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

We extend our previous analysis of cosmological supernova type Ia data (Padmanabhan &amp; Choudhury 2003) to include three recent compilation of data sets. Our analysis ignores the possible correlations and systematic effects present in the data and concentrates mostly on some key theoretical issues. Among the three data sets, the first set consists of 194 points obtained from various observations 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 three data sets strongly rule out non-accelerating models. Interestingly, the first and the second data sets favour a closed universe; if Ω<SUB>tot</SUB>≡Ω<SUB>m</SUB>Ω<SUB>Λ</SUB>, then the probability of obtaining models with Ω<SUB>tot</SUB> &gt; 1 is ≳ 0.97. Hence these data sets are in mild disagreement with the "concordance" flat model. However, this disagreement is reduced (the probability of obtaining models Ω<SUB>tot</SUB> with being ≈ 0.9) for the third data set, which includes the most recent points observed by HST around 1 &lt; z &lt; 1.6. (ii) When the first data set is divided into two separate subsets consisting of low (z &lt; 0.34) and high (z &gt; 0.34) redshift supernova, it turns out that these two subsets, individually, admit non-accelerating models with zero dark energy because of different magnitude zero-point values for the different subsets. This can also be seen when the data is analysed while allowing for possibly different magnitude zero-points for the two redshift subsets. However, the non-accelerating models seem to be ruled out using only the low redshift data for the other two data sets, which have less uncertainties. (iii) We have also found that it is quite difficult to measure the evolution of the dark energy equation of state w<SUB>X</SUB>(z) 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<SUB>X</SUB> &lt; −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 per cent confidence level for Ω<SUB>m</SUB>≳ 0.2