[Paper Review] Findings of the Joint Dark Energy Mission Figure of Merit Science Working Group

Andreas Albrecht, Luca Amendola+9 more|ArXiv.org|Jan 6, 2009

Gamma-ray bursts and supernovaePhysics and Astronomy11 references84 citations

TL;DR

This paper establishes a Figure of Merit (FoM) framework for the Joint Dark Energy Mission (JDEM) to quantify the performance of dark energy experiments. It combines Fisher matrix analyses of supernovae, baryon acoustic oscillations, weak lensing, and Planck cosmic microwave background data to evaluate constraints on dark energy parameters $w_0$ and $w_a$, with key results showing that combining multiple probes significantly improves sensitivity to the time evolution of dark energy beyond the cosmological constant.

ABSTRACT

These are the findings of the Joint Dark Energy Mission (JDEM) Figure of Merit (FoM) Science Working Group (SWG), the FoMSWG. JDEM is a space mission planned by NASA and the DOE for launch in the 2016 time frame. The primary mission is to explore the nature of dark energy. In planning such a mission, it is necessary to have some idea of knowledge of dark energy in 2016, and a way to quantify the performance of the mission. In this paper we discuss these issues.

Motivation & Objective

• To define a standardized Figure of Merit (FoM) for evaluating the scientific performance of the Joint Dark Energy Mission (JDEM) in probing dark energy.
• To quantify the sensitivity of various cosmological probes—supernovae, baryon acoustic oscillations, weak lensing, and cosmic microwave background—toward constraining dark energy parameters $w_0$ and $w_a$.
• To develop a unified Fisher matrix formalism that enables comparison and combination of different observational techniques in a consistent, quantitative way.
• To provide a public software toolkit for computing principal components, marginalized errors, and FoM values for dark energy parameters using pre-JDEM data forecasts.

Proposed method

• Uses the Fisher matrix formalism to compute parameter uncertainties for dark energy models parameterized by $w_0$ and $w_a$, with $w(a) = w_0 + w_a(1-a)$.
• Applies the Fisher matrix to four key cosmological probes: Type Ia supernovae (SN), baryon acoustic oscillations (BAO), weak gravitational lensing (WL), and Planck CMB observations.
• Combines individual Fisher matrices from each probe using matrix addition to compute joint constraints, enabling assessment of synergistic gains from multi-probe experiments.
• Employs a principal component analysis (PCA) technique to decompose the Fisher matrix into orthogonal modes of dark energy evolution, revealing the most informative redshift bins.
• Develops and releases a C-based software package that computes marginalized errors, principal components, pivot redshifts, and FoM values from input Fisher matrices.
• Provides a flexible software interface allowing users to input custom Fisher matrices and combine them in various configurations to evaluate different mission design scenarios.

Experimental results

Research questions

• RQ1 How do different cosmological probes—supernovae, BAO, weak lensing, and CMB—contribute individually and jointly to constraining the time evolution of dark energy?
• RQ2 What is the optimal combination of probes that maximizes the Figure of Merit (FoM) for measuring $w_0$ and $w_a$?
• RQ3 How does the inclusion of weak lensing data affect constraints on the growth index $\gamma$ and the effective gravitational constant $G_0$?
• RQ4 What is the pivot redshift $z_p$ and the uncertainty in the equation of state at that redshift, and how does it vary across different probe combinations?
• RQ5 How do marginalized errors on $w_0$ and $w_a$ change when priors are applied, and what is the resulting improvement in FoM?

Key findings

• The combination of supernovae, BAO, weak lensing, and Planck CMB data yields a FoM for $w_0$ and $w_a$ that is significantly higher than any single probe, demonstrating strong synergy.
• The pivot redshift $z_p$ for the dark energy equation of state is found to be around 0.5–0.8, depending on the probe combination, indicating that the most informative redshift range for constraining $w(a)$ lies in the intermediate universe.
• Including weak lensing data improves constraints on the growth index $\gamma$ and its FoM, with $\sigma(\Delta\gamma)$ being measurable to better than 0.05 in some configurations.
• The software tool successfully computes principal components and marginalized errors, with the first few eigenvectors capturing most of the information on dark energy evolution across redshift bins.
• The Fisher matrix for the combined SN+BAO+WL+Planck setup yields a FoM of approximately $\sigma(w_a) \times \sigma(w_0)^{-1} \approx 1.5$ for the DETF FoM definition, indicating high sensitivity to dark energy evolution.
• The principal component decomposition reveals that the most informative redshift bins for probing $w(a)$ are in the range $0.3 < z < 1.5$, with decreasing sensitivity at higher and lower redshifts.