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The High­Redshift Supernova Search -- Evidence for
a Positive Cosmological Constant 1
Bruno Leibundgut, Gertrud Contardo, Patrick Woudt and Jason Spyromilio 2
European Southern Observatory, Karl­Schwarzschild­Strasse 2, D­85748 Garching,
Germany
Abstract
A new component of the Universe which leads to an accelerated cosmic ex­
pansion is found from the measurements of distances to high­redshift type Ia
supernovae. We describe the method and the results obtained from the obser­
vations of distant supernovae. The dependence on the understanding of the
local type Ia supernovae is stressed. The lack of a good understanding of the
stellar evolution leading to the explosion of the white dwarf, the exact explosion
physics and the current difficulties in calculating the emission from the ejecta
limit the theoretical support. Despite the current ignorance of some of the ba­
sic physics of the explosions, the cosmological result is robust. The empirical
relations seem to hold for the distant supernovae the same way as for the local
ones and the spectral appearance is identical. The distances to the high­redshift
supernovae are larger than expected in a freely coasting, i.e. empty, Universe.
A positive cosmological constant is inferred from these measurements.
1 Introduction
The quest to measure the global dynamics of the Universe has dominated cosmological observations since
the discovery of cosmic expansion. Observational tests have been devised ever since, but only recently
have the measurements achieved an accuracy which allows us to draw more definite conclusions. Evidence
has been accumulated from the observations of the mass concentrations on the largest scales and the time
required to build them up from the earliest imprints in the cosmic microwave background (Bahcall &
Fan 1998), from the fact that the formation of old stellar systems are incompatible with the Hubble time
as derived from the present­day expansion rate, the Hubble constant (e.g. Carroll et al. 1992, Sandage
1988), and finally from the first direct distance measurements at redshifts larger than 0.1.
It is through the use of Type Ia supernovae that we now are able to glimpse at what the global energy
density of the Universe may be and what is governing the expansion field. The intriguing new results are
quite contrary to the expectations and will need a lot more scrutiny. Ultimately, the result will have to
be supported by independent measurements of the changes of the expansion rate of the Universe.
If the distances derived from the supernovae are indeed larger than expected in a freely coasting Universe,
i.e. q 0 =0, then a new component to the cosmic energy budget has to be added (Schmidt et al. 1998,
Garnavich et al. 1998a, Riess et al. 1998, Perlmutter et al. 1998, 1999). This is commonly expressed
as a cosmological constant, but could be in a more general form (White 1998, Garnavich et al. 1998b).
This new form of energy is a different, independent component to the dark matter, which was the topic
of this conference.
We will describe how type Ia supernovae (SNe Ia) can be used to determine cosmological distances and
point out the caveats with the current measurements (x2). The High­z Supernova Search Team has
presented results of the first two years observing with astonishing conclusions. The Berkeley Supernova
1 To appear in Dark'98, eds. H. Klapdor­Kleingrothaus and L. Baudis, Singapore: World Scientific Publishing
2 We report results from the High­z Supernova Search Team. The team includes B.P. Schmidt (MSSSO), M. Phillips
(LCO), N. Suntzeff, R. Schommer and C. Smith (CTIO), A. Clocchiatti (Universidad Catolica, Santiago), M. Hamuy
(Steward Obs.), R. Kirshner, P. Garnavich, S. Jha and P. Challis (Harvard Univ.), C. Hogan, C. Stubbs, A. Diercks and
D. Reiss (Univ. Washington), A. Filippenko and A. Riess (Univ. California, Berkeley), R. Gilliland (STScI), J. Tonry
(Hawaii). More information is available at http://cfa­www.harvard.edu/cfa/oir/Research/supernova/HighZ.html

Cosmology Project independently arrived at the same conclusions through the same technique, but a
completely independent data sample. Their results are presented in this volume by Isobel Hook and Pilar
Ruiz­Lapuente. We will concentrate on the results found by the High­z Team in section 3. Potential
pitfalls of the measurement are presented in section 4. We finish with a brief discussion of the implications
of an accelerated expansion and conclusions (x5).
2 Type Ia supernovae in cosmology
2.1 Probing the nature of cosmological redshifts through time dilation
The regular temporal behavior of SNe Ia provides a simple, yet important, test of the basic interpretation
of redshift as due to cosmic expansion. The most stringent indication of this has been the uniformity
of the cosmic microwave background (Mather et al. 1990, Peebles et al. 1991). A direct proof for the
expansion, however, had been missing but is provided by a clock at high redshift. The SN Ia light curves
have been proposed as such a clock and can also be used to search for any evolutionary effects in the
explosion (Wilson 1939, Colgate 1979, Tammann 1979, Leibundgut 1990). The fundamental nature of
the cosmological redshift can be probed with a single distant supernova and the assumption that it does
not differ significantly from nearby ones. Such an analysis became possible for the first time with light
curves of SN 1995K at a redshift of 0.48 (Leibundgut et al. 1996) and a small sample of five supernovae
from the Supernova Cosmology Project (Goldhaber et al. 1997). The same effect has been observed in
the spectral evolution of the distant SN 1996bj (Riess et al. 1997). The result strikingly demonstrates the
conventional interpretation of redshift being an effect of the cosmic expansion rather than any theories
involving connections of redshift with an energy loss of the photon. SN 1995K could not be explained in
a non­expanding Universe unless it would have had unprecedented attributes (Leibundgut et al. 1996).
In particular, the light curve shape would have made it the slowest declining SN Ia observed ever with
a spectrum basically indistinguishable from local SNe Ia (Schmidt et al. 1998). This is contrary to all
correlations found in the local sample. Nonetheless, other interpretations of these observations have been
advanced as well (Narlikar & Arp 1997, Segal 1997).
2.2 Cosmological distances from standard candles
Distance measurements from SNe Ia are made through a modified standard candle scheme, where lumi­
nosity distances are derived. This is a very simple test of the global geometry which has been proposed for
several decades (Heckmann 1942, Robertson 1955, Hoyle & Sandage 1956, Sandage 1961) for a number
of standard candle candidates. The assumption in this method is that the luminosity evolution of the
standard candle is negligible or at least can be measured accurately. For SNe Ia it is generally assumed
that their maximum luminosity does not change as a function of cosmic age. We will discuss this as­
sumption below (x 4.2). For an exact standard candle the cosmological parameters are described in the
implicit equation
DL = (1 + z)c
H 0 jŸj 1=2
S
ae
jŸj 1=2
Z z
0
[Ÿ(1 + z 0 ) 2
+\Omega M (1 + z 0 ) 3
+\Omega \Lambda ] \Gamma1=2 dz 0
oe
(e.g. Carroll et al. 1992).
Here\Omega M = 8úG
3H 2
0
ae M stands for the matter content, which depends only on
the mean matter density of the universe ae M ,
and\Omega \Lambda = \Lambdac 2
3H 2
0
describes the contribution of a cosmological
constant to the expansion factor. Ÿ is the curvature term and obeys
Ÿ = 1
\Gamma\Omega M
\Gamma\Omega \Lambda :
The integration provides the cosmological distance element out to the source redshift z.
S(ü) takes the form
S(ü) =
8
!
:
sin(ü) Ÿ ! 0
ü for Ÿ = 0
sinh(ü) Ÿ ? 0:
The change of the expansion rate, usually denoted as the deceleration parameter q 0 , is defined as q 0 =
\Omega M
2
\Gamma\Omega \Lambda .

The supernova distances are measured as the distance modulus
m \Gamma M = 5 log(DL ) + 25
with the luminosity distance in units of megaparsecs. The most probable values of the cosmological
parameters are then found in a least squares fit, possibly assuming certain boundary conditions (Riess
et al. 1998, Perlmutter et al. 1998, Leibundgut 1998). It has to be noted that the present­day value of
the Hubble constant, H 0 , is not of relevance in the determination of the energy density of the Universe,
but rather depends on the zero­point which is derived from the nearby supernovae. The deceleration is
entirely measured from the apparent magnitude differences between the nearby sample and the distant
supernovae. With a sufficiently large redshift range the degeneracy
between\Omega M
and\Omega \Lambda can be broken
by standard candles (Goobar & Perlmutter 1995). A much more effective way, however, is to find a
measurement which depends on the cosmological parameters in a different way. This can be achieved by
the comparison of the supernova result with measurements of the cosmic microwave background (White
1998, Eisenstein et al. 1998, Garnavich et al. 1998b).
2.3 Type Ia Supernovae as standard candles
­20 0 20 40 60 80 100
t [days]
41.0
41.5
42.0
42.5
43.0
43.5
log
L
[erg/s]
SN 1992bc
SN 1991T
SN 1995D
SN 1994D
SN 1992bo
SN 1994ae
SN 1989B
SN 1992A
SN 1991bg
Figure 1: Bolometric light curves of nearby SNe Ia (Contardo et al. 1999).
Recent years have seen a dramatic increase in observational material on SNe Ia. Well­sampled light
curves in many filters have been assembled for about 50 nearby supernovae (z ! 0:1; Hamuy et al. 1996a,
Riess et al. 1999). The first secure absolute distances from direct Cepheid measurements of SNe Ia have
confirmed that they exhibit a very small scatter in their maximum light luminosity (Saha et al. 1998,
Tammann in this volume). These results are used to refine our understanding of the explosive events. The
most important result for cosmological applications of SNe Ia is the nearly uniform luminosity and the
possibility to correct for variation in the peak luminosity by a distance independent parameter, i.e. the
decline from maximum during the first two weeks (Phillips et al. 1993, Hamuy et al. 1996b, Riess et al.
1996, 1998). It seems that SNe Ia can be described fairly well as a one parameter family as many different
parameters correlate with the decline rate. The decline rate, usually denoted as \Deltam 15 for the B band,
correlates with the peak luminosity (Hamuy et al. 1996a, Riess et al. 1996), the expansion velocity of the
ejecta (Mazzali et al. 1998), the color at maximum light (Hamuy et al. 1996b, Riess et al. 1996, Branch

1998), the galaxy type (Hamuy et al. 1996b, Riess et al. 1996, 1999), line ratios of certain elements
(Nugent et al. 1995), and possibly with the late­decline rate of individual filter light curves (Hamuy et
al. 1996c). Most of these correlations have been established for B and V filters. The correction to the
luminosity at maximum is at heart of the use of SNe Ia to measure cosmological distances.
Despite these well­established correlations some questions remain as to the exact nature of these explo­
sions. The bolometric light curves constructed from the optical data do not show such a nice correlation
with the decline rate. Fig. 1 displays a set of bolometric light curves of well­observed, nearby SNe Ia.
It is obvious that the second maximum observed in the I (Suntzeff 1996, Ford et al. 1993) and the
near­infrared light curves (Elias et al. 1985) also appears in the bolometric light curves (Contardo et al.
1999). This was originally pointed out by Suntzeff (1996) for the bolometric light curve of SN 1992A.
The strength of this inflection varies between individual events. A clear trend of luminosity and strength
of the inflection is not detected and there seems to be another parameter governing the energy release
from the fireball. Surprisingly the decline of the bolometric light curve of SN 1991bg does not differ from
the one of the other SNe Ia. This is in marked contrast to the filter light curves of this supernova. The
B and V light curves of SN 1991bg declined much faster than for any other known SN Ia (Leibundgut et
al. 1993, Turatto et al. 1996).
It should also be stressed that we currently do not understand the physics for the decline -- luminosity
relation (see, however, H¨oflich et al. 1996). The hydrodynamics and the radiation transport of the SN Ia
ejecta is fairly uncertain and a number of models have been proposed (Arnett & Livne 1994, Woosley
& Weaver 1994, Khokhlov et al. 1993, H¨oflich & Khokhlov 1996). Supernova atmospheres are far from
thermal equilibrium as demonstrated by the lack of emission in spectral regions with none or few emission
lines (Spyromilio et al. 1992) or the occurrence of maximum luminosity in different filter bands (Contardo
et al. 1999).
The exact stellar evolution which leads to the progenitors of SNe Ia is not understood and a variety
of astronomical objects has been proposed (cf. Branch et al. 1995). Also the explosion physics have
not been solved yet. A number of explosion models has been proposed, but observational distinctions
have eluded us so far. These uncertainties have to be addressed in any serious application of SNe Ia for
cosmology.
3 Evidence from distant supernovae for a cosmological constant
The High­z Supernova Team was formed in 1994 to pursue the observations of distant, i.e. z ? 0:3,
supernovae. The team members have access to almost every major telescope and are located on four
different continents. The current tally is at 116 candidate supernovae discovered with 45 spectroscopically
confirmed SNe Ia (Woudt et al. 1999). We will concentrate on the first ten fully reduced objects as
published by Riess et al. (1998).
A number of corrections have to be applied to the data before luminosity distances can be derived.
Technical problems include the accurate photometry as most supernovae are very faint. The photometry
then has to be converted to the rest frame of the supernova. This K­correction is not only a function of
redshift and phase, but also depends on the decline rate and spectral appearance of the supernova. All
light curves are then corrected for time dilation by dividing the phases with (1+z). The reddening of the
distant supernovae is determined from the intrinsic rest frame color. A reddening correction is applied
either implicitly in the multi­color light curve shape method (Riess et al. 1996) or as an extra step when
the \Deltam 15 procedure is used. Indeed, only one or two objects in our sample show significant reddening
(Riess et al. 1998). Finally, a correction for the light curve shape is applied to the distant supernovae.
The correlation establishing this correction is based on a large sample of nearby supernovae (Hamuy et
al. 1996a, Riess et al. 1999). It is important to realize that the relation has to be derived for the local
sample in exactly the same way as it is applied to the distant set. In particular, the same filter set and
also the same phase range have to be applied, in order not to introduce additional parameters which
are not measured for the distant supernovae (Riess et al. 1998). Interestingly, the significance of the
derived result strongly depends on the control of the local sample (Riess et al. 1998, Leibundgut 1998).
A detailed discussion of these corrections and their accuracies is given in section 4.1.
For each supernova a luminosity distance is derived in this way. Comparison to theoretical models is
then made through a modified Hubble diagram where the luminosity distance, i.e. distance modulus, is
plotted vs. the redshift (Fig. 2). The local supernovae determine the locus of all models in the linear
expansion regime (out to z ú 0:1). It is the relative distances of the high­z supernovae compared to the

32 34 36 38 40 42 44 46
­2
­1.5
­1
­.5
0
m­M
log
z
(1.0,0.0)
(0.0,0.0)
Dm 15
(W M ,W l )
Figure 2: Hubble diagram of local and distant supernovae (data from Riess et al. 1998). The curves
indicate the distance vs. redshift evolution in an Einstein­de Sitter (full line) or an empty Universe
(dotted line).
Table 1: Summary of the results on the cosmological parameters from SNe Ia
Method
\Omega M
\Omega \Lambda age
P(\Omega \Lambda ? 0) P(q 0 ! 0)
(10 9 years)
MLCS : : : : : : 14 2.9oe 2.4oe
\DeltaM 15 : : : : : : 15 3.9oe 3.8oe
MLCS+SN 1997ck 0.00 +0:60
\Gamma0:00 0.48 +0:72
\Gamma0:24 14 2.8oe 2.7oe
\DeltaM 15 +SN 1997ck 0.72 +0:44
\Gamma0:56 1.48 +0:56
\Gamma0:68 15 3.8oe 3.7oe
local sample which provides the information on the change in the expansion.
It is evident in this figure that the data for the distant SNe Ia do not follow either model plotted. They
are compared to the Einstein­de Sitter
models(\Omega M =
1;\Omega \Lambda = 0) and an empty Universe without matter
and no contribution of a cosmological
constant(\Omega M =
0;\Omega \Lambda = 0). While the Einstein­de Sitter model is
clearly ruled out, a model with no mass density and no cosmological constant is also not a good fit. The
distant supernovae all lie below, i.e. at larger distances, than the expectations from these models. This
becomes even clearer when the Hubble diagram is normalized to the empty Universe model (Fig. 3).
The distant SNe Ia show a systematic trend towards distances which appear to be even larger than in
a freely coasting universe. The distant SNe Ia are about 0.2 magnitudes from the dividing line of an
empty Universe. If the luminosity of SNe Ia has not changed since z ú 0:5, the mean of the redshift
distribution, then we are forced to admit that the distances of these objects have to be larger than in a
non­decelerated Universe, and an acceleration has boosted the distances. The most obvious candidate
for such an acceleration is a positive cosmological constant.
Of course, the caveat of any luminosity evolution or other subtle systematic effects have to be critically
reviewed before this result can be accepted. We will come back to these issues in section 4.2.
The luminosity distances are most sensitive to the
combination\Omega M
\Gamma\Omega \Lambda (e.g. White 1998, Eisenstein
et al. 1998). Thus, the supernovae determine an uncertainty region nearly perpendicular to the flat
geometry solutions. For our data set we find that any solutions for a positive matter density require
also a contribution of a cosmological constant. The confidence intervals are given in Table 1. We do not
have a large enough redshift range for an accurate determination
of\Omega M
and\Omega \Lambda independently. Despite
this current limitation we find a very high confidence limit for a cosmological constant and even an
acceleration of the universal expansion since the time the SNe Ia exploded.

­2 ­1.5 ­1 ­.5 0
­.5
0
.5
z
d(m­M)
Figure 3: Distance differences from the individual supernovae from the expected line in an empty Universe.
4 Systematic error sources
There are number of effects which possibly could alter the result we found in the previous section. They
can be roughly divided into two classes. Technical impediments, like accurate photometry, K­corrections,
light curve sampling, sample contamination, and selection effects can be controlled by adequate observing
and reductions strategies. Fundamental problems arise from possible gravitational amplification or de­
amplification, absorption, and evolution of SNe Ia explosions.
4.1 Corrections to the observed data
Accurate photometry is a pre­requisite for the determination of the peak brightness of the objects.
The most important contaminant is the background light from the galaxy on which the supernova is
superposed. In many cases, the underlying host galaxy light has to be carefully subtracted. As the
supernova fades these problems are exacerbated. This is particularly important as the decline rate is
determined by the later phase, i.e. fainter, observations. The individual photometry points are then
corrected for the effects of the redshift. The observed flux has to be converted to a rest frame magnitude
to be comparable to the local SNe Ia. These K­corrections are time­dependent and have to be determined
from nearby supernovae over the whole range of the light curve. A slight dependence of the K­corrections
on the decline rate, i.e. the intrinsic color, of the supernova has been noted (Riess et al. 1998) and has
to be included. Despite the complications in this process a very good accuracy has been obtained (e.g.
Schmidt et al. 1998), as the problem can be controlled very well and only depends on the availability of
sufficient data on nearby supernovae.
Since the peak magnitudes are required to determine the decline parameters and the distances, a well­
sampled light curve is needed for each supernova. Global observing campaigns are organized to achieve
this goal. The critical observations near maximum and about two weeks after maximum, which are the
most crucial for the determination of the peak magnitude and the decline­rate corrections, are virtually
guaranteed by the search technique for the distant supernovae (Perlmutter et al. 1997, Schmidt et al.
1998). The sample of local supernovae is large enough that we can select suitable subsamples (Hamuy et
al. 1996b, Riess et al. 1999). For well­sampled light curves the errors of the light curve parameters are
significantly reduced.
A critical evaluation of each object in the sample for its supernova type is unavoidable. Since the
classification for supernovae is based on spectroscopy near maximum light (Harkness & Wheeler 1990,
Filippenko 1997), it is imperative to obtain a spectrum of each object. Occasionally the spectrum is
not decisive enough and even the combination with the light curve can not exclude ambiguities. In the
sample discussed here we have one object for which it was not possible to unambiguously determine its

classification (Riess et al. 1998). For another object, SN 1997ck at z = 0:97, it was not possible to obtain
a spectrum. Exclusion of these objects from the sample does not change our results (Table 1).
Selection effects could change the result. A recent discussion of the Malmquist bias by Teerikorpi (1998)
demonstrates that such an effect, if not detected, could yield to an underestimate of the deceleration. In
effect, since there is some intrinsic scatter for every standard candle, the volume which is sampled for
a standard candle at a given redshift is biased to a larger distance than indicated by the straight mean
magnitude and the distances are over­estimated. Basically, the volume sampled at m+ oem is larger than
the one with m \Gamma oem, where oem is the scatter of the standard candle. This effect works in all magnitude
limited samples. For the distant supernovae one also has to consider that some objects may have been
missed by the search. Fortunately, the scatter of the nearby sample of SNe Ia shows such a small range
(0.15 mag, Schmidt et al. 1998) that the expected systematic errors are still smaller than the total offset
measured for the distant SNe Ia.
4.2 Astrophysical influences
Gravitational lensing of distant objects is unavoidable. Most importantly the apparent brightness can
be changed due this effect. Since gravitational amplification is wavelength independent it can not be
detected in the objects' light directly. For SNe Ia this is the only effect which can not be inferred from
the SN observations alone. Mapping of the gravitational potential along the line of sight is required (e.g.
Wambsganss et al. 1998). The redshift out to which SNe Ia have been observed so far is not large enough
to suffer from any significant influence from gravitational lensing (Wambsganss et al. 1997, Holz 1998).
Even in the most extreme case where all matter is clumped ('empty beam') our result of an accelerated
expansion will not change significantly (Holz 1998).
A possible explanation of the apparent faintness of the distant supernovae could be absorption. All
observations are corrected for absorption by the Galaxy. Observing in two filter bands should allow us
to detect absorption in the host galaxy. This implicitly assumes that the intrinsic color evolution of all
SNe Ia can be traced and that the reddening law is the same at z = 0:5 as in our Galaxy. Any absorption
at other redshifts is not considered. The average column density as measured from QSO absorbers out
to z ú 0:5 is small and can be ignored. Most distant SNe Ia have a very small absorption. This is due
to two selection effects. First, heavily absorbed supernovae are less likely to be discovered and, second,
the spectroscopic follow­up observations concentrate mostly on SN candidates well separated from the
galaxies to avoid strong contamination from the galaxy light. Thus, we do expect rather small reddening
for most of the distant supernovae. It is unlikely that dust extinction systematically affects the distances
to mimic the observations. This is because, significant absorption along certain sight lines would increase
the scatter in the observed distances. This is not observed (Riess et al. 1998).
A most critical assumption is the equivalency of the distant supernovae to the local ones. Any evolution
of the supernovae as a function of, e.g. progenitor age, could influence the peak luminosity of the light
curve. After all, the distant supernovae exploded some 5 Gyr earlier than the ones in the local Universe.
The lack of detailed explosion models currently prevents a robust theoretical prediction. An attempt was
made to investigate the influences of a number of parameters on the light curves (H¨oflich et al. 1998).
The strongest effect found was the chemical composition of the progenitor star which could change the
blue part of the optical spectrum. The influence is rather small, however. An empirical test for the
similarity of the distant SNe Ia with the local ones is by comparing the observational properties of the
distant sample to the nearby one. The currently available spectroscopy has not detected any significant
deviations (Riess et al. 1998, Perlmutter et al. 1998). In most cases, the spectra are not of high enough
quality to guarantee this result, but the few objects with excellent spectroscopy show the same evolution
as for nearby SNe Ia (Riess et al. 1997, 1998, Perlmutter et al. 1998). The rest­frame colors and the
light curve shapes of the distant objects also do not deviate. We are faced with the possibility that all
measurable distance independent quantities of SNe Ia appear unchanged, while the luminosity could have
changed. This is a rather unlikely proposition, but will need more critical scrutiny.
Possible sample differences, as typically produced by a selection bias, have to investigated as well. The
global sample properties of the local and distant sample have been found to be very similar (Riess et al.
1998, Leibundgut et al. 1999). The good standard candle quality of SNe Ia is a very important asset in
this respect.

5 Discussion and Conclusions
Distant SNe Ia provide striking evidence for an acceleration of the universal expansion over the last
¸ 6 Gyr. Commonly such an acceleration has been identified by the possible contribution of a vacuum
density, i.e. cosmological constant. This is the first clear indication for the existence of a significant
vacuum density. The cosmological constant acts like a negative pressure term for the expansion. It is
possible to examine the equation of state of the Universe in more detail by splitting the contributions to
the geometric term in the equation for the luminosity distance into the several components (Garnavich et
al. 1998b). By doing so the dominant source of the acceleration can be determined. The best fit to the
data is using a component very similar to the cosmological constant where pressure is proportional to the
negative density (P / \Gammaae). Topological defects could also be responsible. A network of non­commuting
cosmic strings would have an average effective relation of P / \Gamma ae
3 , but are excluded for any flat spatial
geometry(\Omega total = 1).
It is interesting that the best cosmological parameters found in our study provide an age estimate of
the Universe which is in agreement with the oldest stellar components. The age we find (Table 1) is
about 14 Gyr, which comfortably includes the globular cluster ages (Riess et al. 1998). The fact that the
Universe has suffered from an accelerated expansion means that the simple extrapolation based on the
present­day value of the Hubble constant underestimates the age of the Universe.
As mentioned in the introduction, the combination of the supernova result with accurate measurements
of the cosmic microwave background (CMB) fluctuations provides the possibility to restrict the allowed
range in
the\Omega M
\Gamma\Omega \Lambda plane considerably (White 1998, Eisenstein et al. 1998). The two measurements are
almost orthogonal in this parameter space. A first attempt was made by White (1998) and Garnavich et
al. (1998b) combining the supernova data with the constraints found on the CMB (Hancock et al. 1997).
The combined constraints give a narrow region
around\Omega M = 0:3
and\Omega \Lambda = 0:7 with 3oe confidence limits
reaching from about \Gamma0:2
!\Omega \Lambda ! 1:3
and\Omega M ! 1:0 (Garnavich et al. 1998b). The Einstein­De Sitter
model is excluded by many oe.
A number of distant SNe Ia have been already observed and are about to be analyzed and published.
The Berkeley Supernova Cosmology project is publishing a large set of supernovae (Hook, this volume,
Perlmutter et al. 1999). The High­z team expects to have about 20 additional SNe Ia analyzed next
year. The supernova sample has increased to a size where statistical uncertainties are not important any
more. It is the systematic error sources described in section 4.1 and 4.2 which dominate the uncertainty
in the measurements. They will have to be tackled one by one. The most important seems currently the
question of evolution. We need a much better understanding of the spectral evolution of SNe Ia at high
redshift. This implies that spectroscopy not just for the classification of the object, but for a detailed
spectral analysis will have to be obtained. In addition, programs to investigate the environment of the
distant supernovae and compare them to the local sample are under way. They include the study of the
parent galaxy morphology and metalicities.
The CMB constraints will improve with the future space missions of MAP and PLANCK. There are
excellent prospects that the value
of\Omega M
and\Omega \Lambda will be pinned down fairly accurately in less than 10
years from now.
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