Cosmic Dawn

by George Rhee

  Fig. 1.5Georges Lemaître who proposed the idea that later became known as the Big Bang theory of the origin of the universe (Credit: Archives Georges Lemaître, Université catholique de Louvain, Centre de recherche sur la Terre et le Climat G. Lemaître, Louvain-la-Neuve, Belgique)

  One can use Hubble’s constant to get an estimate of the age of the universe. Hubble’s estimate of his constant was about ten times too big, implying an age of the Universe of 2 billion years–rather discomforting, given that the oldest rocks on Earth were believed to be about 4 billion years old. Conflicts with geologists had already arisen when physicists in the nineteenth century estimated the age of the Sun to be 100 million years, which contradicted the evidence from geology. When Hubble’s distance scale was revised, it resulted in a universe that was at least 10 billion years old, the most recent estimate being about 14 billion years.

  Hubble also studied the shapes of the nebulae on photographic plates and produced a classification scheme that is still used today. Not all nebulae have a spiral shape. Some appear elliptical. Hubble proposed a scheme suggesting that elliptical nebulae might have evolved into spiral nebulae.

  While the debates about the nature of our galaxy and the spiral nebulae were fermenting, Albert Einstein (1879–1955) was working on including the concept of curved space into a theory of gravitation. This work was done in the years 1912–1914. The theory produced a set of equations that could be used to express the geometry of the universe. The simplest solution he found to these equations implied that the universe was expanding. By this we mean that the distances between objects in the universe are increasing. This conclusion in 1917, came about 10 years before the formulation of Hubble’s law. Since Einstein believed that we live in a static universe, he modified the equations to produce a static universe proposing the constant Λ. Thus Einstein very nearly predicted–but not quite–the expansion of the universe.

  Interestingly, de Sitter (1872–1935) had stated in 1917 that one of the solutions of Einstein’s equations indicated a displacement of spectral lines for distant objects. This effect, now known as the redshift, is just what Hubble was to observe in the decade that followed. Willem de Sitter was appointed Professor of Astronomy at Leiden in 1908. His portrait hangs in the hall of Leiden observatory where astronomers (at least in my time) gathered for their morning coffee. I used to have an occasional beer in a bar in Leiden in the 1980s. I remember being puzzled when I saw a small portrait of Einstein almost hidden away in a corner. I asked the owner why this portrait was there. He said that Einstein had frequented this bar when he had visited Leiden. He must have come there to relax when he visited de Sitter.

  The Idea of the Big Bang

  The expansion of the universe implies that the universe has evolved from a dense state. This theory or idea is now known as the Big Bang. In the 1930s it was realized that nuclear reactions provided the energy to fuel the stars. Might it not be possible that nuclear reactions had taken place in the early universe when temperatures reached millions of degrees? In 1948, George Gamow (1904–1968), a Russian physicist working in the United States, considered this hypothesis. He predicted that if a hot Big Bang had indeed taken place, some radiation left over from the intense heat of the early universe should be present today. It was not until 1965 that this radiation was discovered by scientists who were not trying to test this theory at all. They were scanning the sky in search of background radiations that interfered with communications satellites.

  We have come a long way from the start of this chapter, which began with the Hopi creation myths. We went on to discuss the Greek concept of the universe and focused on the problem of explaining planetary motion. This was the central cosmological problem for almost 2,000 years. The universe consisted of a few thousand stars and the planets wandering among them. The attempt to solve this problem led to the formulation of a theory of motion and gravity culminating in the work of Newton. We discussed problem of the dark night sky (Olbers’ paradox) as viewed by various thinkers. The next major historical theme concerned the nature of our galaxy and its relation to other galaxies. The realization that the spiral nebulae were large galactic systems led to the concept of an expanding universe.

  What drives the growth of knowledge? Tools provided by developments in technology are essential to this process. The discovery that planets move on elliptical orbits was dependent on the measurements made with Tycho’s precision instruments. Galileo’s telescope increased light gathering power and the amount of detail that could be seen (resolving power) by a factor of ten. This enabled him to remove any doubts about the Sun centered model of the solar system. The same is true in the field of theoretical astronomy. Many of the ideas that Newton used in his theory of motion and gravitation were not original. Newton did however invent a crucial mathematical tool (calculus) that made it possible to explain the elliptical orbits of the planets as well as the motion of comets and projectiles on earth.

  Martin Harwit has put it best in an article published in the journal Physics Today:

  The history of science so often alludes to the importance of great ideas. That notion needs to be carefully qualified. In astrophysics, new ideas are afloat all the time. Ideas are, of course, needed. But at critical junctures in the history of astronomy, there is generally an overabundance of ideas on how to move ahead. Supporters of the various ideas debate them vigorously, mostly with no clear-cut outcome. Resolution is usually attained only with the arrival of new tools that can cut through to new understanding and set a stagnating field in motion again.

  In the next chapter we discuss the Big Bang theory. The concept of expansion suggests that the universe was different in the past. We have run the clock forward from about 300 BC to the mid twentieth century in this chapter. In what follows, I will take you back in time to a split second after the Big Bang. It is quite amazing that we can discuss in a sober manner what happened in the universe a few minutes after its creation.

  Further Reading

  Man Discovers the Galaxies. R. Berendzen, R. Hart and D. Seeley. New York: Science History Publications, 1976.

  Discovering the Expanding Universe. H. Nussbaumer and L. Bieri. Cambridge: Cambridge University Press, 2009.

  The Book Nobody Read: Chasing the revolutions of Nicolaus Copernicus. Owen Gingerich. New York: Walker and Company, 2004.

  Cosmic Discovery; The search, scope, and heritage of astronomy. Martin Harwit. New York: Basic Books, Inc., 1981.

  The Discoverers. Daniel Boorstin. New York: Random House, Inc., 1983.

  Longitude. Dava Sobel. New York. Walker and Company., 1995

  The Day we Found the Universe. Marcia Bartusiak. New York: Random house, Inc., 2009.

  The Cosmic Century, A History of Astrophysics and Cosmology. Malcolm Longair. Cambridge University Press, 2006.

  George RheeAstronomers' UniverseCosmic Dawn2013The Search for the First Stars and Galaxies10.1007/978-1-4614-7813-3_2© Springer Science+Business Media, LLC 2013

  2. The Three Pillars of the Big Bang Theory

  George Rhee1

  (1)Department of Physics & Astronomy, University of Nevada, Las Vegas, Nevada, USA

  Abstract

  In this chapter we present the three main lines of evidence for the Big Bang theory of the beginnings of our universe. This Big Bang idea leads us to ask how matter behaves as we subject it to higher and higher temperatures and densities? This question can be answered in part in our laboratories. We can also speculate about the behavior of matter in the first few seconds of the universe. We will spend the latter part of this chapter traveling into the distant past. As a review we will go forward from the Big Bang to the present marking the significant times in the history of our universe. You may find some of the concepts discussed below rather strange. No wonder, the early universe not resemble the everyday world in which we live. The study of the early universe is based on the assumption that the laws of physics discovered by studying the behavior of matter on Earth apply throughout the universe.
This is the legacy of Newton and the other great seventeenth-century thinkers.

  The evolution of the Universe can be compared to a display of fireworks that has just ended: some few wisps, ashes and smoke. Standing on a cooled cinder, we see the slow fading of the suns, and we try to recall the vanished brilliance of the origin of the worlds.

  Abbé George-Henri Lemaître

  Evidence for the Big Bang

  The Big Bang theory has gained general acceptance by its ability to explain in a simple manner three key cosmological observations. These three observations are (1) the expansion of the universe as measured by the redshift of light emitted from galaxies (2) the existence of the cosmic background radiation and (3) the relative amounts of hydrogen, helium and deuterium in the universe. The theory states that the expansion of the universe began at a finite time in the past, in a state of enormous density and pressure. As the universe grew older it cooled and various physical processes came into play which produced the complex world of stars and galaxies we see around us.

  The Big Bang theory enables us to understand many different facts about the universe in a cohesive manner. Almost all astronomers believe it to be the best theory of the universe. Let us keep in mind, however, that the finest scholars were completely mistaken about the nature of our universe for most of recorded history. We present-day scientists can only do what any jury does: find the theory that is most consistent with the available facts. We now turn to the details of the three observational pillars of evidence for the Big Bang theory.

  The First Pillar: Hubble’s Law

  In Chap.​ 1, we learned of the history of astronomy culminating in the debate concerning the nature of the spiral nebulae. The correct answer turned out to be that the spiral nebulae are galaxies much like our own. Vesto Slipher had determined that these galaxies are moving away from us at very high speeds. By measuring their distances, Edwin Hubble demonstrated that the galaxies farthest from us are moving away at the highest speeds–Hubble’s law. Let us see what this implies.

  Imagine a race among three cars. Car number one travels at a steady speed of 60 miles an hour, car number two travels at a steady speed of 70 miles an hour, and car number three travels at a steady speed of 80 miles an hour. One hour after the start of the race we check on the location of the cars. Car one has gone 60 miles, car two 70 miles, and car three 80 miles. Seen from the starting gate, these cars obey Hubble’s law. The car that is farthest from us is the one that is traveling fastest. The first and third car are now separated by a distance of 20 miles after 1 h. In another hour, their separation will have grown to 40 miles. By looking at the cars 1 h after the race started and working back in time, we can conclude that they all left the starting line at the same time. Since galaxies obey Hubble’s law, we can draw the same conclusion. In the past, the galaxies were all closer together, and, in the future, they will be farther apart. We thus encounter one fundamental property of the universe: it is evolving. The universe looked different in the past and will look different in the future. The reader may ask why the cars acquire different initial speeds. This is where our simple analogy breaks down. When we look in more detail, we see that, in fact, it is the fabric of space that is expanding rather than objects moving in space.

  A simple estimate of the age of the universe can be obtained using Hubble’s constant. We can calculate for a given galaxy, knowing its current distance and velocity how long it took to reach its distance from us. This time is equal to (d/v) which turns out to be one divided by Hubble’s constant for every galaxy. This rough estimate gives an answer of 14 billion years for the age of the universe, quite close to our correct answer of 13.73 billion years calculated using the proper cosmological models.

  Measurements of Redshift and Distance

  Hubble’s law can be stated in the equation v = H × d. Establishing Hubble’s law involves measuring distances (d) and velocities (v) of galaxies. In practice, distance is much harder to measure than velocity. We measure the distances to galaxies in a number of ways, but the principle involved is always the same. We have to be able to identify objects of known luminosity in galaxies. We know how luminous the Sun is. If, for example, we could identify a star like the Sun in another galaxy we could then note how much fainter than the Sun that star appears to us. If the star was a million times fainter than the Sun in the sky, that star would be a 1,000 times farther from us than the Sun is. The problem of measuring distances in astronomy boils down to finding reliable indicators of distance. The indicators used by Hubble were variable stars. Figure 1.​4 shows the image that Hubble used to discover a variable star in the Andromeda galaxy. These stars are still used for that purpose today. They vary in brightness because they pulsate (Fig. 2.1). It turns out that pulsation time depends on luminosity. A star with a slow pulsation time is brighter on average than a star with a short pulsation time. A star with a 3-day pulsation period is about one 1,000 times more luminous than the Sun, whereas a star with a 50 day pulsation period is about 10,000 times as luminous as the Sun. By knowing the true luminosity of a star and comparing it with the star’s apparent brightness, we can calculate the distance to that star and hence to the galaxy containing that star.

  Fig. 2.1The variation of brightness with time for the Cepheid variable star SU Cas measured by the Hipparcos satellite. The time interval from peak brightness to the next peak is about 2 days. We can use the pulsation time to infer the total luminosity of this star and hence its distance from us. This star is about 1,500 times as luminous as the Sun and 6 times as massive. The distance to the star is about 1,400 light years

  But how do we determine the true luminosities of stars? How was the original period luminosity relation discovered? We can determine the distances to nearby stars using parallax and hence deduce their luminosities. Parallax is the motion in the night sky of nearby stars relative to distant stars over a period of months. Parallax is caused by the Earth’s motion around the Sun, it can be used to estimate distances to nearby stars once the Earth-Sun distance is known. We see that variable stars whose distances are known exhibit a period luminosity relation, and we use this relation to deduce the distances to more distant variable stars.

  Distance estimation in astronomy is difficult. Absorption of starlight by dust and gas can make stars look dimmer than they really are. Also, nature has contrived to make different kinds of variable stars, and we must not get them confused. Hubble thought that only one kind of variable star existed. This error caused him to underestimate the distances to galaxies by a factor of 10. Today we measure the distances to nearby galaxies to an accuracy of a few percent. For example if we say that a galaxy is 10 million light-years away, a 10 % error means that its distance may lie anywhere between 9 and 11 light years.

  What about galaxy velocities? To understand how we measure velocities we must understand something about light and atoms. Atoms are built from particles called electrons, protons, and neutrons. The protons and neutrons are located in the nucleus of the atom, and the electrons orbit this nucleus. Atoms consist mostly of empty space. If you make a fist and imagine your fist is the size of an atomic nucleus, then the atom is as big as the US Capitol and if it happens to be a hydrogen atom then it has a single electron like a moth flitting about in an empty cathedral.

  Electrons in atoms of a given element can only have certain specified energies. The electrons can change their energy by emitting and absorbing light or by colliding with other atoms. An atom of a given element, say hydrogen, can emit light only at specific energies or wavelengths. The wavelength of light is a detailed measure of its color. Broadly speaking, red light has a long wavelength and blue light has a short wavelength. Each element (hydrogen, helium, lithium, and so on) has its own set of wavelengths associated with it, much like a fingerprint. Figure 2.2 illustrates that atoms can absorb light in a very narrow band of wavelengths and leave their mark on the broad colors emitted by stars and galaxies. It is one of the triumphs of twentieth-century physics that we can cal
culate these wavelengths theoretically. These developments started with the work of Einstein, Bohr and their students. The work culminated in the development of quantum electrodynamics by Feynman, Dyson, Schwinger and Tomonaga.

  Fig. 2.2We measure redshifts using the patterns that are present in the spectra of galaxies. The upper spectrum shows schematically where the dark narrow absorption bands might appear in a spectrum of the Sun (in practice we see many more features than are shown). These features would be shifted towards the red for a galaxy as shown in the lower spectrum. The amount of the shift tells us how fast the galaxy is moving away from us, about 7 % of the speed of light in this case. We can then use Hubble’s law to compute the distance to the galaxy in question, which turns out to be about a billion light years, in this example

  There is one more detail you need to know. When light is emitted by an atom that is moving away from us, its wavelength is shifted toward the red end of the spectrum. When the atom is moving toward us, the light is shifted toward the blue end of the spectrum. Sound waves behave in a similar manner. We can all hear how the pitch of a car engine increases when the car is moving toward us and decreases when the car is moving away. This effect is known as a Doppler shift. The effect is common to sound and light because both these disturbances propagate as waves. In the case of light, the effect is known as the redshift. Slipher and Hubble observed that the light coming to us from galaxies was shifted toward the red and inferred that these galaxies are moving away from us. You may think we have misidentified the light from the galaxies and that what we think is hydrogen at high redshift is say neon at zero redshift. The answer is that the light we receive from galaxies consists of a pattern of emitted and absorbed light known as a spectrum. From one galaxy to the next we see the whole pattern shifted towards the red and it is hard to make an error. The concept is illustrated in Fig. 2.2.