative potentials, the parametrization reproduces $w_Q(a)$ with percent-level accuracy for $z<10$ and enables inclusion of dark-energy clustering and high-redshift observables. This framework enables constraints on the evolution of dark energy from current and future data in a model-independent manner, potentially distinguishing dynamical dark energy from a cosmological constant.

Abstract

The consensus of opinion in cosmology is that the Universe is currently undergoing a period of accelerated expansion. With current and proposed high precision experiments it offers the hope of being able to discriminate between the two competing models that are being suggested to explain the observations, namely a cosmological constant or a time dependent `Quintessence' model. The latter suffers from a plethora of scalar field potentials all leading to similar late time behaviour of the universe, hence to a lack of predictability. In this paper, we develop a model independent approach which simply involves parameterizing the dark energy equation of state in terms of known observables. This allows to analyse the impact dark energy has had on cosmology without the need to refer to particular scalar field models and opens up the possibility that future experiments will be able to constrain the dark energy equation of state in a model independent manner.

Figures (5)

• Figure 1: Evolution of $w_{Q}$ against the scale factor for an inverse power law model (solid blue line), SUGRA model (BRAX) (dash red line), two exponential potential model (BARRE) (solid magenta line), AS model (ALB) (solid green line) and CNR model (COPE) (dot orange line).
• Figure 2: Plot of $w_Q^{p}(a)$ best fit for different potentials
• Figure 3: Absolute value of the difference between $w_Q(a)$ and $w_Q^{p}(a)$ for the models of fig.1.
• Figure 4: Time evolution of $w_Q^p(a)$ as in the case of K-essence (blue solid line), late time transition (red dash-dot line) end with $w_Q^o<-1$ (green dash line).
• Figure 5: Absolute value of the difference between $w_Q(a)$ and the low redshift formula Eq. (\ref{['lowz']}) for the models of fig.1.