Chasing the phantom: A closer look at Type Ia supernovae and the dark energy equation of state

TL;DR

This study assesses whether the dark energy equation of state $w$ shows phantom behavior ($w<-1$) by combining geometric probes: SN Ia data from Union2.1, SNLS3, and PS1 with BAO measurements and CMB constraints from Planck and WMAP9. Using a grid-based likelihood and analytic marginalization over SN nuisance parameters, the authors find that Planck+BAO+SNLS3/PS1 mildly favors $w<-1$ at about $1.9\sigma$, whereas Union2.1 is consistent with $w=-1$; the strength of the phantom signal is highly sensitive to the assumed external prior on the Hubble constant $H_0$. The analysis also shows that a more flexible, redshift- and mass-dependent SN host-mass correction (six $\mathcal{M}$ parameters) weakens the constraints and can shift the best-fit $w$ toward $-1$, highlighting the impact of environmental SN systematics. The paper emphasizes that external $H_0$ measurements and SN host-mass evolution modeling are crucial for robust inferences about phantom dark energy, and it cautions that Planck-systematics or a lower $H_0$ value could reconcile the data with a cosmological-constant scenario.

Abstract

Some recent observations provide $> 2σ$ evidence for phantom dark energy -- a value of the dark energy equation of state less than the cosmological-constant value of $-1$. We focus on constraining the equation of state by combining current data from the most mature geometrical probes of dark energy: Type Ia supernovae (SNe Ia) from the Supernova Legacy Survey (SNLS3), the Supernova Cosmology Project (Union2.1), and the Pan-STARRS1 survey (PS1); cosmic microwave background measurements from Planck and WMAP9; and a combination of measurements of baryon acoustic oscillations. The combined data are consistent with $w = -1$ for the Union2.1 sample, though they present moderate ($\sim 1.9σ$) evidence for a phantom value when either the SNLS3 or PS1 sample is used instead. We study the dependence of the constraints on the redshift, stretch, color, and host galaxy stellar mass of SNe, but we find no unusual trends. In contrast, the constraints strongly depend on any external $H_0$ prior: a higher adopted value for the direct measurement of the Hubble constant ($H_0 \gtrsim 71~\text{km/s/Mpc}$) leads to $\gtrsim 2σ$ evidence for phantom dark energy. Given Planck data, we can therefore make the following statement at $2σ$ confidence: either the SNLS3 and PS1 data have systematics that remain unaccounted for or the Hubble constant is below 71 km/s/Mpc; else the dark energy equation of state is indeed phantom.

Figures (6)

• Figure 1: Likelihood curves for a constant equation of state $w$ in a flat universe, using Planck CMB data (left panel) and WMAP9 CMB data (right panel). We compare constraints from CMB + BAO data alone (dashed black) to those which additionally include SN Ia data from SNLS3 (blue), Union2.1 (green), or PS1 (dashed red). All likelihoods are marginalized over other cosmological and nuisance parameters, as explained in the text.
• Figure 2: Evolution of the mass step predicted from a toy model calibrated using data from the Nearby Supernova Factory. This is similar to Fig. 11 of Rigault:2013gux, though we include a region of uncertainty by propagating errors in the mass step and local star-forming fraction measured at $z = 0.05$ from the Nearby Supernova Factory data. Vertical lines separate the three redshift bins, each of which contains two $\mathcal{M}$ nuisance parameters, one for each host galaxy mass range.
• Figure 3: Effect of allowing for evolution of the mass step in redshift bins in the SN Ia analysis. Left: 68.3%, 95.4% and 99.7% likelihood contours in the $\Omega_m$--$w$ plane for SNLS3 data analyzed the standard way with two $\mathcal{M}$ nuisance parameters (filled blue) and a new way with six $\mathcal{M}$ parameters (open red), one for each of two mass bins and three redshift bins. Planck + BAO constraints (open black) are overlaid for comparison. Right: 68.3% contours in the same plane for combined Planck + BAO + SNLS3 data using one, two, or six $\mathcal{M}$ parameters.
• Figure 4: Residuals of SN Ia magnitudes, binned by redshift (inverse-covariance weights), for SNLS3 (blue) and Union2.1 (red). All curves and data points are relative to a flat $\Lambda$CDM cosmology with $\Omega_m = 0.3$, which is roughly the best-fit value from CMB and BAO data. The plot shows the degree to which SNe in each redshift range pull toward $w < -1$, and we show several theory curves with constant $w$ for comparison.
• Figure 5: Effect of each individual SNLS3 SN on the combined constraint on the equation of state, as a function of redshift (top left), host galaxy stellar mass (top right), stretch (bottom left), and color (bottom right). The blue points show the shift $\Delta w$ in the final constraint on $w$ due to each individual SN. The red circles show the combined (summed) pull from each bin in the particular quantity.