tChapter 7
Modern measurements, dark energy and the accelerating universe
In this chapter, we will see how recent satellite measurements of the cosmic microwave background gives
convincing support for both the big bang model and the theory of inflation. We shall also see how a new method
of estimating astronomical distance led to the discovery of the accelerating universe. These measurements
combine to form today’s model of a flat, accelerating universe that contains dark matter and dark energy.
We saw in chapter six that the discovery of the cosmic microwave background (CMB)
heralded a new era in cosmology. The ensuing search for the parameters of the big bang
model led to several puzzles, which led to the development of the theory of cosmic inflation
(chapter 7). However, inflation left something of a divide between theorists and
experimentalists. Many theoreticians now believed in an inflationary universe of flat
geometry, containing a great deal of some as-yet undiscovered dark matter; on the other hand,
astronomers measured a universe with a low mass density and thus open geometry. Which
was the real universe?
A second disjunction of theory and experiment came to the fore. Despite painstaking studies
of increasing accuracy, non-uniformities were not observed in the cosmic microwave
background1. This was puzzling as one would expect the seeds of today’s galaxies and galaxy
clusters to be manifest as fluctuations in the temperature of the background radiation1. Yet
the radiation appeared stubbornly smooth to astronomers throughout the 1980s2 .
The COBE mission
In 1989, the Cosmic Background Explorer (COBE) was launched into orbit 900 km above the
earth (figure 10). This was the world’s first satellite measurement of the cosmic background
radiation; the project had been planned since the 1970s, but had suffered a number of delays
and mishaps3. The mission had two main aims; to measure the shape of the spectrum of the
background radiation (including wavelengths obscured by the earth’s atmosphere) and to
detect possible inhomogeneities in the radiation. The spectrum was mapped by an instrument
known as FIRAS and the inhomogeneities measured by a Differential Microwave Radiometer
(DMR). In 1990, the first results from FIRAS were announced; the spectrum of the
background radiation fitted the theoretical spectrum of a black body precisely (figure 11).
This was a result of great significance, as it constituted evidence that the radiation was of
primeval origin, effectively ruling out many alternative models4. The data were presented in
real-time at a famous meeting of the American Astronomical Society and led to a standing
ovation for John Mather, the instrument’s chief designer.
Figure 10a; the COBE satellite at an altitude of 900 km above earth
Figure 10b; spectrum of the CMB as measured by the FIRAS instrument aboard the COBE satellite. The data (
squares) fit perfectly to the theoretical spectrum of a perfect blackbody (solid curve)
In a separate experiment, the DMR instrument on board COBE provided sensitive
measurements of the background radiation from two different directions in space
simultaneously. These data were collected over several years, and in 1992, the results were
announced; small variations in the temperature of the radiation had been detected. However,
the fluctuations were tiny indeed, of the order of 1 in 100,000 or 0.001%. Small wonder that
they had not been observed earlier!
Hence, the COBE measurements provided a significant boost to the big bang model; the
spectrum of the microwave background was exactly as predicted and inhomogeneites in the
radiation corresponding to the seeds of structure had at last been observed. Granted, these
non-uniformities were extremely small; it was hard to see how they would lead to today’s
galaxies in the standard big bang model. However, the theory of inflation provided a ready
answer, as we saw on page 77. When George Smoot, chief scientist on the DMR instrument,
presented the results at a press conference in 1992, he described the data as ‘direct evidence
of the birth of the universe’ and said that looking at the data was ‘like seeing God if you are
religious’5. Soon afterwards, the famous cosmologist Stephen Hawking described the result
as ‘the most significant scientific finding of the twentieth century’. A few years later, John
Mather and George Smoot were awarded the 2006 Nobel prize in physics “for their discovery
of the blackbody form and anisotropy of the cosmic microwave background radiation".
The Hubble Space Telescope
Another important advance was the launch of the famous Hubble Space Telescope (HST).
The concept of an observatory orbiting in space had been mooted since the 1960s and, after
many delays, the HST was finally launched aboard the space shuttle Discovery in 1990. After
some initial problems, the telescope began taking breathtaking images of deep space from
1993 onwards6. These images have become icons of our age and led to a great upsurge of
interest in astronomy (see figure 11).
As regards cosmology, the Hubble Space Telescope extended measurements of astronomical
distance by detecting Cepheid variables in galaxies much further way than ever before (see
chapter 1). The result was a new estimate of Hubble’s constant (73 +/- 1 km/s/Mpc), settling
the Sandage-de Vancouleurs debate (see p 55). However, this revised value was something of
a puzzle; assuming a value of Ω = 0.3 for the density of matter, it suggested an age for the
universe of about 8 billion years, somewhat in conflict with the known age of some galaxy
clusters.7
Figure 11a; the Hubble space telescope
Fgure 11b Iconic image of the ... galaxy taken by the Hubble space telescope
Dark energy and the accelerating universe
In the 1990s, a new method of extending our view into the cosmos emerged. This was the
technique of using supernovae as standard candles8. A supernova is what occurs when a
certain type of star collapses to form a black hole; during this event, the material of the star is
spewed outwards in a gigantic explosion (recall from chapter 4 that it is this process that
gives rise to the formation of the heaviest chemical elements). Supernova events are
extremely luminous, but they are also very rare. As more sophisticated telescopes reached
further into space (and back in time), more supernovae were observed. Most importantly, it
was discovered that the luminosities of a particular type of supernova – type 1a - are
extremely uniform, making them ideal standard candles for the calibration of the largest
distances9.
In the late 1990s, two teams of astronomers sought to obtain new estimates of the Hubble
constant using type 1a supernovae; the Supernova Cosmology Project led by American
physicist Saul Permutter and the High-Z Supernova Research Team led by the astronomer
Martin Schmidt. Both teams were surprised to measure distant supernovae as dimmer (i.e.
further way) than expected from simple extrapolations of the Hubble graph, by a factor of
about 25%! This was a curious finding indeed. Although we refer continually to the ‘Hubble
constant’, physicists had long expected to observe a decrease in the rate of the expansion of
the universe at the largest distances, due to the gravitational pull of the galaxies. But the
supernova measurements pointed to a rate of expansion that is increasing, a finding now
known as the acceleration of the universe.
Despite initial scepticism, painstaking reviews of the supernova data suggested that the effect
was real and that there was an unknown force of expansion at work in the cosmos10. It
seemed ordinary matter and dark matter did not comprise the total energy density of the
universe; the remainder was an unknown form of energy that was named dark energy. 11 This
discovery marked yet another paradigm shift in cosmology. But what was the nature of dark
energy?
Several explanations were proposed, but the simplest was an old friend; perhaps the
accelerated expansion was evidence of a cosmological constant. Recall that Einstein added a
cosmological constant to the equations of relativity in order to predict a static universe,
interpreting it as an energy of space that acts to counterbalance the inward force of gravity at
the largest scales. With Hubble’s observation of the galaxy redshifts, Einstein dropped his
cosmological constant, declaring it his ‘greatest blunder’ (see chapter 2). However, Lemaitre
and others considered it an important addition to relativistic models of the universe and made
use of it to reconcile the age of the universe measured from Hubble’s law with the known age
of stars (see figure 3). When Hubble’s estimates of astronomical distance were revised by
Baade and Sandage in the 1950s, it seemed the cosmic constant could safely be set to zero.
However, it never really disappeared from theoretical models of the universe and now it was
back with a vengeance.
Considering the new Hubble graph of figure 12, a quantitative estimate of the contribution of
dark energy can be obtained by attempting to fit a curve to the data. Recall that the density of
matter in the universe is defined in terms of the parameter ΩM, the ratio of the actual density
of matter to that required to close the universe. This definition must now be extended to
include a new term ΩΛ , representing the contribution of dark energy. Thus, the geometry of
the universe will be determined by the sum of two contributions i.e. Ωtotal = ΩM + ΩΛ. (As
before, Ω <1 denotes a universe of open geometry, Ω >1 denotes a universe of closed
geometry and Ω=1 is the special case of a flat universe). It is clear that the astronomer’s
favourite, an open universe of low matter density and no dark energy (ΩM = 0.3, ΩΛ = 0) does
not fit the data well. A universe of flat geometry with no dark energy (Ωtotal = 1, ΩΛ = 0) is
also a poor fit. By far the best fit is obtained if one assumes a universe of flat geometry (Ωtotal
= 1) with a dark energy contribution of over twice that of matter. Taking the observational
value of ΩM = 0.3 for the matter density suggests a value of about 0.7 for ΩΛ. However,
these estimates were provisional as the fit only provides an estimate of the relative
contributions of dark energy and matter; it does not provide an independent estimate of
either, or indeed of the overall geometry of the universe12.
Figure 12 Supernovae measurements show the Hubble graph is not linear at the largest distances. Three possible
fits to the data are shown; the best fit is obtained with a model with ΩM = 0.3 and ΩΛ = 0.7 (top line). Data and
fits from [12]
In sum, the discovery of an accelerated expansion indicated a universe with two contributions
to its energy density and thus to its geometry. One contribution, ΩM, comprises both ordinary
matter and cold dark matter. Another contribution, ΩɅ, acts to oppose the gravitational effect
of matter and became known as dark energy. Fits to the data suggested a relative contribution
of about 30% from matter and 70% from dark energy respectively; from the known density of
matter this in turn suggested a universe of flat geometry, in pleasing agreement with the
predictions of inflation. However, further measurements were needed in order to obtain
independent estimates of each contribution and of the overall geometry of the universe.
Could the observed acceleration be some type of systematic error in our measurement of the
largest distances? This possibility was ruled out when subsequent measurements of extremely
distant supernovae showed evidence of a de-accelerated expansion13. It seems dark energy
emerged only when the universe reached a certain age; after a gradual slowing of the
expansion over the first 7 billion years or so, the universe began to speed up and may
continue to do so from now on!
Dark energy and the cosmic microwave background
It was soon realised that the cosmic microwave background might also reveal the presence of
dark energy. This is because the angular scale of the temperature fluctuations in the
background radiation provides a measure of the geometry of the universe.14 Accurate
measurements of the ripples in the microwave background should reveal whether the
geometry is open, closed or flat - and thus provide an estimate of the total energy density of
the universe. The COBE satellite had already detected ripples in the CMB, but more accurate
measurements were needed in order to determine their scale.
In 1999, two experiments reported new measurements of fluctuations in the cosmic
microwave background. These experiments monitored the radiation using instruments in
high altitude balloons in order to minimise interference from the atmosphere. (This allowed
massive cost reduction compared to a satellite probe, though only a small part of the sky
could be scanned). The BOOMERANG project took observations at an altitude of 42
kilometres above the Antarctic for a period of ten days, and a similar project, MAXIMA, was
launched from Texas. Both experiments suggested that the geometry of the universe is indeed
flat to within an experimental error of less than 5% i.e. Ωtotal = 1.00+/- 0.05. This was an
important advance; taking a value of ΩM = 0.3 for the density of matter from astrophysics, it
suggested a dark energy contribution of 0.7, in good agreement with the supernova results15.
It is always a good moment in science when different lines of enquiry point towards the same
result and the next experiment was to prove even more satisfying..
Fig 15. The boomerang experiment gave the first direct experimental measurement of the geometry of the
universe
The WMAP mission
In 2001, the Wilkinson Microwave Anisotropy Probe (WMAP) was launched into orbit. This
experiment comprised highly sensitive instruments aboard a satellite 1.5 million kilometres
from earth, calibrated to measure fine variations in the microwave background. The measured
variations are plotted as a function of angle in figure 13, a plot known as the angular power
spectrum (the temperature is expressed in multipoles and the intensity is plotted as a function
of multipole number, a representation that arises from a mathematical co-ordinate system
known as spherical harmonics) . The dominant feature of the spectrum is the large peak on
the left hand side, known as the ‘first acoustic peak’. Theory predicts that this feature is a
direct measure of the curvature of space and the WMAP spectrum gives a value of Ωtotal =
1.0 +/- 0.02, in excellent agreement with the balloon experiments. Analysis of the acoustic
peaks also gives an estimate of the contribution of matter density alone, suggesting a value of
ΩM = 0.27, in good agreement with astrophysical observation. Combined together, these
results suggest a value of ΩΛ = 0.73 for the contribution of dark energy, in excellent
agreement with the supernova results.
A theoretical fit (solid line) to the data is also shown in figure 13. This fit has been computed
with the use of the parameters Ωtotal = 1.0, ΩΛ = 0.73 and ΩM = 0.27 16. It can be seen from
the diagram that these parameters give a very good fit indeed to the data. By contrast, none of
the main alternative models (a flat universe with no dark energy, a non-flat universe with
dark energy or a non-flat universe with no dark energy) give a good fit, as can be seen in
figure 14. By far the best fit is obtained by assuming a model of a flat universe containing
ordinary matter, cold dark matter, and dark energy.
Fig 13 Anisotropies of the CMB as a function of angle, known as the power spectrum. The solid line is that
predicted by the ɅCDM model with inflation with the parameters Ωtotal = 1.0, ΩΛ = 0.73 and ΩM = 0.27
Fig 14 Alternative fits to the power spectrum. The solid line is that predicted by the ΛCDM model with inflation
with the parameters Ωtotal = 1.0, ΩΛ = 0.73 and ΩM = 0.27
The Λ-CDM model
The experiments of this chapter - the COBE satellite mission, the supernova measurements,
the BOOMERANG and MAXIMA balloon experiments and the WMAP mission – lead
inexorably to a new version of the big bang model. This view is now known as the standard
or Λ-CDM model; it states that we live in an expanding universe of flat geometry that
contains ordinary matter, cold dark matter (CDM) and dark energy. The term Λ-CDM
indicates that the dark energy is thought to arise from a non-zero cosmological constant
indicative of a natural tendency of space to expand, opposing the gravitational effect of
matter. Note that the moniker is slightly misleading as there are three contributions to the
mass/energy density of the universe; we currently estimate these contributions as
approximately 74%, 22% and 4% for dark energy, dark matter and ordinary matter
respectively (see figure 15).
Figure 14 Pie chart of the relative contributions of ordinary matter, dark matter and dark energy to the
mass/energy density of the universe
It should be noted that the observation of flat geometry fits very nicely with the hypothesis of
inflation; as we have seen, it is very hard to explain how the universe should have this
geometry without some form of inflation in the first fractions of a second. We also saw in
chapter 6 that inflation predicts fluctuations in the cosmic microwave background of the right
order of magnitude. Indeed, the theory predicts that the spectrum of fluctuations will have a
shape that is very nearly independent of scale (characterized by a scalar spectral index ns that
is close, but not exactly equal to 1.0 to an accuracy of 10%). It is exciting to note the
spectrum in figure 13 has exactly such a shape; the fit has been computed by taking a spectral
index of ns = 0.95 +- 0.0216.
Finally, we note that, for all the exciting successes of this chapter, the term Λ-CDM also
highlights the shortcomings of the model; we do not know what physical substance comprises
either dark matter or dark energy and hence it could be argued that we do not know what
comprises 96% of the universe! This puzzle will be discussed further in the next chapter,
along with other outstanding problems.
Notes
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
Fluctuations in density at the time of recombination are measured as variations in temperature in the
CMB.
There is a very good overview of this period in chapter ... of Marcus Chown’s book. (Chown 1997).
Including the tragedy of the Challenger Disaster. There is a very good overview of the buildup to the
COBE experiment in chapter 6 of Smoot’s book (Smoot, 1997)
For example, a background of numerous stellar and gaseous emissions could not produce such a
spectrum
Unfortunately, this statement was truncated to ‘like seeing God’ in many press reports
One of the telescope mirrors was found to be flawed, and had to be replaced by astronauts.
This calculation assumes a matter-filled universe with no cosmological constant
The idea was first suggested by Fritz Zwicky and later by Walther Baade; as supernovae are rare events
it did not become practical until the 1990s
Type 1a supernovae occur when a white dwarf star collapses to a black hole. The process leads to a
luminous source that is extremely uniform and ideal for calibration of distance
The fascinating story of the discovery of the accelerating universe is told in great detail in Robert
Kirshner’s book (Kirshner 2002).
It is not known who first coined the term dark energy, but it is probably named in analogy with dark
matter. It is an unfortunate term as students often confuse the two, and the confusion is heightened
when one recalls the mass-energy equivalence of relativity.
The data and fitting of figure 12 is taken from Perlmutter’s 1999 publication
This point is very important and is often overlooked. If the acceleration was a systematic error, it would
get larger the further back we look. In fact, measurements of supernova at the largest redshifts suggest
a deaccelerated expansion; thus the universe underwent a change from a slowing expansion to an
accelerated one.
A measurement of the angle covered by an object of known size at a known distance gives information
about whether the geometry of the universe is open, closed or flat. The maximum size of fluctuations in
the CMB is 300,000 light years (because recombination occurs at 300,000 years) and they are viewed
at a distance of 14 billion light years; hence a measurement of the angle gives the geometry of the
universe.
15. Actually, one doesn’t need to assume a value for ΩM. Since the balloon measurements give an estimate
of the sum ΩM + ΩΛ, and the supernova measurements give an estimate of the difference ΩΛ - ΩM,
the two equations combined give independent estimates of each.
16. Figure 13 and 14 are provided by David Kaiser of MIT. There is a very nice overview of fitting the
predictions of inflation to this data in(Guth and Kaiser 2002)
Bibliography
PerlmutterS, Aldering G, Goldhaber G et al (1999) Measurements of omega and lambda from 42 high-redshift
supernovae Astronomical Journal vol 517 ((2) p 565
Chown Marcus
Guth A and Kaiser D
Smoot George: Ripples on the cosmos
Rowan-Robinson
Zlatev, I.; Wang, L.; Steinhardt, P. (1999). "Quintessence, Cosmic Coincidence, and the Cosmological
Constant". Physical Review Letters 82 (5): 896–899. Or arXiv: astro-ph/9807002