Can luminosity distance measurements probe the equation of state of dark energy

TL;DR

This work analyzes how luminosity-distance measurements from Type Ia supernovae can probe the dark energy equation of state $w_X(z)$ in a flat two-component universe. By deriving the governing equations and employing Fisher-matrix techniques on a high-statistics SN sample, it shows that $w_X(z)$ is encoded in the distance via derivatives of $d_L(z)$, leading to strong degeneracies when $\Omega_M$ is not fixed. The paper investigates how redshift distribution, priors on $\Omega_M$, and control of systematics affect the precision on $w_0$ and $w_1$ (parameterizing $w_X(z)$), concluding that meaningful constraints require accurate $\Omega_M$ priors and modest optimization of the redshift sampling. It also demonstrates that priors and systematic error budgets can substantially improve or bias the inferred $w$ parameters, and discusses synergy with weak lensing for self-consistent cosmological constraints. Overall, the results guide SN survey design (e.g., SNAP-like missions) toward robust measurements of dark-energy dynamics.

Abstract

Distance measurements to Type Ia supernovae (SNe Ia) at cosmological distances indicate that the Universe is accelerating and that a large fraction of the critical energy density exists in a component with negative pressure. Various hypotheses on the nature of this ``dark energy'' can be tested via their prediction for the equation of state of this component. If the dark energy is due to a scalar field, its equation of state will in general vary with time and is related to the potential of the field. We review the intrinsic degeneracies of luminosity distance measurements and compute the expected accuracies that can be obtained for the equation of state parameter from a realistic high statistic SNe Ia experiment.

Figures (3)

• Figure 1: Logarithmic derivatives of the luminosity distance w.r.t $\,{\Omega_{\rm M}}$, $w_0$ and $w_1$, for the 3 models under study (see text), as a function of redshift. One may notice similar shapes of the three derivatives for every model.
• Figure 2: value of the square root of the largest eigenvalue of C as a function of the redshift where one adds 40 supernovae to the sample.
• Figure 3: 1 and 2 $\sigma$ (39% filled areas,86% dotted lines) confidence contours for ($w_0$,$w_1$) with a Gaussian prior $\sigma_{\,{\Omega_{\rm M}}} = 0.05$ (large contours), and with an infinite precision (small elongated contours). For model A, the 2 $\sigma$ contour escapes in an unphysical region.