Parameterizing and Measuring Dark Energy Trajectories from Late-Inflatons

TL;DR

This paper develops a three-parameter model for dark energy evolution, uses observational data to constrain these parameters, and forecasts future observational improvements, revealing limitations in reconstructing potential details beyond basic properties.

Contribution

Introduces a three-parameter approximation for dark energy trajectories and constrains it with current data, assessing the potential to distinguish models and forecast future constraints.

Findings

Best constrained parameter is low redshift slope, psilon_s

Current data rules out some quintessence and phantom models

Future observations could improve constraints on psilon_s and psilon_{\,phi\, extinfty} by a factor of five

Abstract

Bulk dark energy properties are determined by the redshift evolution of its pressure-to-density ratio, $w_{de}(z)$. An experimental goal is to decide if the dark energy is dynamical, as in the quintessence (and phantom) models treated here. We show that a three-parameter approximation $w_{de}(z; \epsilon_s, \epsilon_{\phi\infty}, \zeta_s)$ fits well the ensemble of trajectories for a wide class of late-inflaton potentials $V(\phi)$. Markov Chain Monte Carlo probability calculations are used to confront our $w_{de}(z)$ trajectories with current observational information on Type Ia supernova, Cosmic Microwave Background, galaxy power spectra, weak lensing and the Lyman-${\alpha}$ forest. We find the best constrained parameter is a low redshift slope parameter, $\epsilon_s \propto (\partial \ln V / \partial \phi)^2$ when the dark energy and matter have equal energy densities. A tracking parameter $\epsilon_{\phi\infty}$ defining the high-redshift attractor of $1+w_{de}$ is marginally constrained. Poorly determined is $\zeta_s$, characterizing the evolution of $\epsilon_s$, and a measure of $\partial^2 \ln V / \partial \phi^2$ . The constraints we find already rule out some popular quintessence and phantom models, or restrict their potential parameters. We also forecast how the next generation of cosmological observations improve the constraints: by a factor of about five on $\epsilon_s$ and $\epsilon_{\phi\infty}$, but with $\zeta_s$ remaining unconstrained (unless the true model significantly deviates from $\Lambda$CDM). Thus potential reconstruction beyond an overall height and a gradient is not feasible for the large space of late-inflaton models considered here.