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Cosmology with Supernovae
Bruno Leibundgut
European Southern Observatory
Karl­Schwarzschild­Straúe 2, D­85748 Garching, Germany
Bruno.Leibundgut@eso.org;
http://www.eso.org/#bleibund
Abstract
Modern cosmology is using many different methods to determine the structure
of the universe. Supernovae are among the most important ones due to their
extreme luminosity, the time­variability that allows to separate the different su­
pernova explosions and relative ease with which they can be observed.
Since the recognition of supernovae as a separate class of astrophysical
objects they have been proposed and used to measure the distance scale and the
geometry of the universe.
There are several independent applications with supernovae to measure the
current expansion rate, Hubble's constant, and the expansion history of the uni­
verse. The latter has led to the surprising discovery that the expansion is actu­
ally accelerating and a new component for the universe is needed. Supernovae
are also poised to be a major player in the characterisation of the nature of the
dark energy.
1 Introduction
In a small, but very influential, book Otto Heckmann (1942) summarised the sta­
tus of cosmology after the major theoretical developments were done in the first
decades of the 20 th century. In that monograph, he developed the tools required for
observers to measure the parameters, which govern the history of the universe. The
cosmology he described is the same we use for the interpretation of modern data.
It is based on the assumption that the universe is governed essentially by gravity,
described through the theory of general relativity, acting in a globally homogeneous
and isotropic background.
About a decade before Heckmann published his book, two European astronomers
in California described supernovae as a distinct class of exlosive events in the uni­
verse. Walter Baade and Fritz Zwicky (1934) realised that supernovae are explo­
sions on a stellar scale with cosmological consequences. The first to suggest that
there might be a class distinct from ordinary novae was Lundmark (1925). He
based his proposal mostly on the observation of `S Andromeda' observed in 1885
Reviews in Modern Astronomy 17. Edited by R. E. Schielicke
Copyright c
# 2004 Wiley­VCH Verlag GmbH & Co. KGaA, Weinheim. ISBN 3­527­40476­7

222 Bruno Leibundgut
(designated SN 1885A in modern nomenclature), which appeared about 10 mag­
nitudes brighter than a sample of about two dozen regular novae in the Andromeda
galaxy. Lundmark later seemingly was also the first to suggest the name `super­nova'
(Lundmark 1932).
Here I review the current status of supernova cosmology. I will concentrate on
the discovery of the accelerated expansion of the universe, often encapsulated in the
designation `Dark Energy', through the use of Type Ia supernovae. The problems
connected with the determination of the Hubble constant will be touched upon first,
however.
There are some recent monographs and review articles available on supernovae.
Last year two books on supernovae appeared (Hillebrandt & Leibundgut 2003 and
Weiler 2003). Specific reviews on Type Ia supernovae are Leibundgut (2000) and
Meikle (2000). Reviews dealing with supernova cosmology can be found in Perl­
mutter & Schmidt (2003), Leibundgut (2001) and Riess (2000).
The recent paradigm changes in the cosmological model are based on several
new insights. The flatness of space­time as measured by the cosmic microwave
background (CMB) fluctuations and the recognition, that the global matter density
is near 30 % of the critical density, require an additional component in the energy
content of the universe. At the same time the observation that the luminosity dis­
tances derived from Type Ia supernovae are larger than the expectation in any non­
accelerated universe model have conspired to change our view of the history of the
cosmic expansion. The three measurements are complementary to each other and
the combination of any two of them provides independent evidence for an additional
component in the Friedman equation. However, only the supernova measurement
gives a direct indication that we need a repulsive component in the universe. It will
also be the supernovae that will provide a first indication to the nature of the dark
energy.
2 Supernova Cosmology
Cosmology with supernovae has developed over the second half of the last century.
Their extreme luminosities always made them attractive candidates to measure large
distances. Various methods were devised to use supernovae to measure cosmological
parameters ranging from simple standard candle paradigms to physical explanations
of the supernova explosions and subsequent derivation of distances. Essentially, su­
pernovae have been used to determine luminosity distances, i. e. the comparison of
the observed flux to the total emitted radiation. The luminosity distance DL is de­
fined by
DL = # L
4#F (1)
with the absolute luminosity of the object L and the observed flux F . Of course, this
is nothing but the inverse square law. The trick is to find a reliable way to measure
the absolute luminosity of the objects.
There are several fundamental tests that will need to be performed until we can
be sure that the current paradigm will persist. It is very appealing to think we know

Cosmology with Supernovae 223
all constituents of the universe by now, but further surprises may still be in store for
us. The testing has to concentrate on the reliability of the individual measurements.
The Type Ia supernovae have been criticised for the fact that they are based on a
rather simple assumption, namely that the distances derived from them are accurate.
Many publications oversimplify this picture by calling Type Ia supernovae standard
candles. This is not only incorrect, also it is misleading and belittles the result. The
tests done on supernovae are solid and the theoretical work is progressing steadily.
There are two major cosmological parameters that can be determined through
supernova observations. They are the classical parameters, which govern the expan­
sion of the universe in Friedmann­Robertson­Walker models: the Hubble constant,
H 0 = —
R/R, i. e. the first time derivative of the cosmic scale parameter R, and the
deceleration parameter, q 0 = - ˜
RR/ —
R 2 (see section 4 for the detailed equations for
these entities and some historical remarks about their use). The former sets the scale
of the universe and the magnitude of the current expansion of space and the latter
describes the change of the expansion with time (e. g. Sandage 1961, Sandage 1988,
Weinberg 1972, Peebles 1993, Peacock 1999). There is a rich literature on the Hub­
ble constant and Type Ia supernovae (SNe Ia) (see Branch & Tammann 1992, Branch
1998, Leibundgut 2001 for reviews). The deceleration parameter has been replaced
by more modern formulations specifically including the cosmological constant or
some variants thereof (Carroll et al. 1992).
3 The Hubble Constant
3.1 Type Ia Supernovae
The best way to show that objects provide good luminosity distances is to plot them
in a Hubble diagram. Originally, this diagram was using recession velocity vs. ap­
parent magnitude (Hubble 1936, Sandage 1961). The underlying assumptions are
that the Hubble law of linear cosmic expansion holds and that the objects are all of
the same luminosity, i. e. standard candles, so that the apparent brightness directly
reflects distance.
Since no astronomical standard candle is known -- all proposed objects have been
shown to be essentially non­uniform in one way or another -- we nowadays have to
calculate and plot the distance modulus for the objects. The scatter around the linear
expansion line is less than 0.2 magnitudes or 20 % (Tonry et al. 2003). Independent
of our ignorance of the exact explosion mechanism or the radiation transport in the
explosions (see discussions in Hillebrandt & Niemeyer 2000 and Leibundgut 2000
on outstanding problems with SN Ia physics) this proves that SNe Ia can reliably
be used as a distance indicator in the local universe. This situation is very much
comparable to the Cepheid stars, where the period­luminosity relation is based on
empirical data of objects in the Magellanic Clouds.
3.1.1 Type Ia Supernovae as Standard Candles
How well do SNe Ia fare as standard candles? The raw, uncorrected scatter of well­
observed supernovae is around 0.2 to 0.4 magnitudes (Tammann & Leibundgut 1990,

224 Bruno Leibundgut
Sandage & Tammann 1995, Parodi et al. 2000). These translate into uncertainties of
about 10 % to 20 % in distances.
However, some SNe Ia have been observed that clearly were much fainter (about
2.5 magnitudes, i. e. corresponding to a full factor of 5 in distance!). From direct
distance measurements to SNe Ia the luminosity appears to be rather uniform, but
only a limited sample is available for this test (Saha et al. 1999). At first sight the
case for SNe Ia is unclear.
The standard candle character does not only imply that the objects always reach
the same luminosity at maximum, but that they also have a uniform appearance.
Since supernovae are variable phenomena their light curves and spectral evolution
can be checked for uniformity. The observables of supernovae are the light curves
(at different wavelengths), the colour evolution, the details in their spectrum (line
strengths, abundances and velocities), the luminosity (again at different wavelengths)
and the supernova environment. In addition, there are several correlations between
observables that have been used.
The most intriguing feature of SNe Ia -- and critical for the distance determination
-- is the relation between the light curve shape and the peak luminosity. This immedi­
ately shows that SNe Ia are not standard candles, but they can be normalised to give
exceedingly accurate relative cosmological distances. First found by Phillips (1993),
the correlation has been elaborated in different forms in Hamuy et al. (1995, 1996),
Riess et al. (1996, 1998), Perlmutter et al. (1997), Tripp (1998), Tripp & Branch
(1999), Phillips et al. (1999) and Goldhaber et al. (2001). Essentially, there are three
methods describing this relation: the original template method (often referred to as
#m 15 ), the multi­colour light curve shape (MLCS) relation and the stretch relation.
The easiest test is provided by SNe Ia in the cosmic expansion flow. Phillips et al.
(1999) found that the scatter around the expansion line, after correction for extinc­
tion and light curve shape is 0.15 magnitudes in B and 0.18 in V , i. e. better than
10 % in relative distances.
Direct distance measurements through Cepheids have found a scatter in the aver­
age absolute magnitude of SNe Ia at maximum of 0.15 magnitudes (0.05 as error of
the mean, Saha et al. 1999). Figure 1 shows the tight relation SNe Ia define around
the expansion line in the Hubble diagram. The slope of this line is fixed for all cos­
mological models with a linear expansion in the local universe. The SNe Ia trace
this line exceedingly well with a fitted slope of 5.069 ± 0.053 (see also Tammann &
Leibundgut 1990, Riess et al. 1996). The 108 objects (taken from Tonry et al. 2003)
in the redshift range from 0.01 to 0.1 show a scatter of 0.20 magnitudes around the
canonical line. Parodi et al. (2000) find a scatter of less than 0.13 magnitudes for a
comparable sample. The intercept for zero redshift together with the absolute lumi­
nosity of SNe Ia provides the Hubble constant (e. g. Leibundgut & Pinto 1992). It is
the exact value of the absolute peak magnitude of the SNe Ia, which contributes the
major uncertainty in this measurement and the ongoing debate.
While there is general agreement that the light curve shape corrections provide
a great improvement over the use of SNe Ia as pure standard candles, it has to be
noted that the individual methods do not produce identical corrections for a given
supernova data set (Drell et al. 2000, Leibundgut 2000). The MLCS (Riess et al.
1996, 1998) and #m 15 (Hamuy et al. 1996, Phillips et al. 1999) method yield similar

Cosmology with Supernovae 225
Figure 1: Hubble diagram of nearby Type Ia supernovae. The distances are derived from
light curve shape corrected luminosities (data from Tonry et al. 2003).
corrections with an offset for different normalisations, but with a scatter much larger
than the typical errors. The stretch method (Perlmutter et al. 1997, Goldhaber et al.
2001) deviates significantly in its mean corrections. The reasons for these discrep­
ancies have yet to be resolved.
It should be noted that the correlations have been mostly determined for the B
and V bands, but strong deviations are apparent in all other filter light curves. Most
striking is the time evolution in the near infrared where the light curves display strong
secondary maxima between 20 and 40 days after maximum depending on filter and
supernova (Meikle 2000, Krisciunas et al. 2003). It is this characteristic together
with the peculiar objects that are the most obvious indicator that SNe Ia can not be
considered as standard candles.
Attempts to include several filter light curves for a multi­dimensional normalisa­
tion include MLCS (Riess et al. 1996, 1998), the #m 15 method (Phillips et al. 1999)
and a multi­colour stretch method (Wang et al. 2003). It has to be seen whether
the physics can be evaluated sufficiently to put these empirical methods onto a firm
theoretical basis.
For the best­studied objects subtle differences in all light curves are becoming
more and more apparent (Stritzinger et al. 2002). Clearly, the differences are not
very large, but they are real and hamper our ability to employ the normalisation. We
should start to consider that no two SNe Ia are identical.
Other parameters that are showing differences among SNe Ia are the colours
and the epochs of maximum light. The colours are difficult to disentangle from
the absorption, but a significant difference between a sample of nearby SNe Ia and
distant ones has been pointed out (Leibundgut 2001). The majority of the distant
objects is bluer than the bluest SNe Ia in the nearby universe. This can not be due to
dust as we expect to observe at least some of the nearby objects with their intrinsic

226 Bruno Leibundgut
colours and not affected by dust in the host galaxies. Although there could be a
selection effect at work, this distinction is worrisome. Note, however, that this effect
is not present in Knop et al. (2004) and Riess et al. (2004). Both of these analyses are
using different methods and improved K­corrections. Unfortunately, the details of
how the reddening and the intrinsic colours were derived are not provided in either
publication.
Most surprisingly a new study of infrared light curve finds that SNe Ia might be
rather accurate standard candles in the near­infrared (Krisciunas et al. 2004). The
first significant IR sample shows very small scatter without prior correction for light
curves shape.
3.1.2 The Nearby SN Ia Hubble Diagram
One has to adopt that the luminosity normalisation of the distant objects follows what
has been found in the nearby sample. Although the High­z Supernova Search Team
(HZT; Schmidt et al. 1998, Riess et al. 1998, Tonry et al. 2003, Barris et al. 2004) and
the Supernova Cosmology Project (SCP; Perlmutter et al. 1999, Knop et al. 2004)
make this assumption in different forms, it is essentially identical. The SCP derives
the corrections from all supernovae in their sample, i. e. nearby and distant ones,
while the HZT derives the correlations from the (large) nearby sample and applies it
to the distant objects (cf. Leibundgut & Suntzeff 2003). It is also interesting to note
that the SCP claims that both light curve shape correction and correction for host
galaxy reddening affect their result rather little (Perlmutter et al. 1999, Knop et al.
2004). On the other hand, the normalisation and absorption correction done by the
HZT (in three different implementations) are important for the cosmological result.
This discrepancy between the two teams will need to be resolved at some point.
The first to plot a Hubble diagram of Type Ia Supernovae was Kowal (1968).
There are essentially three quantities that can be derived from such a Hubble diagram
in the nearby universe: the slope of the expansion line, the scatter around the expan­
sion line and the value of the local Hubble constant from the intercept at zero redshift
(e. g. Tammann & Leibundgut 1990, Leibundgut & Pinto 1992). The slope gives an
indication of the local expansion and for a linear expansion in an isotropic universe
it has a fixed value. The scatter around the expansion line provides a measure of the
accuracy of the standard candle and the measurement errors. The intercept of the
line, finally, together with an estimate of the absolute luminosity gives the Hubble
constant.
More accurate light curve data are becoming available (e. g. Krisciunas et al.
2001, 2003, Li et al. 2001, 2003, Candia et al. 2003, Benetti et al. 2004) and it should
be possible to further investigate the correlations between light curve shape, colour
and luminosity of SNe Ia. For these reasons modern Hubble diagrams show the dis­
tance modulus (m - M ) rather than the directly observed apparent magnitude m.
The latest version with over 200 SNe Ia has been assembled by Tonry et al. (2003;
see also Barris et al. 2004 and Riess et al. 2004) and is shown in Figure 1. For the
derivation of the Hubble constant the (normalised) luminosity of the SNe Ia has to
be known. The most direct way to achieve this is through the distance ladder and in
particular the calibration of nearby SNe Ia by Cepheids (for the most recent results

Cosmology with Supernovae 227
see Saha et al. 1999, Freedman et al. 2001). The main discrepancy for the published
values of the Hubble constant from SNe Ia is coming from the different interpre­
tations of the Cepheids, the assumed distance to the Large Magellanic Cloud and
application of the light curve shape correction.
The problem with this measurement is apparent from Fig. 1. At very low red­
shifts (z < 0.01) the universal expansion field is disturbed by the Virgo cluster and
the recession velocity of the galaxies is not directly proportional to the distance. The
most distant galaxies with accurate Cepheid distances, however, have a recession ve­
locity of less than 1500 km s -1 , i. e. z < 0.05. Even at double the redshift the scatter
around the expansion line is still considerable. Hence connecting the supernovae
in the Hubble flow with the local counterparts with Cepheid distances leaves some
ambiguity on the correct value of the Hubble constant.
3.2 Core­collapse Supernovae
The brilliance of core­collapse supernovae has enticed people to investigate their
capabilities as distance indicators as well. Following early work by Baade (1926),
originally done for Cepheid stars, the expanding photosphere method (EPM; East­
man et al. 1996) has been applied to several supernovae. The most comprehensive
data sample has been assembled by Hamuy (2001). A critical test has become the
distance to SN 1999em, which was determined through EPM (Leonard et al. 2001,
Hamuy et al. 2002, Elmhamdi et al. 2003) and which also has a Cepheid distance
available (Leonard et al. 2003). The discrepancy is most likely attributable to the
fact that the correction factor for the dilution of the black body flux in EPM are
strongly model dependent and need to be calculated for each supernova individually.
Recently, Mario Hamuy has realised that the expansion velocity and the lumi­
nosity during the plateau phase correlate and that Type II SNe may be quite good
distance indicators (Hamuy 2003). The distance accuracy achieved this way can be
better than 20 %. These determinations are based on the physical understanding of
the plateau phase of SNe II and are linked to physics of the supernova atmosphere.
This means that they are independent of the distance ladder, which is needed, e. g.,
for the SNe Ia. Typical values for the Hubble constant from SNe II are in the range
of 65 to 75 km s -1 Mpc -1 (Hamuy 2003).
4 Cosmology with Standard Candles
The principle of standard candles is probably the simplest and most often used
method to measure cosmological parameters. The combination of the distance mod­
ulus and the Hubble law at small redshifts provides a direct way to measure the
Hubble constant, H 0 . The dimming of a standard candle as a function of redshift z
(z # 0.1) is described by
m = 5 log z + 5 log c
H 0
+M + 25. (2)
Given the fixed absolute magnitude M of a known standard candle any measure­
ment of the apparent magnitude m of an object at redshift z provides the value of

228 Bruno Leibundgut
Hubble's constant (in units of km s -1 Mpc -1 ). The speed of light c enters as a form
factor. This is typically shown in a Hubble diagram, m vs. log(cz) (cf. Fig. 1.)
For cosmologically significant distances, where the effects of the matter and en­
ergy content of the universe become substantial, the luminosity distance is defined
by the integration over the line element along the line of sight.
All early papers on this subject used the series expansion
m = 5 log z + 1.086(1 - q 0 )z + 5 log c
H 0
+M + 25 (3)
(Heckmann 1942, Robertson 1955, Hoyle & Sandage 1956, Humason et al. 1956).
Here, q 0 describes the deceleration of the expansion. The integral of the line element
can be solved analytically only in some specific situations (e. g. a negligible cos­
mological constant: Mattig 1958; special cases including a cosmological constant:
Mattig 1968). The earliest publications (McVittie 1938, Heckmann 1942) already
warned of the dangers involved in the expansion, which assumed a smooth form for
the derivatives of the scale factor. Mattig (1958) showed that for models without a
cosmological constant a second order term makes significant contributions. Mod­
ern versions of the expansions have now been developed (Visser 2003, Caldwell &
Kamionkowski 2004) and are used to explore the characteristics of dark energy (e. g.
Riess et al. 2004).
A modern derivation of the relations for an expanding universe with a cosmo­
logical constant is given in Carroll et al. (1992). Using the Robertson­Walker metric
the luminosity distance, DL , in an expanding universe, allowing for a cosmological
constant #, is
DL = (1 + z)c
H 0 |#| 1/2 S # |#| 1/2 # z
0
[#(1 + z # ) 2
+# M (1 + z # ) 3
+# # ] -1/2 dz # # . (4)
Here# M = 8#G
3H 2
0
#M stands for the matter content, which depends only on the
mean matter density of the universe #M ,
and# # = #c 2
3H 2
0
describes the contribution
of a cosmological constant to the expansion factor. # is the curvature term and obeys
# = 1
-# M
-# # . (5)
S(#) takes the form
S(#) = # # #
sin(#) # > 0
# for # = 0
sinh(#) # < 0.
(6)
The cosmic deceleration in these models is defined as
q 0
=# M
2
-# # . (7)

Cosmology with Supernovae 229
Figure 2: Systematic Hubble diagram of a standard candle. The upper panel shows the clas­
sical Hubble diagram with distance modulus vs. redshift. Lines of four cosmological models
are drawn. The lower panels are normalized to an empty universe.
The dimming of standard candles in different cosmological models is normally
displayed as a set of lines in the Hubble diagram (Sandage 1961, 1988, Perlmutter
et al. 1997, Schmidt et al. 1998, Riess et al. 1998). It is, however, more instructive
to plot a diagram of the magnitude differences between the various world models.
This is the form used in all modern publications of distant supernovae (e. g. Riess
et al. 1998, Perlmutter et al. 1999, Tonry et al. 2003, Knop et al. 2003, Barris et al.
2004, Riess et al. 2004, for reviews see Riess 2000, Leibundgut 2001, Perlmutter &
Schmidt 2003). Fig. 2 shows how this works. The magnitude difference of the lu­
minosity distances of a standard candle are displayed against the one expected in an
empty universe. The magnitude differences between the various cosmological mod­
els are more apparent in this diagram. While the presentation in the regular Hubble
diagram obscures the fine details, which are relevant for the measurement of the ac­
celerated expansion. A standard candle in an empty universe
(# M =
0,# # = 0)
would appear 0.17 magnitudes fainter at a redshift of 0.3 than in an Einstein­de Sitter
universe
(# M =
1.0,# # = 0). This difference increases to 0.28 mag at z = 0.5 and
0.54 mag for z = 1.0. These are small values considering how difficult the observa­
tions are and the corrections that are needed to obtain a significant measurement.
Figure 2 also shows that for any models with only attracting gravity, i. e. only
matter, no objects should lie in the region with #(m -M) > 0. In the old paradigm
this was an excluded region. The only way to populate this area in Fig. 2 with
standard candles is by moving them further away than in the freeling coasting, empty
universe, model.
The present­day cosmic deceleration, q 0 , combines all energy sources contribut­
ing to the change of the expansion rate of the universe. It thus represents a funda­
mental parameter for the description of the universe we live in. For models without

230 Bruno Leibundgut
the cosmological constant the fate of the universe is encapsulated in q 0 . With a cos­
mological constant the value of q 0 does no longer provide a unique combination of
# M
and# # (cf. equation 7).
For the Hubble constant the absolute distances are required, while for the mea­
surement of the cosmic expansion history relative distances are sufficient.
We emphasize that the value of the Hubble constant is not required for the deter­
mination of the combination of the cosmological
parameters# M
and# # , as can be
seen from the equation for the luminosity distance. The apparent magnitude differ­
ence of a standard candle measured at two different redshifts is sufficient under the
assumption that the absolute luminosity has not changed. Distant supernovae must
be compared to a set of nearby supernovae where the curvature # is negligible.
With the above, the road map to the determination of the
parameters# M and
# # through SNe Ia is clear. The comparison of a set of nearby supernovae with their
counterparts at significant redshifts will yield the ratio in luminosity distances, which
then can be used to solve for the cosmological parameters.
5 Universal Acceleration
Measured by Type Ia Supernovae
We will describe here the current status of the supernova research and outline on­
going projects to distinguish between a cosmological constant or a vacuum density
contribution to the energy­momentum tensor in the Einstein equation.
Type Ia supernovae measure luminosity distances to objects out to about a red­
shift of 1.8 (Riess et al. 2004). These distances are the most accurate currently
available to astronomers for cosmological purposes, i. e. beyond the Coma cluster
distance. Since the luminosity distances depend on the evolution of the Hubble pa­
rameter and this in turn depends on the energy content of the universe through the
Einstein equation (e. g. Carroll et al. 1992) one can derive the energy sources dom­
inating over the lookback time covered by the observations. Once the luminosity
distances are derived from the supernova data a likelihood calculation provides the
most statistically suitable values for the complete supernova data under certain as­
sumptions, like the neglect of dust and evolution. It is pointless to divide the super­
nova data into subsamples that do not cover the complete redshift range as the effect
is not detectable on smaller scales. Figure 3 shows that the current data by far do not
warrant such a treatment (as proposed by Padmanabhan et al. 2003, Choudhury et al.
2004, Wang et al. 2004).
The largest available ground­based data set is provided by Barris et al. (2004),
which includes a significant set of supernovae at redshifts near 1. This data set
confirms the earlier results of the HZT (Tonry et al. 2003) and is consistent with
the most recent result of the SCP (Knop et al. 2004). Recently Riess et al. (2004)
published a data sample including the most distant objects observed with HST. All
astrophysical effects, like dust or evolution of the supernovae, have been ignored in
this derivation. The HZT applies a correction for dust in the Milky Way and the
host galaxy of the supernova directly. Only if dust at high redshift is systematically

Cosmology with Supernovae 231
Figure 3: Current status of the SN Ia Hubble diagram (after Tonry et al. 2003). Due to the
large scatter in the nearby universe caused by the peculiar motions of the galaxies all objects
with z < 0.01 were excluded from the analysis. The faintness of the distant objects near
z # 0.5 is the reason for the claimed acceleration of the cosmic expansion.
different from the one in our galaxy is this correction biased. Recent detection of
850 µm emission from host galaxies at z # 0.5 shows that dust is present in some
of these galaxies (Farrah et al. 2004), although the amount may be negligible for the
supernova cosmology. These results are in contrast with the claim by Sullivan et al.
(2003) that the reddening of distant supernovae in spiral galaxies is very small, when
these objects are compared to the SN data from dust­free elliptical galaxies. The
reddening derived by Tonry et al. (2003) for distant SNe Ia is typically smaller than
the one found for nearby objects. This is not surprising considering that the distant
searches are mostly flux limited and will not find many heavily absorped objects,
while the nearby supernovae are drawn from a large heterogeneous sample, which in
several cases includes highly reddened objects. There might be secondary selection
effects at work as well, like the fact that the distant supernovae often have larger
projected distances from their hosts than nearby ones. A last indication that dust
is not a severe problem is the fact that among the first distant SNe Ia of the HZT
were very blue (Leibundgut 2001) objects. In fact, six out of nine objects were bluer
than their nearby counterparts. Although this has now been claimed to possibly be
a selection effect (Knop et al. 2004), it is not clear whether this indeed is the case,
as the effect should be redshift dependent, which it seems not to be, judging from
the small sample in Leibundgut (2001). The recent publication by the SCP (Knop
et al. 2004) does not find the same effect for the objects which have multi­wavelength
light curves. Further analysis of the K­corrections and the dust properties is clearly
required.
Evolution is another potential effect, which could mimic a cosmological sig­
nal. This is much harder to control. For reasonable predictions of how progenitor

232 Bruno Leibundgut
metalicity or age could affect the brightness of SNe Ia one needs a detailed model
of the explosion and the radiation escape (Hillebrandt & Niemeyer 2000). Both
are unsolved problems. A study of the properties of the SN host galaxies has not
shown any correlation with supernovae distances or properties (Sullivan et al. 2003,
Williams et al. 2003). Progress can only be made through detailed observations of
bright, nearby SNe Ia at all phases. Recent data sets are very encouraging (Krisci­
unas et al. 2001, 2003, Benetti et al. 2004; for a review see Leibundgut & Suntzeff
2003). In addition to the detailed spectral, light and colour curve data one can use
bolometric light curves to derive the total emitted radiation from the explosion (Con­
tardo et al. 2000, Contardo 2001). The latter provides important information on the
physical parameters that govern the explosion, like mass of synthesised nickel and
the #-ray escape fraction at late times.
With no clear indication of evolution, the simplest assumption is to disregard
any evolutionary effects; a very dangerous approach, if it goes unchecked. This is
the reason that the HZT has spectroscopically confirmed its distant SNe Ia. The
spectra have been published together with the light curve data (Riess et al. 1998,
Tonry et al. 2003, Barris et al. 2004) and separately for a few objects (Coil et al. 2000,
Leibundgut & Sollerman 2001). While the signal for some of the distant supernovae
is not very good, and in a few early cases the SN classification may even be doubtful,
there are no obvious strong deviations from the spectral appearance of the nearby
supernovae. In some cases, the supernova spectra can be used to determine the phase
of the distant SNe Ia and to check it with the light curves directly. This provides an
independent consistency argument that the distant supernovae behave rather similar
to their nearby counterparts. This means that the distant supernovae cannot be very
different from the nearby ones. Yet, the colour of the distant objects appears to be
systematically bluer. This could be the signature of evolution and will need to be
worked out in more detail.
Luminosity distances over a limited redshift range result in degenerate likelihood
distributions in
the# #
vs.# M plane along a line corresponding roughly
to# # -
1.4# M = 0.35 ± 0.14 (Perlmutter et al. 1999, Tonry et al. 2003; cf. Fig. 4). These
leads to an increased uncertainty along this direction. It should be noted that the
most recent determinations of the cosmological parameters by the HZT favour values
that are rather different from a flat universe solution (Tonry et al. 2003, Barris et al.
2004). If the universe indeed has a flat geometry, as suggested by the CMB data (e. g.
Spergel et al. 2003) then this would be an indication of some unresolved systematic
effect. In essence, the HZT SN analysis favours higher values
for# M
and# # than
required for a flat universe. This can be seen in Figure 3 where the excess around
a redshift of 0.5 is larger than the concordance model predicts. This would argue
for a higher value of the acceleration and
hence# # . At redshifts higher than 1 the
supernovae would prefer a stronger deceleration and hence a higher value
for# M .
At the moment these are most likely due to hidden selection effects and possible
(small) systematics in the data. Newer data sets and analyses (Riess et al. 2004,
Knop et al. 2004) do not show this effect as strongly. The SCP has not observed a
similar trend (Knop et al. 2004), but the redshift range of their published data does
not extend beyond z # 0.8 so far.

Cosmology with Supernovae 233
Figure 4: Likelihood distribution
for# #
vs.# M . The input data are from (Tonry et al.
2003). This diagram should be compared to similar ones in Riess et al. (1998), Perlmutter
et al. (1999), Riess et al. (2000), Leibundgut (2001), Perlmutter & Schmidt (2003), Barris et al.
(2004), Knop et al. (2004) and Riess et al. (2004). The degeneracy along
0.8# # -
0.6# M is
obvious. The overlap with the flat universe model is not within the 68 % likelihood area here.
The grey contour lines show the dynamical age of the universe H0 · t 0 . Clearly the SN data
favour an age near 1.
6 Characterising Dark Energy
It has been generally accepted that a large fraction of the energy content of the uni­
verse is in a form very similar to the vacuum energy or a cosmological constant.
Competing theories have been developed to explain the low, but non­zero, value
of this energy form. An often used description is the equation of state parameter
(w = p
#c 2 ), which in the case of dark energy has to be negative, i. e. contain negative
pressure p, as the energy density # has to be positive (c stands for the speed of light).
With w < - 1
3 the universe is actually accelerating. For field theories w is most
likely variable with time and different from the value for a cosmological constant
(w = -1). The transition from a matter dominated universe
(# M
># # ) happened
sometime during the second half the history of the universe between 0.4 < z < 0.8.
It should hence be possible to determine this transition and then map the change as
a function of redshift in the interval 0.2 < z < 0.8. With a well­calibrated and con­
trolled data set of SNe Ia in this redshift interval it should be possible to accurately
map the transition and determine the strength of the dark energy and the (integrated)
value of w. Several projects have embarked on such a programme. The HZT has
started the ESSENCE project with the search and photometry carried out with the
CTIO Blanco 4 m­telescope with the supporting spectroscopy from VLT, Gemini,
Keck, Magellan and MMT. The goal is to have 200 spectroscopically confirmed

234 Bruno Leibundgut
SNe Ia with densely sampled light curves in at least two filters evenly distributed in
redshift with z < 0.8 (Smith et al. 2002). The CFHT Legacy Survey is aiming for
about 900 SNe Ia out to a slightly larger redshift with spectroscopy from VLT, Keck,
Gemini and Magellan. In the future the SNAP satellite, in the meantime renamed
to Joint Dark Energy Mission (JDEM), should observe about 2000 SNe Ia out to
z < 1.7.
The supernovae cannot do this alone. They will require an accurate indepen­
dent determination of the matter
density# M from a different source. The required
accuracy of this parameter should be a few percent (cf. Tonry et al. 2003).
In the meantime a survey for supernovae has been done within the GOODS col­
laboration. The goal was to find and follow supernovae at a redshift larger than 1.2,
which was achieved for about one third of the sample (Riess et al. 2004). Spectro­
scopic confirmation of 18 supernovae (nine with z > 1) is available (Strolger et al.
2004, Riess et al. 2004). Some of the distant objects could not be classified with a
spectrum and rely on a spectroscopic redshift from the host galaxies only. These
data
constrain# M more accurately than was possible so far, as the supernovae are
in the deceleration portion of the Hubble diagram. They also show that evolutionary
effects are not likely to explain the faintness of SNe Ia near z = 0.5 and the change
to more luminous objects at redshifts beyond z = 1.
But there never is enough of a good thing. The particle theories predict that w ac­
tually would not be constant in time and hence should show a dependence on redshift.
Lacking a theory to predict the changes the current discussions use parametrisations
of the time dependence. It will be very difficult to measure this time dependence
with supernova data in the foreseeable future. A taster is given in Riess et al. (2004),
which is the most complete SN Ia set covering the largest redshift range. Even
with the exquisite data in that publication are the uncertainties in w # large. Several
untested assumptions already had to be used to reach this level. Claims that this has
already accomplished are based on the believe that it would be possible to separate
the SN data in redshift. The effect is so subtle that it will need a truly accurate and
homogeneous data set to achieve this. Only a dedicated space­based mission appears
to be able to provide this.
7 Conclusions
The supernova cosmology has developed tremendously over the past half century.
From an exotic subfield of variable star research the supernovae have become the
most extensively used distance indicator for cosmology. Together with the measure­
ments of the fluctuations in the cosmic microwave background and the determination
of cluster masses they provide clear evidence for an accelerating component in the
Friedmann equation. In its most simple form this component corresponds to the
Einstein's cosmological constant equivalent to a vacuum energy. Modern physics
prefers to think of an extra component in the energy­stress tensor and hence a new,
decaying, particle field. The current standard model of particle physics does not have
room for either of these explanations.

Cosmology with Supernovae 235
The next step will be to measure the time­dependence of the strength of dark
energy. The cosmological constant would not change over time (or redshift), while
most particle theory do predict a slight change of dark energy. In absence of a formal
theory the change would be sought in the equation of state parameter w. There are
two ways to rule out the cosmological constant. First, if w #= -1, and second, if the
time­dependence is shown explicitely. The ESSENCE project is trying to determine
the integrated value of w over the second half of the history of the universe since the
Big Bang. Attempts to derive the first time derivative of w will require a much larger
and more homogeneous data set over a larger redshift range. First attempts with the
most distant supernovae have yielded interesting indications (Riess et al. 2004), but
also show how difficult this measurement will be. The coming decades will see great
efforts to solve this cosmic riddle and supernovae are likely to play an important part
in its solution.
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