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PUBLICATIONS OF THE ASTRONOMICAL SOCIETY OF THE PACIFIC, 112 : 1284È1299, 2000 October
( 2000. The Astronomical Society of the PaciÐc. All rights reserved. Printed in U.S.A.
Invited Review
The Case for an Accelerating Universe from Supernovae
ADAM G. RIESS1,2
Received 2000 May 4 ; accepted 2000 May 5
ABSTRACT. The unexpected faintness of high-redshift Type Ia supernovae (SNe Ia), as measured by two
teams, has been interpreted as evidence that the expansion of the universe is accelerating. We review the
current challenges to this interpretation and seek to answer whether the cosmological implications are
compelling. We discuss future observations of SNe Ia which could o†er extraordinary evidence to test
acceleration.
included the necessity to account for the redshift of the
observed light using spectrophotometry of SNe in the ultraviolet (i.e., K-corrections), host galaxy extinction, and time
dilation of the light curves.
Yet even before the launch of the Hubble Space T elescope
(HST ), a persistent 2 year ground-based e†ort by a Danish
group was rewarded by the discovery of their Ðrst (and only
reported) high-redshift SN Ia, SN 1988U at z \ 0.31
(NÔrgarrd-Nielsen et al. 1989), as well as modest bounds on
the deceleration parameter, [0.6 \ q \ 2.5. This team
0
employed modern image processing techniques to scale the
brightness and resolution of images of high-redshift clusters
to match previous images and looked for supernovae in the
di†erence frames. Unfortunately, the projectÏs low discovery
rate coupled with the dispersion of SNe Ia when treated as
perfect standard candles (D0.5 mag) suggested that the
determination of the deceleration parameter would require
a scientiÐc lifetime.
However, great progress was made by the Supernova
Cosmology Project (SCP) in the detection rate of highredshift SNe Ia by employing large-format CCDs, largeaperture telescopes, and more sophisticated image-analysis
techniques (Perlmutter et al. 1995). These advances led to
the detection of seven SNe Ia at z B 0.4 between 1992 and
1994, yielding a conÐdence region that suggested a Ñat,
" \ 0 universe but with a large range of uncertainty
(Perlmutter et al. 1997).
The High-z Supernova Search Team (HZT) joined the
hunt for high-redshift SNe Ia with their discovery of SN
1995K at z \ 0.48 (Schmidt et al. 1998). Both teams made
rapid improvements in their ability to discover ever greater
numbers of SNe Ia at still larger redshifts. One-time redshift
record holders included SN 1997ap at z \ 0.83 (SCP ; Perlmutter et al. 1998), SN 1997ck at z \ 0.97 (HZT ; Garnavich
et al. 1998a), SN 1998eq at z \ 1.2 (SCP ; Aldering et al.
1998), and SN 1999fv at z \ 1.2 (HZT ; Tonry et al. 1999)
(see Table 1). Before either teamsÏ claimed samples of highredshift SNe Ia were large enough to detect the acceleration
1. INTRODUCTION
Two teams have presented observational evidence from
high-redshift Type Ia supernovae (SNe Ia) that the expansion of the universe is accelerating, propelled by vacuum
energy (Riess et al. 1998 ; Perlmutter et al. 1999). The
primary evidence for this hypothesis is the faintness of
distant SNe Ia relative to their expected brightness in a
decelerating universe. The question we propose to answer in
this review is whether the observations of distant supernovae compel us to conclude that the expansion is accelerating.
2. SUPERNOVA MEASUREMENTS
2.1. Past Work
Supernovae have a long history of employment in the
quest to measure HubbleÏs constant (see Branch 1998 for a
review) and currently provide a column of support for a
strong consensus that H \ 60È70 km s~1 Mpc~1. The
0
history of utilizing supernovae to measure the time evolution of the expansion rate is far briefer. All initial proposals
for using high-redshift SNe to constrain global deceleration
recognized the necessity of an optical space telescope to
collect the data. Wagoner (1977) envisioned application of
BaadeÏs method or the expanding photosphere method
(Kirshner & Kwan 1974) to measure the angular diameter
distance of Type I (hydrogen deÐcient) and Type II
(hydrogen rich) supernovae at z \ 0.3. Colgate (1979)
demonstrated even greater prescience, suggesting that SNe I
at z \ 1 could be used as standard candles for ““ determining
the cosmological constant with greater accuracy than other
standard candles.ÏÏ Further thoughts by Tammann (1979)
ÈÈÈÈÈÈÈÈÈÈÈÈÈÈÈ
1 Space Telescope Science Institute, 3700 San Martin Drive, Baltimore,
MD 21218.
2 1999 ASP Trumpler Award winner for an outstanding Ph.D. thesis.
1284
CASE FOR ACCELERATING UNIVERSE FROM SUPERNOVAE
1285
TABLE 1
RECORD REDSHIFT TYPE Ia SUPERNOVAE
SN Ia
SN
SN
SN
SN
SN
SN
SN
SN
SN
1988U . . . . . . .
1992bi . . . . . . .
1995K . . . . . . .
1995at . . . . . . .
1996cl . . . . . . .
1997ap . . . . . .
1997cka . . . . . .
1998eq . . . . . .
1999fv . . . . . . .
z
Discoverers
IAU Circ.
0.31
0.46
0.48
0.66
0.83
0.83
0.97
1.2
1.2
NÔrgaard-Nielsen, Nielsen, and coworkers
SCP
HZT
SCP
SCP
SC
HZT
SCP
HZT
4641
5652
6160
6270
6621
6596
6646
7046
7312
Date
1988
1992
1995
1995
1996
1997
1997
1998
1999
Aug
Apr
Mar
Dec
Mar
Mar
Apr
Oct
Nov
a Poor spectrum of SN but light curve consistent with SN Ia at measured z of host.
signal, both teams found the data to be inconsistent with a
universe closed by matter (Garnavich et al. 1998a ; Perlmutter et al. 1998).
These observational feats were preceded by increased
understanding and ability to make use of SNe Ia observations to constrain the cosmological parameters. Empirical correlations between SN Ia light-curve shapes and peak
luminosity improved the precision of distance estimates
beyond the standard candle model (Phillips 1993 ; Hamuy
et al. 1995 ; Riess, Press, & Kirshner 1995 ; Perlmutter et al.
1995 ; Tripp 1997 ; Saha et al. 1999 ; Parodi et al. 2000).
Studies of SN Ia colors provided the means to distinguish
supernovae which were reddened by dust from those which
were intrinsically red (Riess, Press, & Kirshner 1996 ; Riess
et al. 1998 ; Phillips et al. 1999 ; Tripp & Branch 1999).
Goobar & Perlmutter (1995) showed that measurements of
SNe Ia at di†erent redshift intervals could break degeneracies between ) and ) . Additional work on cross-Ðlter
M
"
K-corrections provided the ability to accurately transform
the observations of high-redshift SNe Ia to the rest frame
(Kim, Goobar, & Perlmutter 1996).
2.2. Observations
In order to resolve whether the results from high-redshift
SNe Ia are compelling, it is important to review how the
measurements were obtained.
Both the SCP and the HZT detected their samples of
high-redshift SNe Ia by using large-format CCDs at telescopes with large apertures (most commonly the Cerro
Tololo Inter-American Observatory 4 m Blanco telescope).
Using two sets of deep images in the R or I band spaced
across a lunation, the ““ template ÏÏ images are subtracted
from the second-epoch images, and automated software
searches for sources in the di†erence images whose intensity
surpasses a speciÐc threshold. The observations taken in
pairs are spaced over a small time interval of a few minutes
to eliminate moving transients. Human inspectors ““ Ðlter ÏÏ
the automated results in an e†ort to maximize the likeli2000 PASP, 112 : 1284È1299
hood that candidates are supernovae (Schmidt et al. 1998 ;
Perlmutter et al. 1999). Because the resources available for
collecting spectral identiÐcations for all the candidates are
insufficient, candidates which appear most likely to be SNe
Ia are given priority. The factors which are favored in the
human selection criteria include candidates which are
separated from the host galaxy nuclei and those that show
good contrast with the host galaxy (especially those with
little or no apparent host). The signal-to-noise ratios of the
identifying spectra vary greatly (Perlmutter et al. 1995,
1998 ; Riess et al. 1998) but have improved with the availability of the Keck Telescope and an increased emphasis on
the search for clues of SN Ia evolution. Most of the spectral
identiÐcations were made by visual comparison to template
spectra of nearby SNe Ia. More recently, automated crosscorrelation techniques have been employed (Riess et al.
1997). Approximately half of the SN Ia redshifts were determined from narrow emission lines or Ca H and K absorption ; the rest were derived from the broad supernova
features. Although formal statistics are not currently available, we are aware that the SCP candidates have yielded a
greater fraction of SNe Ia than the HZT candidates, a signiÐcant number of which turn out to be SNe II. Taken
together, about half of the two teamsÏ candidates are
revealed to be SNe Ia, with the rest classiÐed as SNe II,
active galactic nuclei, Ñare stars, or unclassiÐed objects. SNe
Ia in the desired redshift range are monitored photometrically in two colors by observatories around the world
using red-sensitive passbands ; HST has monitored the light
curves of about two dozen of these objects.
The initial search template images are eventually
replaced by deeper template images obtained with good
seeing and taken 1 or more years after discovery when the
SNe Ia have faded by 5È8 mag. More recently, repeated
searching of the same Ðelds has provided deep template
images before the SN explosion. After the SN images are
bias corrected and Ñat-Ðelded they are geometrically
aligned, and the resolution and intensity are scaled to
match those of the templates. After subtracting the host
RIESS
A B
L [email protected]
,
D \
L
4nF
(1)
where L and F are the SNÏs intrinsic luminosity and
observed Ñux, respectively, and D is in Mpc. Alternately, a
L
logarithmic luminosity distance (i.e., the distance modulus)
is used,
44
Riess et al. 1998
42
m-M (mag)
galaxy light the SN magnitudes are measured. The SCP
uses aperture photometry ; the HZT Ðts point-spread functions. Uncertainties are determined synthetically by the
injection of artiÐcial SNe of known brightness. The SCP
uses standard passbands and Landolt (1992) standards of
comparison while the HZT uses a custom passband system
which is transformed to the Landolt scale (Schmidt et al.
1998). Custom cross-band K-corrections are calculated
using spectrophotometry of nearby SNe Ia whose colors are
reddened to match the high-redshift objects.
The distances are measured by Ðtting empirical families
of light curves to the Ñux observations of individual supernovae. The measured distances are derived from the luminosity distance,
Perlmutter et al. 1999
40
38
ΩM=0.3, ΩΛ=0.7
36
ΩM=0.3, ΩΛ=0.0
34
ΩM=1.0, ΩΛ=0.0
1.5
Δ(m-M) (mag)
1286
1.0
0.5
0.0
-0.5
-1.0
k \ m [ M \ 5 log D ] 25 ,
L
(2)
where M is the SNÏs absolute magnitude and m is the
observed magnitude in a given passband.
Three di†erent light-curve Ðtting methods have been used
to measure the distances, each of which determines the
shape of the best-Ðtting light curve to identify the individual
luminosity of the SN Ia. The HZT has used both the multicolor light-curve shape method (MLCS ; Riess et al. 1996 ;
Riess et al. 1998) and a template-Ðtting approach based on
the parameter *m (B) (Phillips 1993 ; Phillips et al. 1999),
15
while the SCP uses the ““ stretch method ÏÏ (Perlmutter et al.
1995 ; 1999).
Nearby SNe Ia provide both the measure of the Hubble
Ñow and the means to calibrate the relationship between
light-curve shape and luminosity. The SCP uses D20
nearby SNe Ia in the Hubble Ñow from the Cala" n/Tololo
Survey (Hamuy et al. 1996a, 1996b) while the HZT adds to
this set an equal number of SNe from the CfA sample (Riess
et al. 1999a).
Dust extinction is handled somewhat di†erently by the
two teams. The HZT measures the extinction from the
B[V reddening (i.e., the color excess) and then combines
this measurement in a Bayesian formalism using a prior
host galaxy extinction distribution calculated by Hatano,
Branch, & Deaton (1998). This treatment assumes that
extinction makes supernovae appear dimmer (farther),
never brighter (closer). The SCP uses a number of di†erent
approaches (including the HZT approach) but favors
making no individual extinction corrections and discarding
-1.5
0.01
0.10
z
1.00
FIG. 1.ÈHubble diagrams of SNe Ia from Perlmutter et al. (1999 ; SCP)
and Riess et al. (1998 ; HZT). Overplotted are three cosmologies : ““ low ÏÏ
and ““ high ÏÏ ) with ) \ 0 and the best Ðt for a Ñat cosmology, ) \
M
"
M
0.3, ) \ 0.7. The bottom panel shows the di†erence between data and
"
models from the ) \ 0.3, ) \ 0 prediction. The average di†erence
M
"
between the data and the ) \ 0.3, ) \ 0 prediction is 0.28 mag.
M
"
outliers. Figure 1 shows a single Hubble diagram made with
the data from both teams (Riess et al. 1998 ; Perlmutter et al.
1999).
The measured distances are then compared to those
expected for their redshifts as a function of the cosmological
parameters ) , ) , and H :
M "
0
D \ cH~1(1 ] z) o ) o [email protected] ] sinn
L
0
k
G
o ) o [email protected]
k
P
z
dz
0
H
] [(1 ] z)2(1 ] ) z) [ z(2 ] z)) ][email protected] , (3)
M
"
where ) \ 1 [ ) [ ) , and sinn is sinh for ) º 0 and
k
M
"
k
sin for ) ¹ 0 (Carroll, Press, & Turner 1992). The likelik
hoods for cosmological parameters are determined by minimizing the s2 statistic between the measured and predicted
distances (Riess et al. 1998 ; Perlmutter et al. 1999). Determination of ) and ) are independent of the value of H or
M
"
0
2000 PASP, 112 : 1284È1299
CASE FOR ACCELERATING UNIVERSE FROM SUPERNOVAE
the absolute magnitude calibration of SNe Ia. The conÐdence intervals in the ) -) plane determined by both
M "
teams are shown in Figure 2. In this plane, acceleration is
deÐned by the region where the deceleration parameter, q ,
0
is negative,
)
q \ M[) \0 .
0
"
2
(4)
2.3. Results
The visual impression from Figures 1 and 2 is that the
supernova observations favor the parameter space containing a positive cosmological constant and an accelerating
universe with high statistical conÐdence. The conÐdence
regions determined by the two teams are in remarkably
good agreement. Both teams claim that these results do not
result from chance with more than 99% conÐdence (Riess et
al. 1998 ; Perlmutter et al. 1999). However, the speciÐc conÐdence of these cosmological conclusions depends on which
FIG. 2.ÈSNe Ia joint conÐdence intervals for () ,) ) from Perlmutter
M "
et al. (1999 ; SCP) and Riess et al. (1998 ; HZT). Regions representing
speciÐc cosmological scenarios are indicated.
2000 PASP, 112 : 1284È1299
1287
parameter space intervals one considers to be equally likely,
a priori. This point is addressed by Drell, Loredo, & Wasserman (2000), who suggest that models with ) \ 0 and
"
) D 0 could be considered equally probable, a priori.
"
While Riess et al. (1998) and Perlmutter et al. (1999) considered the probability that ) [ 0 with a Ñat prior in a
"
linear ) space, an alternative is to use a Ñat prior in a
"
logarithmic ) space (Gott et al. 2000). Using the latter
M
prior reduces the signiÐcance of a cosmological constant
because it gives greater weight to regions in parameter
space where ) D 0 and the cosmological constant is
M
reduced.
Another useful way to quantify the SN Ia constraints has
been given by Perlmutter et al. (1999) as 0.8) [ 0.6) \
M
"
[0.2 ^ 0.1, a result which applies equally well to the Riess
et al. (1998) data.
A more illuminating way to quantify the evidence for an
accelerating universe is to consider how the SN Ia distances
depart from decelerating or ““ coasting ÏÏ models. The
average high-redshift SN Ia is 0.19 mag dimmer or D10%
farther than expected for a universe with no cosmological
constant and negligible matter () \ 0, ) \ 0). Of course,
"
M
it is apparent that the universe has more than negligible
matter and the current consensus from the mass, light,
X-ray emission, numbers, and motions of clusters of galaxies is that ) B 0.3 (Carlberg et al. 1996 ; Bahcall, Fan, &
M
Cen 1997 ; Lin et al. 1996 ; Strauss & Willick 1995). The
high-redshift SNe Ia from both teams are 0.28 mag dimmer
or 14% farther than expected in a universe with this much
matter and no cosmological constant. The statistical uncertainty of these values is 0.08 and 0.06 mag (or 4% and 3% in
distance) for the HZT and SCP, respectively. The observed
dispersion of the high-redshift SNe Ia around the best-Ðt
cosmology is 0.21 mag for the HZT and 0.36 mag for the
SCP. A frequentist would consider the accelerating universe
to be statistically likely at the 3È4 p level (i.e., [99%), while
the Bayseian likelihood would depend on a statement of the
natural space and scale for ) and ) . Likewise, analysis
"
M
methods which make di†erent assumptions about the distribution function of the distance measurements and the
utility of their uncertainties can impact the conÐdence in the
inferred cosmological parameters. For example, the use of
median statistics diminishes reliance on the tails of the SN
distribution, but at the price of discarding valuable uncertainty estimates and e†ectively reducing the already sparse
data sets (Gott et al. 2000).
Simply put, high-redshift SNe Ia are D0.25 mag fainter
than expected in our universe with its presumed mass
density but without a cosmological constant (or which is
not accelerating). The statistical conÐdence that SNe Ia are
fainter than expected is high enough to accept that it does
not result from chance and additional SNe Ia continue to
support this conclusion (B. P. Schmidt 2000, private
communication). Rather, this result is challenged only by
1288
RIESS
systematic uncertainties not reÑected in the variance of
high-redshift SN Ia distance measurements. In the following
sections we review the challenges to the cosmological interpretation of the SN Ia observations and consider whether
the evidence compels us to believe that the universe is accelerating.
3. CHALLENGES AND TESTS OF THE
ACCELERATING UNIVERSE
3.1. Evolution
Could SNe Ia at z \ 0.5, a look-back time of D5 Gyr, be
intrinsically fainter than nearby SNe Ia by 25% ? For the
purpose of using SNe Ia as distance indicators near and far,
we are concerned only with an evolution which changes the
luminosity of a SN Ia for a Ðxed light-curve shape. Evolution is a major obstacle to the measurement of cosmological
parameters, having plagued workers who tried to infer the
global deceleration rate from brightest cluster galaxies in
the 1970s (Sandage & Hardy 1973). We will consider both
the theoretical and empirical indications for SN Ia evolution.
Theoretical understanding of SNe Ia provides reasons to
believe that evolution is not a challenge to the accelerating
universe. SNe Ia are events which occur on stellar scales,
not galactic scales, and therefore should be less subject to
the known evolution of stellar populations. However, our
inability to conclusively identify the progenitor systems (see
Livio 2000 for a review) and our lack of a complete theoretical model (see Leibundgut 2000 for a review) means we
cannot rely exclusively on theory to rule out the critical
degree of evolution.
Nevertheless, theoretical calculations can provide some
insight into this question. Ho# Ñich, Wheeler, & Thielemann
(1998) have calculated models of spectra of SNe Ia with
solar and one-third solar metallicities and have found little
di†erence between the spectral energy distribution over the
wavelengths where the SNe Ia have been observed (see Fig.
3). However, extreme changes in progenitor metallicity from
Population I to II may yield more signiÐcant changes
(Ho# Ñich et al. 2000). In principle, changes in the age and
hence initial mass of the progenitor star at high redshift
could yield white dwarfs of varying carbon-to-oxygen (C/O)
ratio. It is currently difficult to assess if such a variation
could produce signiÐcant evolution as these calculations
lack the necessary precision (Dominguez et al. 1999 ; von
Hippel, Bothun, & Schommer 1997). Umeda et al. (1999)
suggest that a change in the C/O ratio is the source of the
inhomogeneity in SN Ia luminosity, but they conclude that
calibration of the luminosity via light-curve shape relations
e†ectively inoculates the cosmological measurements to an
evolution in the C/O ratio. Similarly, Pinto & Eastman
(2000) Ðnd that the family of SN Ia light-curve shapes and
their corresponding luminosities result from a variation in
synthesized 56Ni mass and the calibrating relation is
unlikely to be a†ected by evolutionary changes in the progenitors.
To date, answers to the question of whether SNe Ia
evolve have been sought from empirical evidence. In the
nearby sample, SNe Ia are observed in a wide range of
host-galaxy morphologies including ellipticals, poststarburst galaxies (e.g., SN 1972E in NGC 5253), low
surface brightness galaxies (e.g., SN 1995ak in IC 1844),
irregulars (e.g., SN 1937C in IC 4182), S0s (e.g., SN 1995D
in NGC 2962), and early- to late-type spirals (van den Bergh
1994 ; Cappellaro et al. 1997 ; Hamuy et al. 1996a, 1999b ;
Riess et al. 1999a). The range of metallicity, stellar age, and
interstellar environments probed by the nearby hosts is
much greater than the mean evolution in these properties
for individual galaxies between z \ 0 and z \ 0.5. Some
variation in the observed characteristics of SNe Ia with host
morphology has been seen in the nearby sample in the sense
FIG. 3.ÈType Ia supernova model spectral energy distributions for solar and 1 solar metallicities. Superposed are the transmission functions for standard
3
passbands ; from left to right is U, B, V , and R. From Ho# Ñich et al. (1998)
2000 PASP, 112 : 1284È1299
CASE FOR ACCELERATING UNIVERSE FROM SUPERNOVAE
that the brightest SNe Ia occur preferentially in late-type
hosts (Hamuy et al. 1996a, 1996b ; Branch, Romanishin, &
Baron 1996). Yet after correction for the light-curve shape/
luminosity relationship and extinction, the observed
residuals from the Hubble Ñow do not correlate with host
galaxy morphology (see Fig. 4). A similar result has been
documented in the relationship between nearby SNe Ia and
their hostsÏ B[V color (Hamuy et al. 2000) ; brighter SNe
Ia occur in bluer galaxies but light-curve shape corrected
distances do not appear to correlate with host color (see
Fig. 5). This empirical evidence may indicate that the peak
luminosity attained by an SN Ia is related to the age of its
progenitor (Ivanov, Hamuy, & Pinto 2000), though lightcurve shape corrections would guard the cosmological conclusions against such evolution. It is also possible to screen
SN Ia distance estimates for a metallicity bias by comparing
nearby SNe Ia at a wide range of distances from their hosts
centers. Hubble Ñow residuals show no correlation with the
projected distance from the host center as seen in Figure 6
(Riess et al. 1999a) or with distance estimates from late-type
host centers deprojected to be coplanar with visible disks
Standard Candle
LOG V (km/s)
4.5
4.0
3.5
Late-Type
Early-Type
1289
FIG. 5.ÈResiduals of the Hubble diagram in the V band vs. the B[V
color of the SN host galaxy (Hamuy et al. 2000).
(Ivanov et al. 2000).
The body of empirical evidence indicates that SN Ia distance estimates are insensitive to variations in the supernova progenitor environment and is the strongest argument
against signiÐcant biases due to evolution to z \ 0.5.
However, this evidence is still circumstantial as we cannot
be sure that the local environments of the SN Ia progenitors
are similar to the average environments of the hosts. Future
studies which probe the local regions of nearby SNe Ia
should be better able to explore their variance.
The other empirical test of evolution has been to compare
the observed characteristics of low-redshift and highredshift SNe Ia. The assumption of this test is that a luminosity evolution of D25% would be accompanied by other
visibly altered characteristics of the explosion. Here too our
lack of Ðrm theoretical footing makes it difficult to gauge
the correspondence between any evolution in distanceindependent quantities and luminosity. Therefore we must
3.0
MLCS
1.0
Hubble Flow Residual (mag)
LOG V (km/s)
4.5
4.0
3.5
3.0
32
34
36
38
m-M
FIG. 4.ÈNearby Hubble diagram of SNe Ia in di†erent host galaxy
morphologies. In the top panel the SNe Ia are treated as standard candles,
and in the bottom panel distances are determined with the MLCS method
(Riess et al. 1996, 1998). After MLCS corrections are made, the distance
Hubble Ñow residuals are independent of host galaxy morphology.
2000 PASP, 112 : 1284È1299
0.5
0.0
-0.5
-1.0
0
10
20
30
40
Projected Distance from Host (kpc)
50
FIG. 6.ÈMLCS distance residuals from the Hubble Ñow for nearby
SNe Ia vs. their projected distance from their host centers (Riess et al.
1999a).
1290
RIESS
conservatively demand that observations of all observables
of distant SNe Ia be statistically consistent with the nearby
sample.
3.1.1. Spectra
Comparisons of high-quality spectra between nearby and
high-redshift SN Ia, such as those seen in Figure 7, have
revealed remarkable similarity (Riess et al. 1998 ; Perlmutter
et al. 1998, 1999 ; Coil et al. 2000). The spectral energy distribution is sensitive to the atmospheric conditions of the
supernova (i.e., temperature, abundances, and ejecta
velocities). Even primitive modeling indicates that it would
be difficult to retain the primary features of the SN Ia spectrum while altering the luminosity by about 20%È30%.
Further, comparisons of temporal sequences of spectra
reveal no apparent di†erences as the photosphere recedes in
mass (Filippenko et al. 2000), indicating that the superÐcial
similarities persist at deeper layers. However, among the
variety of nearby SNe Ia are objects which are both D25%
SN 1992a (z=0.01)
Relative Flux
SN 1994B (z=0.09)
SN 1995E (z=0.01)
SN 1998ai (z=0.49)
SN 1989B (z=0.01)
fainter than the average and also display very typical spectral features (e.g., SN 1992A, see Fig. 7). Therefore, the existing spectral test alone is not sufficient to check for this
degree of evolution.
While spectral similarity between nearby and distant
SNe Ia provides no indication of evolution, a lack of any
spectral peculiarities among high-redshift SNe Ia could
signal some changes at high redshift. Li et al. (2000) Ðnd
from the most unbiased survey of nearby SNe Ia to date
that D20% of SNe Ia are spectroscopically similar to the
overluminous SN 1991T. SN 1991TÈlike objects show weak
Ca II, Si II, and S II, but prominent features of Fe III
(Filippenko 1997), and close cousins, such as SN 1999aa,
have similar characteristics with the exception that Ca II
absorption is more normal. Monte Carlo simulations of the
search criteria used by the SCP and the HZT team performed by Li, Filippenko, & Riess (2000) indicate that such
overluminous objects should comprise approximately 25%
of high-redshift SNe Ia (with some uncertainty due to a
possible link between such objects and circumstellar dust).
To date, neither team has reported the existence of a single
SN 1991TÈlike object among D100 high-redshift objects.
It is certain that the low signal-to-noise ratio of the
spectra of high-redshift SNe Ia, coupled with the redshifting
of spectral features out of the observable window makes it
much more difficult to identify individuals from this peculiar class. In addition, the spectroscopic peculiarities of SN
1991TÈlike objects are only apparent close to maximum
light (or earlier), and some high-redshift SNe Ia may not
have been observed early enough to identify their spectral
peculiarities. This same e†ect may also explain why the
Cala" n/Tololo survey of 29 SNe Ia yielded no SN 1991TÈ
like objects (Hamuy et al. 1996a, 1996b). If, however, these
observational biases are not to blame, the absence of SN
1991TÈlike SNe Ia at high redshift could result from an
evolution of the population of progenitor systems (see Livio
2000 for a review) or a subtle di†erence in selection criteria
(see ° 3.6). If true, this type of evolution may yield important
clues which help identify the progenitor systems (RuizLapuente & Canal 1998), but it is unlikely to a†ect the
measurement of the cosmological parameters since spectroscopically normal SNe Ia at low and high redshift have been
used to derive the cosmological constraints.
3.1.2. Broad Band
3500
4000
4500
5000
5500
6000
Rest Wavelength (Angstroms)
6500
FIG. 7.ÈSpectra of four nearby and one high-redshift SN Ia at the same
phase (Riess et al. 1998). Within the observed variance of SN Ia spectral
features, the spectra of high-redshift SNe Ia are indistinguishable from the
low-redshift SNe Ia. The spectra of the low-redshift SNe Ia were resampled
and convolved with Gaussian noise to match the quality of the spectrum of
SN 1998ai.
The distributions of light-curve shapes for nearby and
distant SNe Ia are statistically consistent (Riess et al. 1998 ;
Perlmutter et al. 1999). Such consistency appears to extend
to infrared light curves of high-redshift SNe Ia which show
the characteristic second maximum of typical, low-redshift
SNe Ia (Riess et al. 2000).
An analysis by Drell et al. (2000) indicates that di†erent
light-curve Ðtting methods may not be statistically consis2000 PASP, 112 : 1284È1299
CASE FOR ACCELERATING UNIVERSE FROM SUPERNOVAE
tent and that the apparent di†erences may be a function of
the light-curve shape. However, these conclusions are
highly sensitive to estimates of the correlated distance
uncertainties between di†erent Ðtting methods and these
correlated uncertainties are difficult to estimate.
Evolutionary changes in the continuum temperature and
hence the thermal output of the explosion could be detected
from the colors of prenebular supernovae. The most signiÐcant analysis of B[V colors, performed by Perlmutter et al.
(1999) and shown in Figure 8, demonstrated consistency
between low- and high-redshift SNe Ia at maximum light.
Likewise, Riess et al. (2000) found that the B[I colors of a
SN Ia at z \ 0.5 were consistent with those of nearby
SNe Ia. However, Falco et al. (1999 ; see also McLeod et al.
1999) suggested that the B[V colors of high-redshift SNe
Ia from the HZT may be excessively blue, a conclusion
which cannot be rejected by the B[I color measurements
by Riess et al. (2000). More data are needed to conÐrm or
refute this possibility. If true, this could indicate either evolution or the existence of a halo of Milky Way dust which
12
10
Calan/Tololo
Survey
(a)
8
NSNe
6
4
1291
would redden the observed wavelengths of nearby SNe Ia
more than redshifted objects. This latter possibility has been
suggested by recent Milky Way dust maps of Schlegel,
Finkbeiner, & Davis (1998) in contrast to the previous maps
of Burstein & Heiles (1982), but it would augment rather
than fully explain the faintness of distant SNe Ia.
The rise time (i.e., the time interval between explosion
and maximum light) is sensitive to the ejecta opacity and
the distribution of 56Ni. The rise time of nearby SNe Ia
(Riess et al. 1999b) and the high-redshift SNe Ia of the SCP
(Goldhaber 1998 ; Groom 1998) were initially strongly discrepant (Riess et al. 1999c). However, a reanalysis of the
SCP high-redshift data by Aldering, Knop, & Nugent
(2000) Ðnds the high-redshift rise time to be longer and
much more uncertain than indicated by Groom (1998). The
remaining di†erence could be no more than a D2.0 p
chance occurrence. More early photometry of distant SNe
Ia is needed to increase the signiÐcance of this test of evolution.
Evolution is arguably the most serious challenge to the
cosmological interpretation of high-redshift SNe Ia.
Further studies, currently underway, seek to compare the
host galaxy morphologies and luminosity versus light-curve
shape relations for nearby and distant SNe Ia. The results
reviewed in this section do not appear to provide any clear
evidence of evolution. However, absence of evidence is not
necessarily evidence of absence. The paucity of high signalto-noise ratio observations of high-redshift SNe Ia and the
current lack of a comprehensive theoretical model or a wellunderstood progenitor system keeps the embers of skepticism aglow.
2
0
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
E(B-V)
8
Consideration of a noncosmological explanation for the
dimming of distant supernova light must invariably turn to
a famous pitfall of optical astronomy : extinction. Trouble
has often followed dust in astronomy, a point Ðrst appreciated by Trumpler (1930) when analyzing the spatial distribution of Galactic stars.
Supernova
Cosmology
Project
(b)
3.2. Dust
6
NSNe
4
3.2.1. Ordinary Dust
2
0
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
E(B-V)
FIG. 8.ÈComparison of color excess, E
, for nearby SNe Ia from the
B~V
Cala" n/Tololo survey (Hamuy et al. 1996a, 1996b) and high-redshift SNe Ia
from Perlmutter et al. (1999 ; SCP). The color excesses at high and low
redshift are consistent, indicating negligible extinction and/or no evidence
for color evolution.
2000 PASP, 112 : 1284È1299
An additional D25% opacity of visual light by dust in the
light paths of distant supernovae would be sufficient to
nullify the measurement of the accelerating universe. Both
teams currently measure SN Ia colors to correct for the
ordinary kind of interstellar extinction which reddens light.
Galactic extinction maps from Burstein & Heiles (1982) and
Schlegel et al. (1998) were used by the HZT and the SCP,
respectively, to correct individual SNe Ia for Milky Way
extinction. Such corrections were typically less than 0.1 mag
due to the high Galactic latitudes of the SNe Ia. Even a
1292
RIESS
previously unknown halo of Galactic dust would dim the
rest-frame light of nearby SNe Ia more than highly redshifted SNe Ia and would therefore not explain the cosmological indications.
Measurements of B[V colors have been used by both
teams to test for and remove host galaxy extinction (Riess et
al. 1998 ; Perlmutter et al. 1999 ; see Fig. 8). Totani &
Kobayashi (1999) have suggested that the remaining uncertainty in the mean measured B[V color excess (p \ 0.02
mag ; Perlmutter et al. 1999), when multiplied by reddening
ratios of 3È4 to determine the optical opacity, may be too
large to discriminate between open and "-dominated cosmologies with high conÐdence. However, such concern
seems unwarranted as this uncertainty remains 3È4 times
smaller than the size of the cosmological e†ect of an accelerating universe.
Another measurable e†ect of the critical amount of mean
interstellar extinction is that it would introduce more dispersion in the distance measurements than is currently
observed. A random line of sight into a host galaxy will
intersect a nonuniform amount of extinction. Hatano et al.
(1998) have calculated the expected distribution of extinction along random lines of sight into host galaxies. A mean,
uncorrected extinction of 0.25 mag would induce twice the
distance dispersion observed by the HZT (Riess et al. 1998).
In addition, high-redshift surveys are biased toward Ðnding
SNe Ia which have even less extinction than would be
expected from the distributions of Hatano et al. (1998).
A more powerful way to search for reddening by dust is
to observe high-redshift SNe Ia over a large wavelength
span : from the optical to the infrared. Infrared color
excesses would be more than twice as large as E
for
B~V
ordinary dust. A set of such observations for SN 1999Q
(z \ 0.46) disfavor A \ 0.25 mag of dust with GalacticV
type reddening at high conÐdence (Riess et al. 2000), but
more SNe Ia need to be observed in the near-infrared to
strengthen this conclusion.
3.2.2. Gray Dust
More pernicious than ordinary dust is ““ gray ÏÏ dust which
could leave little or no imprint on the spectral energy distribution of SNe Ia. Perfectly gray dust is only a theoretical
construct, but dust which is grayer than Galactic-type dust
(i.e., larger reddening ratios) does exist (Mathis 1990) and
could challenge the cosmological interpretation of highredshift SNe Ia.
Gray dust can be made with large spherical dust grains or
elongated ““ whiskers.ÏÏ Past studies of whiskers (Aguirre
1999a ; Rana 1979, 1980) indicate that they would distort
the cosmic microwave background (CMB), an e†ect which
has not been seen. Like nongray extinction, gray interstellar
extinction does not provide an acceptable explanation for
the dimness of SNe because the inherent variations in the
opacity along random lines of sight would induce more
distance dispersion than is observed (Riess et al. 1998).
Gray intergalactic extinction could a†ect measurements
of the deceleration parameter (Eigenson 1949) without telltale dispersion or reddening. Indeed, observations of neither
SNe Ia nor other astrophysical objects rule out a 30%
opacity by large semispherical dust grains (Aguirre 1999b).
Aguirre (1999a, 1999b) has shown that a uniformly distributed component of intergalactic gray dust with a mass
density of ) B 5 ] 10~5 and graphite grains greater
dust
than 0.1 km could explain the faintness of high-z SNe Ia
without detectable reddening and without overproducing
the currently unresolved portion of the far-infrared (far-IR)
background (but see Simonsen & Hannestad 1999).
However, this physical model of dust would provide some
reddening which can readily be detected with observations
in the optical and infrared. Measurements by Riess et al.
(2000 ; see Fig. 9) of E
for a single high-redshift SN Ia
B~I
disfavor a 30% visual opacity of gray dust at the D2.5 p
conÐdence level, but more observations are needed to
strengthen this conclusion. Additional studies of the faint
far-IR sources seen with SCUBA may soon provide deÐnitive constraints on the unresolved component of the far-IR
background and the viability of extragalactic gray dust.
3.3. Gravitational Lensing
The inhomogeneous distribution of matter in the universe typically deampliÐes and very rarely ampliÐes the
observed brightness of distant SNe Ia compared to the
average. (Note that the mean observed brightness must
equal the unampliÐed value expected in a perfectly smooth
universe.)
The size of the typical deampliÐcation is a function of the
SN Ia redshift, the mass density of the universe and the
fraction of dark matter locked into compact objects. This
e†ect has been quantiÐed by a wide range of techniques
(Kantowski, Vaughan, & Branch 1995 ; Frieman 1996 ;
Wambsganss et al. 1997 ; Holz & Wald 1998 ; Kantowski
1998 ; Metcalf 1999 ; Barber 2000). The e†ect of weak lensing
on the observed distribution of luminosities of SNe Ia at
z \ 1 and z \ 0.5 can be seen in Figure 10. In the most
relevant regime for the current SNe Ia at z \ 0.5 (i.e., ) B
M
0.3, and mostly di†use dark matter) the typical deampliÐcation is D2%, much smaller than the cosmological e†ect. An
extreme case (i.e., ) B 0.5, all matter in point masses)
M
could deamplify the median SN Ia at z \ 0.5 by 5% (Holz
1998), but this model is unlikely to be correct and the e†ect
is still not large enough to negate the cosmological interpretation of high-redshift SNe Ia. Perlmutter et al. (1999) considered lensing by up to ) \ 0.25 in compact material in
M
the determination of their conÐdence intervals. They found
little impact on the likelihood of a positive cosmological
2000 PASP, 112 : 1284È1299
CASE FOR ACCELERATING UNIVERSE FROM SUPERNOVAE
SN 1999Q (z=0.46)
B-I (mag)
1.5
1.0
0.5
Normal Dust
(AV=0.3,ΩΛ=0)
0.0
"Grey" Dust
(AV=0.3,ΩΛ=0)
-0.5
No Dust
(AV=0,ΩΛ > 0)
EB-I (mag)
0.50
0.25
0.00
-0.25
-0.50
0
10
20
30
Age (days)
40
50
FIG. 9.ÈColor evolution, B[I, and color excess, E , of a highB~I
redshift SN Ia, SN 1999Q (Z \ 0.46), compared to the custom MLCS
template curve with no dust and enough dust (of either Galactic type or
grayer) to nullify the cosmological constant. The smaller error bars are
from photometry noise ; the larger error bars include all sources of uncertainty such as intrinsic dispersion of SN Ia B[I color, K-corrections, and
photometry zero points. The data for SN 1999Q are consistent with no
reddening by dust, moderately inconsistent with A \ 0.3 mag of gray dust
V
(i.e., graphite dust with minimum size greater than 0.1 km ; Aguirre 1999a,
1999b) and A \ 0.3 mag of Galactic-type dust. From Riess et al. (2000).
V
constant (see Fig. 11). Wang (2000) suggests that by Ñuxaveraging (i.e., binning the SNe Ia distances by redshift) one
can reduce the bias due to weak lensing. In the future, any
bias due to weak lensing will naturally vanish as the sample
sizes become larger and the mean observed luminosity more
robust. It is interesting and potentially useful to note that
the observed distribution of SN Ia distances (see Fig. 10)
can in principle be used to determine the fraction of gravitating matter contained in compact objects (Seljak & Holz
1999 ; Metcalf & Silk 1999).
3.4. Measurement Biases
In this section we consider whether biases in the measurement process of high-redshift SNe Ia could mimic the evidence for an accelerating universe. An exhaustive list of
2000 PASP, 112 : 1284È1299
1293
such biases has been considered by Hogg (2000) and Hogg
& Turner (1998). Here we discuss how these biases may
apply to the supernova measurements.
The observational challenge is to measure the distance to
high-redshift SNe Ia which are 6È7 mag fainter and have
lower signal-to-noise ratio than those which delineate the
Hubble Ñow. Di†erences in the way low- and high-redshift
SNe Ia are observed must not introduce biases in their
distance measures at more than the few percent level.
Indeed, Hogg (2000) has noted that the proximity of highredshift SNe Ia to any reasonable world model is a testament to the feasibility of measuring distances across such a
large range. However, because the goal of these observations is precision cosmology (and not simply to demonstrate the dynamic range of useful photometry), our scrutiny
must be greater.
Charge-transfer inefficiency (CTI) and detector nonlinearities can cause faint objects to appear fainter. However,
ground-based observations of high-redshift SN Ia are
limited by the bright sky, a regime in which these e†ects are
widely found to be negligible. For space-based observatories such as the Hubble Space T elescope (HST ), CTI is far
more troublesome but quite correctable (Whitmore, Heyer,
& Casertano 1999). In addition, only a subset of the highredshift SNe Ia have been measured with HST , and the
cosmological conclusions do not depend on the inclusion of
these objects.
High-precision, Ñux-conserving algorithms have been
developed to properly subtract images of the host galaxy
from images with SN light (Alard & Lupton 1998). Correctly employed, these methods reduce any biases in the measurement of the SN brightness to less than a few percent.
Tests for measurement biases and estimates of uncertainty
are performed by both teams by the injection of artiÐcial
SNe into the observed images.
Hogg & Turner (1998) discuss a bias toward higher
observed Ñuxes which naturally occurs when measuring the
brightness at discovery of low signal-to-noise ratio sources.
This bias results from the preferential selection of faint
sources on the bright side of the Poisson distribution of
photon statistics. Follow-up observations of the source
would not incur this bias. This e†ect would have little
impact on the supernova distances measured by the HZT
and SCP because the light curves are dominated by observations made after discovery. In addition, the direction of
this e†ect is opposite to the signal of an accelerating universe. However, this e†ect may become more important for
SNe Ia found at z [ 1 for which the discovery observation
may provide one of the most signiÐcant measurements.
3.5. Selection Biases
Do the HZT and SCP preferentially select faint SNe Ia at
high redshift ? Because we have already considered evolu-
1294
RIESS
100
80
P!Μ" 60
40
20
0
100
80
P!Μ" 60
40
20
0
compact objects
"m #0.5,"$ #0.5
z#0.5
40
30
P!Μ" 20
10
1
Μ
1.1
1.2
compact objects
"m #0.5,"$ #0
z#0.5
0
40
30
P!Μ" 20
1
Μ
1.1
1.2
galaxies
"m #0.5,"$ #0.5
z#0.5
15
0
5
2
1
Μ
1.1
1.2
galaxies
"m #0.5,"$ #0
z#0.5
20
15
0
1.1
1.2
5
2
Μ
1.1
1.2
0.9
0
1.1
1.2
1
Μ
1.1
1.2
galaxies
"m #0.5,"$ #0
z#1
8
P!Μ" 6
4
1
Μ
galaxies
"m #0.5,"$ #0.5
z#1
10
10
1
0.9
8
P!Μ" 6
4
0
1
Μ
compact objects
"m #0.5,"$ #0
z#1
10
P!Μ" 10
P!Μ"
0.9
10
20
0
compact objects
"m #0.5,"$ #0.5
z#1
0.9
1
Μ
1.1
1.2
FIG. 10.ÈProbability distribution P(k) for supernova apparent brightness k normalized to k \ 1 for a Ðlled beam (i.e., a homogeneous universe). The
vertical lines are at the empty-beam value. ““ Galaxies ÏÏ are treated as isothermal spheres and truncated at a radius of 380 kpc ; ““ compact objects ÏÏ are point
masses. From Holz (1998).
tion in ° 3.1, here we are only concerned with the characteristics of a high-redshift sample which is drawn from the
same population as the nearby sample. In so doing, we must
also consider if the nearby sample is a fair representation of
that population.
As an example, consider the set of nearby SNe Ia which
appear fainter than expected for their redshift in the bottom
panel of Figure 1. Presumably these objects appear dim due
to the intrinsic random scatter of SNe Ia. If, however, these
SNe Ia had a characteristic in common which, in addition,
favored their discovery at high redshift, a bias would result.
To date, no such characteristic has been identiÐed and the
observed dispersion of nearby SNe Ia is consistent with
their measurement errors.
Howell, Wang, & Wheeler (2000) found a di†erence
between the projected distances from the hostsÏ centers for
the nearby and distant SNe Ia (see Fig. 12). Many of the
nearby SNe Ia were found in the photographic
Cala" n/Tololo survey in which saturated galaxy cores
masked SNe near their hostsÏ centers (Shaw 1979 ; Hamuy
& Pinto 1999). The result is that distant SNe Ia are more
centrally located than those in the nearby sample. However,
in an analysis of 44 nearby SNe Ia, Riess et al. (1999a) found
no dependence of the distance measurement on the project2000 PASP, 112 : 1284È1299
CASE FOR ACCELERATING UNIVERSE FROM SUPERNOVAE
1295
FIG. 11.ÈCosmological constraints from Perlmutter et al. (SCP ; 1999)
for three weak lensing scenarios. Fit C assumes a Ðlled beam, Ðt K assumes
an empty beam, and Ðt L is a model with weak lensing by up to ) \ 0.25
M
in compact objects.
ed distance from the host center, so this selection e†ect
appears to have no bearing on the cosmological use of SNe
Ia (see Fig. 6).
Malmquist bias (Malmquist 1924, 1936) can shift the
mean distance too close in a magnitude-limited survey of
SNe Ia. This e†ect seems to contrast with the cosmological
dimming perceived in an accelerating universe. However, if
the nearby sample were more afflicted by Malmquist bias
than the distant sample, this bias could mimic an accelerating universe. Because the intrinsic scatter of SN Ia distances is low (¹0.15 mag), Malmquist bias, which scales
with the square of the dispersion (see Mihalas & Binney
1981 for a derivation), is small for SNe Ia. Perlmutter et al.
(1999) made analytic calculations of Malmquist bias arising
from the intrinsic dispersion of SNe Ia (assumed to be 0.17
mag) and the SCP search incompleteness (determined
empirically) to estimate that the net bias between the
samples is no more than 0.03 mag. (Perlmutter et al. [1999]
notes that the net bias may actually be closer to zero due to
a compensating bias against the selection of light curves
which are ““ fast ÏÏ for their luminosity and therefore spend
less time above the detection limit.) Riess et al. (1998) used a
Monte Carlo exercise to simulate the selection of SNe Ia
near and far. Inputs to this exercise included the time interval between successive search epochs, limiting magnitudes,
observed light-curve shapes, and the distribution of SN Ia
luminosities. They report a net bias of less than 0.01 mag.
These results indicate that the net Malmquist bias has negligible impact on the cosmological conclusions.
2000 PASP, 112 : 1284È1299
FIG. 12.ÈProjected distances from the host centers of nearby SNe Ia
discovered photographically and with CCDs and high-redshift SNe Ia
discovered with CCDs (Howell et al. 2000).
3.6. Alternative Cosmological Models
The conclusions drawn from high-redshift SNe Ia are
predicated on a model with two free parameters, ) and
M
) , and a Friedmann-Robertson-Walker (FRW) cosmol"
1296
RIESS
ogy. In the absence of a sound fundamental motivation for
) B ) , alternate and more general descriptions of an
"
M
energy density with negative pressure have been suggested
(Caldwell, Dave, & Steinhardt 1998). These phenomenological or ““ quintessence ÏÏ models invoke a decaying scalar
Ðeld rolling down a potential as the source of todayÏs acceleration (Wang 2000). A distinction of these models from a
cosmological constant is that w, the ratio of pressure to
energy density, is between [1 and 0, whereas w is exactly
[1 for a cosmological constant. For feasible quintessence
models, w, the equation-of-state parameter, varies slowly
with time and can be approximated today by a constant
equal to
w8 B
/ da) (a)w(a)
Q
,
/ da) (a)
Q
(5)
where a is the scale factor and ) is the energy density of
Q
the vacuum component. The current acceleration for these
models (assuming only two signiÐcant energy components
today, ) and ) ) is
M
Q
q \
0
[a# (t )a(t ) 1
0 0 \ [) ] ) (1 ] 3w)] ,
Q
a5 2(t )
2 M
0
(6)
and is generally less than for a cosmological constant (all
other parameters Ðxed). Inspection of equation (2) reveals
that the universe is accelerating if q is negative [a# (t ) is
0
0
positive], requiring that w \ [1 , independent of the value
3
of ) .
M
Can we determine if the expansion is accelerating in a
quintessence model ? The SN Ia data from Perlmutter et al.
(1999) and Riess et al. (1998) already provide meaningful
constraints on w (Garnavich et al. 1998b ; Perlmutter et al.
1999). Increasing the value of w from [1 (i.e., for a cosmological constant) reduces the acceleration provided by a
Ðxed value of ) , but larger values of ) are needed to
Q
Q
retain an acceptable Ðt to the data. Graphically, increasing
w from [1 rotates the error ellipses in Figure 2 to favor
lower values of ) and greater values of ) . As seen from
M
Q
equation (6), the line separating an accelerating and decelerating universe rotates in the same direction (always
anchored at ) \ 0 and ) \ 0), providing no gain on an
M
Q
acceptable region of parameter space which is not accelerating. The nearest intersection between a nonaccelerating
region of parameter space and one which is preferred by the
data remains when ) > 1 and ) > 1. However, values
M
Q
near ) \ 0 and ) \ 0 are poor Ðts to the data indepenM
Q
dent of the value of w.
Perhaps the simplest way to understand why the SN Ia
data favor an accelerating universe is to consider an FRW
cosmology with ) \ 0 and no vacuum energy. This empty
M
universe must be neither accelerating nor decelerating but
simply coasting. The fact that the high-redshift SNe Ia are
systematically farther for their redshift than expected in this
cosmology means that the distance between low- and highredshift SNe Ia (where redshift is a surrogate for time) grew
faster than expected for a universe which has been coasting
on todayÏs Hubble expansion. This implies that the universe
has been accelerating.
An alternate cosmological explanation to acceleration
has been posited by Goodwin et al. (1999) and Tomita
(2000). They suggest that the supernova data are also consistent with a decrease in the Hubble expansion by
10%È20% beyond z \ 0.1 (300 h~1 Mpc). The distance at
which the Hubble expansion dips would correspond to the
approximate radius of the ““ local ÏÏ underdensity in which
we live. Although a few peculiar Ñow surveys support bulk
motions on scales up to half this size (Lauer & Postman
1994 ; Hudson et al. 1999), most recent surveys do not (Dale
et al. 1999 ; Courteau et al. 2000 ; Colless et al. 1999 ; Riess
1999 ; see Willick 2000 for a review). However, the biggest
problem with such a commodious, local underdensity is its
great improbability. Power spectra demonstrate (Watkins
& Feldman 1995 ; Feldman & Watkins 1998) that the
density of the universe is extremely homogeneous on this
scale, and Ðnding ourselves in the midst of such a vacuous
location would be virtually anti-Copernican. Using cold
dark matter power spectra constrained by CMB observations and large-scale structure, Shi & Turner (1998) and
Wang, Spergel, & Turner (1998) expect 0.5%È1.5% variations in the Hubble constant on 300 h~1 Mpc scales, a
factor of 20 times smaller than required in the local void
model. By Ðlling in the Hubble diagram of SNe Ia at
0.1 \ z \ 0.2 it would be possible to directly test this model.
Outside the FRW cosmologies the SN Ia data can have
signiÐcantly di†erent interpretations. For example, in
steady state cosmologies, SN redshifts do not come from
expansion, but rather through ““ tired-light ÏÏ processes.
However, the SN Ia data exhibit the time dilation e†ect
expected in an expanding universe, implying that the tiredlight hypothesis is incorrect (Leibundgut et al. 1996 ; Goldhaber et al. 1997 ; Riess et al. 1997 ; but see Narlikar & Arp
1997). In the quasiÈsteady state cosmology, the SN Ia data
lead to modiÐcations of the model, such as matter creation
during periodic expansion phases (Hoyle, Burbidge, & Narlikar 2000). A detailed consideration of how to interpret the
SN Ia data in non-FRW cosmologies is beyond the scope of
this review but is thoroughly addressed by Hoyle et al.
(2000). Alternative theories of gravity such as modiÐed
Newtonian dynamics models (MOND ; Milgrom 1983,
1998 ; McGaugh & de Blok 1998a, 1998b) could also modify
the interpretation of the observations of high-redshift SNe
Ia. Within a Lema•ü tre-Tolman-Bondi framework, the SN Ia
data can be interpreted as a challenge to the cosmological
principle rather than evidence for a cosmological constant
(Ce" le" rier 2000).
2000 PASP, 112 : 1284È1299
CASE FOR ACCELERATING UNIVERSE FROM SUPERNOVAE
1297
4. CONCLUSION
5. EPILOGUE
5.1. The Era of Deceleration
If the universe is accelerating, it is a rather recent phenomenon likely commencing between z B 0.4 and 1. Before
this time the universe was more compact and the pull of
matter dominated the push of vacuum energy in the equation of motion. As a result, the universe at z º 1 must be
decelerating. This cosmological signature should be readily
apparent by populating the Hubble diagram of SNe Ia to
z B 1.2. By this redshift SNe Ia in an accelerating universe
will cease to diverge in distance from an equally massive
universe without vacuum energy. Alternatively, if a monotonically increasing, systematic e†ect is the source of the
excessive faintness of high-redshift SNe Ia, the measured
distances of SNe Ia at z º 1 will continue to diverge from a
cosmology without vacuum energy and in addition would
diverge from the cosmological model inferred from SNe Ia
at z \ 0.5 (see Fig. 13). Complex parameterizations of evolution or extinction selected to match both the accelerating
and decelerating epochs of expansion would require a near
conspiracy of Ðne-tuning and are highly doubtful.
E†orts are already underway to Ðnd and measure SNe Ia
at z [ 1. Gilliland, Nugent, & Phillips (1999) used a subsequent epoch of the Hubble Deep Field to detect two SNe,
2000 PASP, 112 : 1284È1299
44
Riess et al. 1998
m-M (mag)
42
Perlmutter et al. 1999
40
38
ΩM=0.3, ΩΛ=0.7
36
ΩM=0.3, ΩΛ=0.0
34
ΩM=1.0, ΩΛ=0.0
L
S in
Ef yst ear
fe em
ct a
t
ic
1.5
Δ(m-M) (mag)
After reviewing the cosmological interpretation of SN Ia
observations and the current challenges to the analysis of
the data, we can now o†er an answer to the question initially posed : do the observations of distant supernovae
compel us to conclude that the expansion of the universe is
accelerating ?
With full consideration of the evidence, we conclude that
an accelerating universe remains the most likely interpretation of the data because the alternatives, individually,
appear less likely. However, the quantity and quality of the
SN Ia evidence alone is not yet sufficient to compel belief in
an accelerating universe. The primary sources of reasonable
doubt are evolution and extinction, as discussed above.
Although the types of studies also described above could
potentially yield evidence that either of these noncosmological contaminants is signiÐcant, the current
absence of such evidence does not suffice as deÐnitive evidence of their absence. Our current inability to identify the
progenitors of SNe Ia and to formulate a self-consistent
model of their explosions exacerbates such doubts. Even
optimists would acknowledge that neither of these theoretical challenges is likely to be met in the near future.
Fortunately there are at least two routes to obtain compelling evidence to accept (or refute) the accelerating universe, one of which employs the use of SNe Ia at even
greater redshifts.
1.0
0.5
0.0
-0.5
-1.0
-1.5
0.01
0.10
z
1.00
FIG. 13.ÈHubble diagram of SNe Ia (see Fig. 1) and the e†ect of a
systematic error which grows linearly with redshift (e.g., evolution or gray
extinction).
one (SN 1997†) with a photometric redshift of z \ 1.32. The
elliptical host of SN 1997† suggests that this object is of
Type Ia, but the observations are insufficient to provide a
useful distance estimate. The SCP reported the discovery of
SN 1998ef at z \ 1.2 (Aldering et al. 1998) and follow-up
observations with the HST will provide a useful distance
estimate (G. Aldering et al. 2000, private communication).
The HZT recently reported the discovery of four SNe Ia at
z [ 1 including SN 1999fv at z \ 1.2 (Tonry et al. 1999).
From this growing sample will likely come the means to
search for the epoch of deceleration.
5.2. Cosmic Complements
We previously sought to determine if the observations of
SNe Ia alone require an accelerating universe. Now we will
brieÑy consider the cosmological constraints provided by
other astrophysical phenomena. A thorough discussion of
these constraints is beyond the scope of this review but can
be found elsewhere (Turner & Tyson 1999 ; Roos & Harunor-Rashid 2000 ; Sahni & Starobinsky 1999).
Current measurements of the CMB power spectrum indicate that the sum total of energy densities is within 10% of
1298
RIESS
FIG. 14.ÈCosmological constraints from SNe Ia, CMB, and matter
(Turner 1999).
unity. This result is seen from the BOOMERANG
(Melchiorri et al. 1999 ; Lange et al. 2000 ; de Bernardis et al.
2000), the TACO (Miller et al. 1999) and MAXIMA experiments (Hanany et al. 2000 ; Balbi et al. 2000) and from a
compilation of all other CMB measurements (Tegmark &
Zaldarriaga 2000). In addition, estimates of ) from the
M
mass, light, X-ray emission, numbers, and motions of clusters of galaxies converge around 0.2È0.3 (Carlberg et al.
1996 ; Bahcall et al. 1997 ; Lin et al. 1996 ; Strauss & Willick
1995). These two pieces of information alone indicate a signiÐcant contribution by vacuum energy, sufficient to
produce an accelerating universe (see Fig. 14). Additional
constraints from observations of the Lya forest, cluster evolution, double radio galaxies, and statistics of gravitational
lenses have been used to tighten these conclusions (Roos &
Harun-or-Rashid 2000 ; Turner 1999 ; Eisenstein, Hu, &
Tegmark 1999 ; Lineweaver 1998).
Although no single cosmological observation yields a
conclusive census of the energy densities in the universe, the
combined constraints from multiple experiments is providing strong bounds on the cosmological parameters. Each
individual experiment has unique sources of systematic
uncertainty. By combining the results of many experiments,
it should be possible to negate their impact on the determination of the cosmological parameters.
I wish to thank Mario Livio, Alex Filippenko, and
Robert Kirshner for helpful discussions and comments.
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