Uncorrelated Estimates of Dark Energy Evolution

TL;DR

The paper develops an uncorrelated, nearly model-independent method to estimate the redshift evolution of dark energy via band powers of the equation of state $w(z)$ and the normalized density $f(z)$ using Type Ia SN data. It constructs these band powers by rotating the parameter vector with ${\bf q}=\widetilde{\bf W}{\bf p}$ where ${\widetilde{\bf W}}={\bf F}^{1/2}$, yielding uncorrelated estimates with localized, mostly positive window functions. An analysis of the Riess et al. gold SN dataset using four redshift bins finds $w(z)\approx -1$ in most bins and no strong evidence for evolution beyond a cosmological constant, with marginal $w<-1$ at $z<0.2$. The method provides an interpretable framework that complements traditional parameterizations and is well-suited to future, larger SN datasets and cross-checks with other cosmological probes.

Abstract

Type Ia supernova data have recently become strong enough to enable, for the first time, constraints on the time variation of the dark energy density and its equation of state. Most analyses, however, are using simple two or three-parameter descriptions of the dark energy evolution, since it is well known that allowing more degrees of freedom introduces serious degeneracies. Here we present a method to produce uncorrelated and nearly model-independent band power estimates of the equation of state of dark energy and its density as a function of redshift. We apply the method to recently compiled supernova data. Our results are consistent with the cosmological constant scenario, in agreement with other analyses that use traditional parameterizations, though we find marginal (2-sigma) evidence for w(z) < -1 at z < 0.2. In addition to easy interpretation, uncorrelated, localized band powers allow intuitive and powerful testing of the constancy of either the energy density or equation of state. While we have used relatively coarse redshift binning suitable for the current set of about 150 supernovae, this approach should reach its full potential in the future, when applied to thousands of supernovae found from ground and space, combined with complementary information from other cosmological probes.

Figures (2)

• Figure 1: Uncorrelated band-power estimates of the equation of state $w(z)$ of dark energy are shown in panel (a). Vertical error bars show the 1 and 2-$\sigma$ error bars (the full likelihoods are shown in panel (c)), while the horizontal error bars represent the approximate range over which each measurement applies. The full window functions in redshift space for each of these measurements are shown in panel (b); they have small leakage outside of the original redshift divisions. The window functions and the likelihoods are labeled in order of increasing redshift of the band powers in panel (a). The window functions satisfy three of our requirements: they make the band-powers uncorrelated, they are fairly well localized in redshift, and they are almost everywhere positive. In panel (a), we have used a uniform prior of $0.22\leq \Omega_M \leq 0.38$ (a Gaussian prior $\Omega_M=0.3\pm 0.04$ gives very similar results), and we have assumed a flat universe throughout.
• Figure 2: Same as Figure 1, but for $f(z)\equiv \rho_{\rm DE}(z)/\rho_{\rm DE}(0)$. Our band powers assume piecewise linear $f(z)$, with the exception of the band power corresponding to the largest-redshift bin, which assumes constant $f(z)$ across that bin.