Cosmological parameters from supernova observations: A critical comparison of three data sets

TL;DR

The paper evaluates cosmological inferences from Type Ia supernova observations by comparing three compilations using a simple $\chi^2$ approach to flat and non-flat geometries with dust-like matter and a cosmological constant, and by exploring constraints on evolving dark energy via a two-parameter $w_X(z)$ model with $w_X(z) = w_0 - w_1(a-1) = w_0 + w_1 \frac{z}{1+z}$. It finds that SN data strongly rule out non-accelerating models, though the implied spatial curvature depends on data set quality: $\mathcal{P}(\Omega_{tot}>1) \approx 0.97$ (TONRY), $0.99$ (RIESS w/o HST), and $0.88$ (RIESS with HST). Constraints on dark energy show a mild preference for $w_0 < -1$ with $w_1$ poorly constrained, yet all data sets remain compatible with $w_0 = -1, w_1 = 0$ (i.e., $\Lambda$CDM) at 99% CL for higher $\Omega_m$. The work highlights the impact of data quality and neglected systematics on parameter errors and underscores the need for robust low-redshift data and broader parameterizations to pin down $w_X(z)$.

Abstract

We extend our previous analysis of cosmological supernova data (Padmanabhan & Choudhury 2003) to include three recent compilation of data sets. Our analysis ignores systematic effects in the data and concentrates on some key theoretical issues. The first data set consists of 194 points while the second discards some of the points from the first one because of large uncertainties and thus consists of 142 points. The third data set is obtained from the second by adding the latest 14 points observed through HST. A careful comparison of these different data sets help us to draw the following conclusions: (i) All the data sets strongly rule out non-accelerating models. Interestingly, the first and the second sets favour a closed universe; i.e., the probability P(Omega_{tot} > 1) \gtrsim 0.97. Hence these sets are in mild disagreement with the ``concordance'' flat model. However, this disagreement is reduced [P(Omega_{tot} > 1) \approx 0.9] for the third data set, which includes the points observed by HST around 1 < z < 1.6. (ii) When the first data set is divided into two separate subsets consisting of low (z < 0.34) and high (z > 0.34) redshift supernova, it turns out that these two subsets, individually, admit non-accelerating models. However, these models seem to be ruled out using only the low redshift data for the other two data sets, which have less uncertainties. (iii) It is quite difficult to measure the evolution of the dark energy equation of state w_X though its present value can be constrained quite well. The best-fit value seems to mildly favour a dark energy component with current equation of state w_X < -1, thus opening the possibility of existence of more exotic forms of matter. However, the data is still consistent with the the standard cosmological constant at 99% confidence level (abridged).

Figures (7)

• Figure 1: Comparison between various flat models and the observational data. The observational data points, shown with error-bars, are obtained from the 'gold' sample of Riess et al. (2004). The most recent points, obtained from HST, are shown in red.
• Figure 2: The observed supernova data points in the $\dot{a} - a$ plane for flat models. The error bars for the data points are correlated (see text for detailed description). The solid curves, from bottom to top, are for flat cosmological models with $\Omega_m = 0.00, 0.16, 0.32, 0.48, 0.64, 0.80, 1.00$ respectively. The left, middle and right panels show data points for the data sets RIESS, RIESS(w/o HST) and TONRY respectively. The vertical dashed line shows the redshift $z = 0.34$.
• Figure 3: Confidence region ellipses in the $\Omega_m - {\cal M}_{1,2}$ plane for flat models with non-relativistic matter and a cosmological constant. The ellipses corresponding to the 68, 90 and 99 per cent confidence regions are shown. The top, middle and bottom rows show data points for the data sets RIESS, RIESS(w/o HST) and TONRY respectively. In the left panels, all the data points in the data set are used. In the middle panel, data points with $z < 0.34$ are used, while in the right panel, we have used data points with $z > 0.34$. We have indicated the best-fit values of $\Omega_m$ and ${\cal M}_{1,2}$ (with 1$\sigma$ errors).
• Figure 4: Confidence region ellipses in the $\Omega_m - \Omega_{\Lambda}$ plane for models with non-relativistic matter and a cosmological constant. The ellipses corresponding to the 68, 90 and 99 per cent confidence regions are shown. The confidence regions are obtained after marginalizing over ${\cal M}_{1,2}$. The dashed line corresponds to the flat model $(\Omega_{~m} + \Omega_{\Lambda} = 1)$. The unbroken slanted line corresponds to the contour of constant luminosity distance, $Q(z) =$ constant. The top, middle and bottom rows show data points for the data sets RIESS, RIESS(w/o HST) and TONRY respectively. In the left panels, all the data points in the data set are used. In the middle panel, data points with $z < 0.34$ are used, while in the right panel, we have used data points with $z > 0.34$. The values of the best-fit parameters, with 1$\sigma$ errors are indicated in the respective panels.
• Figure 5: Confidence region ellipses in the $\Omega_m - \Omega_{\Lambda}$ plane for models with non-relativistic matter and a cosmological constant, allowing for possibly different ${\cal M}_{1,2}$ for the different redshift subsamples. It is assumed that supernovae at $z < 0.34$ have ${\cal M}_{1,2}^{\rm low}$, while those at $z > 0.34$ have ${\cal M}_{1,2}^{\rm high}$. The ellipses corresponding to the 68, 90 and 99 per cent confidence regions are shown. The confidence regions are obtained after marginalizing over ${\cal M}_{1,2}$. The dashed line corresponds to the flat model $(\Omega_{~m} + \Omega_{\Lambda} = 1)$. The dot-dashed line denotes the models having zero deceleration at the present epoch (i.e., $q_0 = 0$), with the region below this line representing the non-accelerating models. The left, middle and right panels show data points for the data sets RIESS, RIESS(w/o HST) and TONRY respectively. The values of the best-fit parameters, with 1$\sigma$ errors are indicated in the respective panels.