Measurements of Omega and Lambda from 42 High-Redshift Supernovae

TL;DR

Using 42 high-redshift Type Ia supernovae plus 18 low-redshift SN Ia data, the study measures Omega_M and Omega_Lambda via the SN Ia magnitude–redshift relation corrected for the width-luminosity relation. The analysis finds a flat universe with Omega_M ≈ 0.28 and Omega_Lambda ≈ 0.72, and rejects Lambda = 0 flat cosmologies with high confidence; the implied age is around 14–15 Gyr. The results are tested against multiple systematic uncertainties, showing robustness to extinction, Malmquist bias, lensing, and possible SN evolution, and are broadly consistent with other cosmological constraints.

Abstract

We report measurements of the mass density, Omega_M, and cosmological-constant energy density, Omega_Lambda, of the universe based on the analysis of 42 Type Ia supernovae discovered by the Supernova Cosmology Project. The magnitude-redshift data for these SNe, at redshifts between 0.18 and 0.83, are fit jointly with a set of SNe from the Calan/Tololo Supernova Survey, at redshifts below 0.1, to yield values for the cosmological parameters. All SN peak magnitudes are standardized using a SN Ia lightcurve width-luminosity relation. The measurement yields a joint probability distribution of the cosmological parameters that is approximated by the relation 0.8 Omega_M - 0.6 Omega_Lambda ~= -0.2 +/- 0.1 in the region of interest (Omega_M <~ 1.5). For a flat (Omega_M + Omega_Lambda = 1) cosmology we find Omega_M = 0.28{+0.09,-0.08} (1 sigma statistical) {+0.05,-0.04} (identified systematics). The data are strongly inconsistent with a Lambda = 0 flat cosmology, the simplest inflationary universe model. An open, Lambda = 0 cosmology also does not fit the data well: the data indicate that the cosmological constant is non-zero and positive, with a confidence of P(Lambda > 0) = 99%, including the identified systematic uncertainties. The best-fit age of the universe relative to the Hubble time is t_0 = 14.9{+1.4,-1.1} (0.63/h) Gyr for a flat cosmology. The size of our sample allows us to perform a variety of statistical tests to check for possible systematic errors and biases. We find no significant differences in either the host reddening distribution or Malmquist bias between the low-redshift Calan/Tololo sample and our high-redshift sample. The conclusions are robust whether or not a width-luminosity relation is used to standardize the SN peak magnitudes.

Figures (10)

• Figure 1: Hubble diagram for 42 high-redshift Type Ia supernovae from the Supernova Cosmology Project, and 18 low-redshift Type Ia supernovae from the Calán/Tololo Supernova Survey, after correcting both sets for the SN Ia lightcurve width-luminosity relation. The inner error bars show the uncertainty due to measurement errors, while the outer error bars show the total uncertainty when the intrinsic luminosity dispersion, 0.17 mag, of lightcurve-width-corrected Type Ia supernovae is added in quadrature. The unfilled circles indicate supernovae not included in Fit C. The horizontal error bars represent the assigned peculiar velocity uncertainty of 300 km s$^{-1}$. The solid curves are the theoretical $m_B^{\rm effective}(z)$ for a range of cosmological models with zero cosmological constant: $(\Omega_{\rm M},\Omega_\Lambda) = (0,0)$ on top, $(1,0)$ in middle and (2,0) on bottom. The dashed curves are for a range of flat cosmological models: $(\Omega_{\rm M},\Omega_\Lambda) = (0,1)$ on top, $(0.5,0.5)$ second from top, $(1,0)$ third from top, and (1.5,-0.5) on bottom.
• Figure 2:
• Figure 3: The distribution of restframe $B$-band magnitude residuals from the best-fit flat cosmology for the Fit C supernova subset, for (a) 18 Calán/Tololo supernovae, at redshifts $z \le0.1$ and (b) 42 supernovae from the Supernova Cosmology Project, at redshifts between 0.18 and 0.83. The darker shading indicates those residuals with uncertainties less than 0.35 mag, unshaded boxes indicate uncertainties greater than 0.35 mag, and dashed boxes indicate the supernovae that are excluded from Fit C. The curves show the expected magnitude residual distributions if they are drawn from normal distributions given the measurement uncertainties and 0.17 mag of intrinsic SN Ia dispersion. The low-redshift expected distribution matches a Gaussian with $\sigma = 0.20$ mag (with error on the mean of 0.05 mag), while the high-redshift expected distribution matches a Gaussian with $\sigma = 0.22$ mag (with error on the mean of 0.04 mag).
• Figure 4: The distribution of lightcurve widths for (a) 18 Calán/Tololo supernovae, at redshifts $z \le0.1$ and (b) 42 supernovae from the Supernova Cosmology Project, at redshifts between 0.18 and 0.83. The lightcurve widths are characterized by the "stretch factor," $s$, that stretches or contracts the time axis of a template SN Ia lightcurve to best fit the observed lightcurve for each supernova kim_stretch98gold_dilate98. The template has been time-dilated by a factor $1+z$ before fitting to the observed lightcurves to account for the cosmological lengthening of the supernova timescale goldhaberaigualeibundgutdilation. The shading indicates those measurements of $s$ with uncertainties less than 0.1, and the dashed lines indicate the two supernovae that are removed from the fits after Fit A. These two excluded supernovae are the most significant deviations from $s=1$ (the highest-stretch supernova in panel (b) has an uncertainty of $\pm$0.23 and hence is not a significant outlier from $s=1$); the remaining low- and high-redshift distributions have almost exactly the same error-weighted means: $\langle s \rangle_{\rm Hamuy} = 0.99 \pm 0.01$ and $\langle s \rangle_{\rm SCP} = 1.00 \pm 0.01$.
• Figure 5: