# Measurements of Omega and Lambda from 42 High-Redshift Supernovae

^{1}, University of California, Berkeley

^{2}, Instituto Superior Técnico

^{3}, Pierre-and-Marie-Curie University

^{4}, Stockholm University

^{5}, European Southern Observatory

^{6}, Collège de France

^{7}, University of Cambridge

^{8}, University of Barcelona

^{9}, Yale University

^{10}, Space Telescope Science Institute

^{11}, European Space Agency

^{12}, University of New South Wales

^{13}

## Summary (2 min read)

### 1. INTRODUCTION

- Since the earliest studies of supernovae, it has been suggested that these luminous events might be used as standard candles for cosmological measurements (Baade 1938).
- Even after an impressive multiyear e†ort by et al. (1989), it was only possible toNÔrgaard-Nielsen follow one SN Ia, at z\ 0.31, discovered 18 days past its peak brightness.
- In particular, Goobar & Perlmutter (1995) showed the possibility of separating the relative contributions of the mass density, and the cosmological constant, ", to) M , changes in the expansion rate by studying supernovae at a range of redshifts.
- Here the authors report on the complete analysis of 42 supernovae from the Supernova Cosmology Project, including the reanalysis of their previously reported supernovae with improved calibration data and improved photometric and spectroscopic SN Ia templates.

### 2. BASIC DATA AND PROCEDURES

- The new supernovae in this sample of 42 were all dis- covered while still brightening, using the Cerro Tololo Inter-American Observatory (CTIO) 4 m telescope with the 20482 pixel prime-focus CCD camera or the 4] 20482 pixel Big Throughput Camera.10.
- The conÐdence regions of Figure 5c and the ) M flat results in Table 3 show that the cosmological parameters found for Ðt H di†er by less than half of a standard deviation from those for Ðt C. 4.1.3.
- Analysis with Reddening Correction of Individual Supernovae.
- To be conservative the authors take the classical Malmquist bias of 0.04 mag for the low-redshift data set and the least biased value of 0.01 mag for the high-redshift data set, and they consider systematic uncertainty from this source to be the di†erence, 0.03 mag, in the direction of low-redshift supernovae more biased than high-redshift.
- The results (Ðt D), as shown in Figure 5b and listed in Table 3, are in extremely close agreement with those of the light-curveÈwidth-corrected Ðt C.

### 5. RESULTS AND ERROR BUDGET

- From Table 3 and Figure 5a, it is clear that the results of Ðts A, B, and C are quite close to each other, so the authors can conclude that their measurement is robust with respect to the choice of these supernova subsets.
- The shaded contours (Ðt C) are the conÐdence regions Note that the statistical error in and aM Bare derived quantities from their four-parameter Ðts.
- To characterize the e†ect of the identiÐed systematic uncertainties, the authors have reÐt the supernovae of Ðt C for the hypothetical case (Ðt J) in which each of the high-redshift supernovae were discovered to be 0.04 mag brighter than measured, or, equivalently, the low-redshift supernovae were discovered to be 0.04 mag fainter than measured.

### 6. CONCLUSIONS AND DISCUSSION

- The conÐdence regions of Figure 7 and the residual plot of Figure 2b lead to several striking implications.
- The best-Ðt model (the center of the shaded contours) indicates that the energy density in the cosmological constant is D0.5 more than that in the form of mass energy density.
- Many of these residual concerns about the measurement can be addressed with new studies of low-redshift supernovae.

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##### Frequently Asked Questions (11)

###### Q2. What are the future works in this paper?

Thus the universe may be Ñat or there may be little or no cosmological constant, but the data are not consistent with both possibilities simultaneously. 2. presented here and future complementary data sets will allow us to explore these possibilities. For their purposes here the authors wish to distinguish between the true probability distribution, P ( A ), and its estimated or assumed distribution, often called the Bayesian prior, which they denote as P ( A ). Third, even if the universe is not Ñat, the conÐdence regions of Figure 7 suggest that the cosmological constant is a signiÐcant constituent of the energy density of the universe.

###### Q3. What is the appropriate measure to compare with their results?

Since there is evidence that dynamical estimates of depend on scale, the most appropriate measures to) Mcompare with their result are those obtained on large scales.

###### Q4. What is the possibility of a strong metallicity eect?

The consistency of slopes in the light-curve widthluminosity relation for the low- and high-redshift supernovae can also constrain the possibility of a strong metallicity e†ect of the type that et al.

###### Q5. Why is the total systematic uncertainty a separate analysis case?

due to small-scale clumping of mass as a separate analysis case rather than as a contributing systematic error in their primary analysis ; the total systematic uncertainty applies to this analysis as well.

###### Q6. What is the stretch factor used to determine the light curves of the Cala n/?

at high redshift the rest-frame B-band photometry is usually much more densely sampled in time than the rest-frame V -band data, so the authors use the stretch factor that best

###### Q7. What is the extinction probability distribution implied by the measured colorexcess?

In brief, in this method the Gaussian extinction probability distribution implied by the measured colorexcess and its error is multiplied by an assumed a priori probability distribution (the Bayesian prior) for the intrinsic distribution of host extinctions.

###### Q8. What is the difference between the rest-frame color and the stretch factor?

Since there is a small dependence of intrinsic color on the light-curve width, supernova colors can only be compared for the same stretch factor ; for a more convenient analysis, the authors subtract out the intrinsic colors so that the remaining color excesses can be compared simultaneously for all stretch factors.

###### Q9. What is the best-t mass density in a at universe?

The best-Ðt mass-density in a Ñat universe for Ðt A is, within a fraction of the uncertainty, the same value as for Ðt B, (see Table 3).

###### Q10. What is the t for the age of the universe for these analyses?

The best Ðts for the age of the universe for these analyses are H0 t0\\and To Ðrst order, the Reiss et0.90~0.05`0.07 H0 t0\\ 0.98~0.05`0.07.al.

###### Q11. What are the two coincidences that must be addressed in future cosmological theories?

If in fact the universe has a dominant energy contribution from a cosmological constant, there are two coincidences that must be addressed in future cosmological theories.