CHAPTER 18
Cosmology: The Nature of the Universe
CHAPTER OUTLINE
18-1 The Search for Centers and Edges
1. Ptolemy’s model placed the Earth at the center of the universe.
2. Copernicus moved the Earth from the center and replaced it with the Sun.
3. Galileo introduced the concept of inertia and argued that stellar parallax was not observed because the stars were too far away.
4. Newton proposed that the universe was infinite because if it were not, gravity would
cause it to collapse to its center.
5. Though Herschel erroneously put the solar system at the center of the Milky Way, he
did expand the boundaries of the known universe. He also argued that fuzzy nebulae were
actually galaxies like ours.
6. Shapley used the globular clusters to show that the solar system is not the center of the
Milky Way Galaxy.
7. Hubble discovered Cepheid variables in the Andromeda “nebula,” proving that it was a
galaxy in its own right. This discovery pushed back the boundaries of the universe still
further.
Einstein’s Universe
1. Einstein’s general theory of relativity substituted curved space for gravitational force.
Space itself is curved near a massive object and it is this curvature that causes the acceleration previously attributed to the force of gravity.
2. In the absence of any exotic forms of energy, if there is enough matter in the universe
to eventually cause its collapse, space is curved enough that the universe is said to be
closed. In a closed universe, its total mass and energy density is greater than a specific
value called the critical density.
3. In the absence of any exotic forms of energy, the amount of matter in an open universe
is not enough to slow its expansion, and such a universe will continue expanding forever.
An open universe is infinite and continues on forever. In an open universe, its total mass
and energy density is less than a specific value called the critical density.
4. At the boundary between an open and closed universe is the special case of a flat universe. In a flat universe, its total mass and energy density is exactly equal to the critical
density, which is equal to 3Ho2/(8G) or equivalent to about 5.5 hydrogen atoms per
cubic meter of space.
5. Einstein could not accept an infinite and expanding universe, so he adjusted his theory
in an ad hoc manner to insure that it would neither collapse on itself nor expand. He introduced in the equations of general relativity the cosmological constant (), a term that
corresponds to a cosmological repulsive force to support the universe against collapse.
6. Without the insertion of his cosmological constant, Einstein would have seen what was
discovered observationally—that the universe is expanding.
7. Recent observations suggest the presence of an exotic form of energy, which results in
a repulsive force helping the universe expand at an accelerating rate as time goes on. We
don’t know the characteristics of this exotic form of energy.
18-2 The Expanding Universe
1. In 1929 Hubble announced that the pattern of redshifts of distant galaxies indicates that
they are moving away from us and that the more distant the galaxy, the faster it is moving
away.
2. The universe of galaxies is expanding and no one galaxy—the Milky Way included—
is in any special, central position.
3. That the universe is expanding is a conclusion based on the observations of redshifts of
distant galaxies, it is not an observation.
What is Expanding and What Is Not? The Cosmological Redshift
1. The observed redshift leads us to conclude that it is clusters of galaxies that are moving away from us. In certain instances, individual galaxies within the local group are
moving toward us. The expansion of the universe corresponds to clusters of galaxies
moving farther apart from each other.
2. A gravitationally bound object is not expanding due to the expansion of the universe.
3. An expanding universe does not mean that the clusters of galaxies are rushing through
space. Instead, space itself is expanding.
4. Though the Doppler effect can be used to calculate the velocities of the galaxies, it is
not an explanation of why they are moving away from us.
5. The cosmological redshift is a shift toward longer wavelengths that is due to the expansion of the universe, i.e., the expansion of space itself. It is the expanding space that
lengthens (or redshifts) an already emitted wave.
Olbers’ Paradox
1. Olbers’ paradox is an argument showing that the sky in an infinite, static universe
could not be dark.
2. If stars and galaxies are distributed throughout space, then in whatever direction one
looked, one should see a star. Yet, the night sky is dark because we see relatively few
stars.
3. The resolution of Olbers’ paradox—the reason the sky is dark—is based on the related
ideas that the universe has a finite age and is expanding.
4. An expanding universe had to have a beginning. This finite age for the universe means
that we cannot see any objects beyond the limits of the observable universe, since light
from beyond these limits did not have enough time to reach us.
5. Also, due to the expansion of the universe, light from distant galaxies is redshifted and
thus loses energy.
18-3 Cosmological Assumptions
1. The assumptions of cosmology are:
(a) The universe is homogeneous.
(b) The universe is isotropic.
(c) The same physical laws apply everywhere in the universe.
2. A homogeneous universe has uniform properties throughout. An isotropic universe
looks the same in all directions.
3. Homogeneity and isotropy comprise the cosmological principle. This principle formalizes the idea that we are not located at a special place in the universe. It holds that on
a large scale the universe is the same everywhere.
4. The principle of universality refers to the assumption that the same physical laws apply
everywhere in the universe.
18-4 The Big Bang
1. The present motion of galaxies suggests that at one time in the past, the matter in the
universe must have been much closer together. Big bang is the theoretical initial explosion that began the expansion of the universe.
2. The universe is not expanding into empty space around it, for space does not exist
apart from the universe.
3. After the initial explosion, the steady decrease in the temperature of the universe allowed the nuclear particles to form into hydrogen and helium atoms, which then clustered
into stars.
Advancing the Model: The Steady State Theory
1. In 1948, a perfect cosmological principle was proposed. It stated that our location in
time is no more special than our location in space. In this model, the overall universe
does not change.
2. In the steady state theory, matter is created in the space between galaxies in such
amounts that the universe maintains its density. This corresponds to the creation of one
hydrogen atom in each cubic meter of space every 10 billion years or so, which is far below the accuracy to which the law of conservation of mass and energy has been verified.
3. Observations made in the 1950s of the relationship between the number density of radio sources and the energy received per unit time per unit area showed that the universe is
evolving, in contradiction to the steady state theory.
4. Also, the amount of helium observed in the universe is greater than what can be expected from stellar evolution. Thus we will have to accept that helium is also spontaneously created or that there was a special period in the universe’s life at which a great
amount of helium was created.
5. Finally, the discovery of the cosmic background radiation made it impossible to reconcile its existence with the steady state theory.
Evidence: Background Radiation
1. The discovery of the cosmic microwave background (CMB) radiation supports the
idea of the big bang.
2. The hot matter at the early universe was opaque to radiation. As a result of the expansion, when matter cooled to 3000 K, the universe became transparent. At this point, the
gas that made up the universe was emitting radiation that had characteristics of a blackbody at 3000 K, and this radiation existed over the entire universe.
3. Over the billions of years since the big bang, this initial radiation would have redshifted so as to give the appearance of a very cold object —one at about 3 K (–270°C).
4. The CMB radiation is long wavelength radiation observed from all directions and believed to be the remnants of radiation from the big bang.
5. Predictions for the existence of the CMB radiation were made in 1948 and again in the
mid-1960s. The discovery of the CMB radiation was made accidentally by Penzias and
Wilson who were doing applied research on microwave transmission. Their antenna
picked up the low-intensity radio waves characteristic of the background radiation.
6. In 1989 the COBE satellite successfully measured the CMB radiation at various wavelengths. The COBE data show that the temperature of this radiation is 2.728 K (± 0.004
K). This data matches the theory to within 0.03%, which is 1000 times better than the
best data before COBE.
Advancing the Model: The Early Universe
1. According to our present understanding of space and time, the smallest interval for
which we can talk about the universe is 1043 seconds.
2. At this time, the universe was hot, about 1032 K, and it was expanding.
3. At about 1035 seconds, a period of inflation may have occurred, lasting for only 1032
seconds but having tremendous implication for the history of the universe.
4. By 106 seconds after the big bang, the temperature dropped to about 1013 K, which
was cool enough for neutrons and protons (hydrogen nuclei) to form.
5. Between 10 and 15 minutes after the big bang, helium nuclei (consisting of two protons and two neutrons) were formed. The easiest way to form helium nuclei is to first
form deuterium nuclei (consisting of a proton and a neutron). By the end of this time period, the temperature had dropped to below about a billion K.
6. The evidence for all of this is in the proportions of hydrogen, helium, and deuterium
we have observed in the universe. The predicted abundances of the light elements agree
very well with the observations if the overall density of ordinary matter is 4% of the critical density.
7. As the universe continued to expand, it cooled, and matter became increasingly dominant.
8. About 2500 years after the big bang, when the temperature dropped to about 75,000 K,
the universe became matter-dominated and became increasingly so since then.
9. About 380,000 years after the big bang, the universe became transparent. Its temperature at this point was 3000 K. This low temperature allowed the formation of hydrogen
atoms, since the photons didn’t have enough energy to keep the protons and electrons
from forming the atoms.
Additional Evidence for the Big Bang
1. The Hubble law, the darkness of the night sky, the homogeneity and isotropy at large
scales support the big bang theory.
2. Additional support for the big bang theory is provided by the following.
(a) The observed time dilation of distant supernova light curves.
(b) The observed relationship between the number density of distant radio sources and
quasars and the energy received from them per unit time and per unit area, which shows
that the universe evolved.
(c) The existence of the CMB radiation and the dependence of its temperature on redshift,
which shows that the universe evolved from a hot and dense state.
(d) The observed abundances of the light elements.
(e) The observed anisotropies in the CMB radiation.
The Age of the Universe
1. The reciprocal of the Hubble constant gives us an upper limit for the age of the uni-
verse. If the constant is 15 (km/s)/Mly, the age of the universe is 20 billion years. If the
constant is 25 (km/s)/Mly, the calculated age of the universe is 12 billion years.
2. The most recent studies of the Hubble constant place it at about 22.5 (km/s)/Mly or 73
(km/s)/Mpc.
18-5 The Future: Will Expansion Stop?
1. Gravity is slowing down the expansion of the universe. But will it slow it down enough
to stop it?
2. A closed universe will stop its expansion only in the absence of an exotic form of energy. An open universe will not stop at all.
3. The oscillating universe model is a big bang theory that holds that the universe goes
through repeating cycles of explosion, expansion, and contraction.
Evidence: Distant Galaxies and High-Redshift Type Ia Supernovae
1. One way to look for evidence whether the universe is slowing its expansion is to compare the speeds of distant galaxies (which are seen as they were far back in time) to that
of nearby galaxies. In practice, such observations are difficult to make.
2. A graph of recessional velocity versus distance for galaxies offers three choices: a
closed universe, an open universe, and a steady state universe.
3. A flat universe is the borderline case between an open and closed universe. Assuming
no cosmological constant, if the universe is flat, it will slow its expansion but stop only
after an infinite amount of time.
4. This borderline is described by the value of the critical density. Astronomers prefer to
work with the ratio of the total mass and energy density of the universe to the critical
density: this ratio is called the density parameter (o). If o is greater than 1, the universe is closed. If it is less than one, the universe is open, and if it is equal to one, the
universe is flat.
5. Contributions to the density parameter come from matter, radiation, and any possible
form of exotic energy: o = m + rad + .
6. Observations suggest that rad is negligible and that dark energy (an exotic form of
energy whose negative pressure currently accelerates the expansion of the universe) does
exist.
7. In order to find whether gravity or dark energy is the main factor in determining the
future of the universe, astronomers study the relationship between recessional velocities
and distances for distant galaxies and Type Ia supernovae.
8. The observational data show that the cosmic expansion is now accelerating and that the
universe is dominated by dark energy: m = 0.3 and  = 0.7. Our universe is flat and
will expand for ever with an ever-increasing rate.
18-6 The Inflationary Universe
1. The standard big bang theory fails to explain two cosmological observations that appear to be coincidences: the flatness problem and the horizon problem.
The Flatness Problem
1. A flat universe is a special case; it has a density that puts it exactly on the border between open and closed. The flatness problem is the inability of the standard big bang
model to account for the apparent flatness of the universe.
2. The inflationary universe model is a modification of the big bang model that holds
that the early universe experienced a brief period of extremely fast expansion.
3. Between 10–35 s and 10–32 s after the big bang, the universe suddenly expanded at an
extremely fast rate, growing by a factor of 1050 during that time.
4. The inflationary universe model holds that an “inflation” of the universe took place so
quickly that any portion of it that had great curvature before the universe became flat as a
result of the inflation.
The Horizon Problem
1. The CMB radiation is remarkably uniform. COBE data show that, after correcting for
the motion of the Earth, the radiation varies in temperature by less than 1 part in 100,000.
This implies a very uniform temperature for the universe at the time the CMB radiation
was emitted.
2. The horizon problem is the inability of the standard big bang model to account for
directional uniformity of the background radiation.
3. According to the inflationary universe model, before inflation occurred the universe
was smaller than the horizon distance. Thus the universe could be at a uniform temperature.
4. Once inflation occurred, two parts of the universe that were originally within each other’s horizons were outside those horizons after inflation. They were still at the same temperature, however, as a result of their condition before inflation. That is why all parts of
the today’s observable universe show a uniform background radiation.
18-7 The Grand Scale Structure of the Universe
1. At first, the inflationary theory had difficulty explaining how galaxies and clusters of
galaxies could form relatively soon after the big bang out of a completely uniform universe.
2. To make matters worse, during the 1980s it was discovered that galaxies are not dis-
tributed uniformly but are arranged as if to form bubbles, with a void between the walls
of the bubbles.
3. The inflationary model includes a random distribution of density perturbations (irregularities) during the earliest moments of the universe. The amplitudes of these perturbations were smoothed out during inflation, resulting in only small-scale anisotropies in the
CMB radiation.
4. About 380,000 years after the big bang, the universe became cool enough (about 3000
K) that protons were able to capture electrons and form neutral hydrogen. At this stage,
matter and radiation decoupled from each other.
5. It is also at this stage that radiation last interacted strongly with matter. Since then, the
wavelengths of these photons have stretched so much due to the cosmic expansion that
we see them as the CMB photons. The CMB radiation carries with it information about
the early universe in the form of temperature anisotropies.
6. In 1992 the COBE team found tiny irregularities (variations) in the CMB radiation
amounting to a deviation of 0.00003 K; these irregularities are due to tiny differences in
the temperature of the early universe.
7. In 1999, the BOOMERANG project gave us a map of the early universe that was about
40 times more detailed. The data suggested that our universe is very nearly flat. Additional confirmation came from MAXIMA in 1999 and WMAP since 2001.
8. The observed temperature fluctuations reflect the conditions set in motion just after the
big bang; they are like fingerprints that we could use to compare with fingerprints predicted by theoretical models. All data from these projects point to the same match: our
universe has about 4% normal matter, 20% dark matter, and 76% dark energy.
9. The WMAP results suggest that the big bang occurred 13.7  0.2 billion years ago. The
Hubble constant is found to be about 73  3 (km/s)/Mpc.
10. The locations, heights, and shapes of the observed peaks and troughs in the angular
power spectrum of the temperature fluctuations in the WMAP full-sky map serve to constraint a number of cosmological parameters.
11. WMAP also mapped the intensity and direction of linear polarization everywhere on
the CMB sky. (Light is linearly polarized when its electric field oscillates in a fixed
plane.) This data suggests that the first stars in the universe formed very quickly, about
200 million years after the era of decoupling.
Advancing the Model: Dark Energy
1. An imprint of this exotic form of energy was found on the CMB radiation in 2003.
2. Two of the leading ideas as to the nature of dark energy are the following.
(i) Einstein’s cosmological constant: a constant energy density that fills space in a homogeneous way.
(ii) Quintessence: a dynamic field whose energy density changes as a function of time
and space.
3. The fate of the universe depends on the nature of the dark energy. It is possible that the
expansion will continue forever; however, it is also possible that the influence of gravity
could lead to a big crunch.
Cosmic Evolution
1. VLT observations reveal that large galaxies formed when the universe was less than a
billion years old. Also, these galaxies seem to cluster close to each other. This supports
the idea that the universe has a spongy structure.
2. HST observations support the idea that the first quasar engines started slightly before
the universe was 1 billion years old.
3. Three-dimensional maps of the large-scale structure of the universe support the case
for dark matter, dark energy, and the spongy structure of the universe.
4. Cosmologists are in fairly good agreement with the basic idea of the inflationary model. The details, however, are tentative.