22. The Big Bang, Inflation, and General Cosmology

Transcript: The problem with using helium 3, helium 4, or lithium 7 for testing cosmic nucleosynthesis in the big bang model is that all three of these are created in stars, and lithium can be destroyed in stars. So it’s difficult to estimate which of the nuclear abundances are primordial, originate in the universe itself, and which are caused by stars. As an alternative technique to the helium abundance astronomers have looked at the deuterium abundance, and they’ve measured it in the intergalactic medium, the space between galaxies, where it’s plausible that we might be looking at gas that’s pristine and primordial and has not been processed since the time of the big bang. It’s a difficult observation based on the spectra of quasars looking for the absorption lines due to hydrogen which is the Lyman-alpha line. If deuterium is present it will show up as a little satellite line in the wings of Lyman-alpha caused because the mass of the deuterium atom is larger than the mass of a hydrogen atom. This faint line has been seen in a number of cases, and careful analysis indicates a deuterium abundance of about 0.01 percent, independent confirmation of the big bang model.

Transcript: In the big bang model it’s possible to calculate the abundance of light elements created by fusion reactions in the early phases of the expansion. This is called cosmic nucleosynthesis. The calculations depend on only one fundamental parameter of the universe which is the density of protons and neutrons. Although dark matter dominates normal matter, dark matter interacts so weakly that it’s not relevant for the calculations of nucleosynthesis in the early universe. These calculations lead to a prediction of the mass fraction abundance of certain light elements. They predict that helium 4 should be about one quarter relative to hydrogen, that deuterium or heavy hydrogen should be at an abundance of ten to the minus four relative to hydrogen, that helium 3 should have an abundance of about ten to the minus five relative to hydrogen, and lithium 7 an abundance of one part in a billion or ten to the minus nine relative to hydrogen. It’s a stunning success of the big bang model that the observed abundances of these four light element species agree within the errors of the predictions of the big bang model.

Transcript: The best traditional test of cosmic nucleosynthesis and the predictions of the big bang model is the helium abundance in the universe. In the model of the big bang the predicted helium abundance is relatively insensitive to the cosmic density, so astronomers need a measurement accurate to three decimal places to make a good test of the model. This is a difficult observation. It’s best made by looking at unevolved stellar systems where the material has not been processed over the entire history since the big bang. Young, unevolved galaxies are looked at, their spectra observed, the helium line is measured, and its strength is interpreted in terms of a model of the emission line. The gas occurs in hot HII regions in the galaxy. Using these observations astronomers show that the helium abundance is consistent with the big bang model, one quarter by mass, and is inconsistent with having been produced in stars. Therefore, the helium abundance that’s being measured is primordial. The helium was present in the universe before the first stars and galaxies were formed.

Transcript: The cosmic abundance of light elements is a primary piece of evidence in favor of the big bang model. Stars are fusion factories, and main sequence stars create helium from hydrogen by the fusion process in their cores. However, a careful accounting of stellar fusion over the history of the universe shows that it’s impossible to create twenty-five percent of the mass of the universe in the form of helium as observed. In fact in the 1940s George Gamow, Russian theorist, speculated that in the early phases of the big bang the universe itself was hot or hotter than the center of a star. This is called cosmic nucleosynthesis, light elements created by fusion process of the entire universe very early in its history. Basically within the first fraction of a second of the universe’s history the temperature starts to drop below a billion degrees, and nuclear reactions can start. In the three stage process similar to that that takes place in the Sun protons and neutrons are combined to form deuterium, H with a superscript 2, a neutron is added to form tritium, H3, and another proton is added to form helium. This all occurs in the first four minutes after the big bang. In the succeeding twenty-five minutes tiny amounts of lithium 7 and beryllium 7 are created. Then because of the expansion and the cooling temperature the nuclear reactions stopped, and so the creation of all heavier elements occurs in the center of stars over the subsequent billions of years.

Transcript: What is the physical meaning of the cosmological constant? Astronomers do not know and physicists are puzzled too, but they’ve both come up with the idea of dark energy. In physics the vacuum is not totally empty. Particles and anti-particles can be created from the vacuum, and the ground state of any particle in the quantum theory has finite energy. Thus there’s a possibility that energy and positive pressure to cause expansion can exist in the vacuum of space. Unfortunately, in the current theories of physics the amount of vacuum energy is far too large to explain the delicate balance in the universe between contraction due to matter attraction and expansion or acceleration due to dark energy, but astronomers and physicists are still looking for an answer to this problem. Essentially, the universe is filled with two components that dominate its dynamics or expansion, neither of which is well understood physically; one is dark matter and the other is dark energy.

Transcript: Why is the universe accelerating, and how does this relate to the more standard cosmological idea that since the big bang the expansion rate has been decelerating due to the action of gravity on all the matter of universe? For the answer to this we have to go back to Einstein in the 1920s. Einstein solved the equations of General Relativity and realized that the solutions naturally indicated expansion or contraction. When told that the universe was static, Einstein added a term to the solution of his equations called the cosmological constant to suppress the natural expansion. Thus the cosmological constant represents something that acts opposite to gravity. Gravity is an attractive force; the cosmological constant represents something that is repulsive. In the standard model of the universe with a cosmological constant the big bang is followed by a period of deceleration due to all the matter in the universe. And then at some epoch several billion years ago the deceleration changes into an acceleration, and the rate of expansion increases. We are currently witnessing a phase of acceleration in the universe and its evidence that the term in gravity is balanced by another term, the cosmological constant.

Transcript: The primary evidence that the universe is currently accelerating comes from distant supernovae. The observation is based on the fact that a standard cosmology filled with only radiation and matter, most of which is dark matter, predicts the brightness of distant objects. Supernovae at redshifts of about a half or greater are observed to be twenty or thirty percent fainter than expected in a standard cosmological model. The explanation is that they are more distant than anticipated and that this is caused by the acceleration over the time since the big bang. It’s worth questioning how good this evidence is based as it is on only one distance indicator. Astronomers have worked hard to measure local calibrators for the distance indicator of supernovae Type Ia, and they understand very well how energy comes out of supernovae. So it looks like supernovae are an excellent distance indicator. When observed at high redshift the supernova is imbedded in a distant galaxy, and the light from the galaxy is mixed with the light from the supernova. Very careful observations with the Hubble Space Telescope are required to dig out the distant supernovae. In some cases only the supernova is seen and not even the galaxy in which it’s imbedded because it’s so faint. These observations have been done with care, and it really does appear that supernovae are fainter than anticipated. Another possibility is that dust distributed through the universe might make supernovae fainter than expected. But dust would also make them redder, and there’s no that the distant supernovae are red due to dust. Thus their faintness looks like increased distance. The clinching evidence has not yet come. It will come when astronomers can look at distant enough supernovae to trace back in time to the phase of deceleration before it turned into acceleration. This is expected in the next decade.

Transcript: Standard cosmological models, where the universe is filled with matter and radiation, always have an expansion rate that slows down with time since the big bang, a deceleration. This is because gravity of all the matter in the universe acts to slow down the expansion rate, but in the late 1990s astronomers got a big surprise. Observations of distant supernovae indicated that the universe is currently in an acceleration phase. Here’s how the observation worked. Astronomers looked at distant Type Ia supernovae. These supernovae in binary systems indicate a situation where matter is spooned onto a white dwarf causing an explosion with a well regulated luminosity. These supernovae are excellent distance indicators. When observations with the Hubble Space Telescope and large ground based telescopes were used to look at the most distant supernovae, distances of about a gigaparsec or redshift of about a half, it was observed that their apparent brightness was twenty or thirty percent fainter than expected in a standard cosmological model. The implication was that the supernovae were further away than expected in a standard cosmological model, and the explanation was that the universe is accelerating placing them at a larger distance.

Transcript: Universe with matter in it will be continuously decelerating over time since the big bang. Cosmologists refer to this as the deceleration parameter, and it’s written as a little q with a subscript zero. In standard cosmologies q0 equals a half for a flat universe, less than a half for an open universe, and more than a half for a closed universe. The relationship is more complex in cosmologies with a cosmological constant. Measuring the deceleration depends on comparing the properties of distant objects like galaxies with nearby objects. This is difficult because of the problem of look-back time. When we look at distant objects we are looking at objects as they were and not as they are now, so when we compare objects that are distant or high redshift with nearby objects we are not comparing like with like. Unless astronomers can model and predict the rate of cosmic evolution of stellar systems like galaxies they can not do cosmological tests based on a comparison of distant objects with nearby objects. To this point it has been very difficult to conduct this type of cosmological test.

Transcript: Another fundamental quantity of the big bang model is the density parameter. It’s defined as the ratio of the mean density of the universe to the density just needed to overcome the cosmic expansion. The density parameter is denoted by the Greek symbol capital omega with a subscript zero. If omega equals one the universe is flat. If omega is less than one the universe is open, and if omega is greater than one the universe is closed. Unlike the deceleration the density parameter is a purely local measurement. All that’s required is to take a large volume of space, typically fifty to a hundred megaparsecs in distance from the Milky Way, add up all the matter that’s contained, luminous and dark, divide by the volume, and compare to the critical density. The answer gives the sense of whether the universe will expand forever. The best current measurements indicate that omega is about 0.3 or only one-third of the amount of density needed to overcome the expansion. Based on these measurements the universe will expand forever.

Transcript: Astronomers often talk about the Hubble constant, capital H with a subscript zero, which represents the local expansion rate of the universe measured with relatively nearby galaxies. When done with the Hubble Space Telescope, the local expansion rate was measured within about fifty to sixty million lightyears. This is a small fraction of the size of the observable universe and a small fraction of the look back time too, and the expansion rate has been constant over this time. However, any universe containing matter will have an expansion rate that decelerates with increasing time due to the attraction of galaxies acting on each other. They act to retard, or slow down, or decelerate the expansion. So if the expansion rate had been measured in the distant past, astronomers would find a higher expansion rate than they measure now. So the correct way to consider the Hubble parameter is as a parameter and not a constant. Its present day value is seventy kilometers per second per megaparsec, but the Hubble parameter has been decreasing in size ever since the big bang.

Transcript: General relativity makes a strong connection between the dynamics of the universal expansion, which is to say the rate of increase of the size with time, the density of matter, and the curvature of space itself. In an empty universe space is not curved. The size of the universe increases linearly forever at the same rate. The Hubble expansion is uniform and unchanging with time. If you have a universe with a certain amount of matter but still low density the size of the universe increases but at an ever slowing rate. In a critical density universe it’s defined as the universe where the scale of the universe increases but at an ever slowing rate where in an infinite time a maximum size will be reached. This is the case of flat space. And in a high density universe, density above the critical density, the radius of the universe initially increases at an ever slowing rate until a maximum size is reached, and then the size begins to decrease at an ever accelerating rate until it reaches zero size at sometime in the future. All of these possible destinies and densities of the universe can be measured, so in principle with observations of the present day universe we can predict its future evolution.

Transcript: The best way to think of the cosmological redshift z is in terms of the scale of the universe. We see regions near us as they are now, nothing has changed. That’s at redshift zero, z equals zero, but in general redshift is defined as the present day scale of the universe divided by the previous scale minus one. The universe was smaller in the past, so waves have been stretched out as they travel through cosmic time and space by the expansion of space itself. When we see light from an object at a redshift of one we are looking at light that was emitted when the universe was half its present size. When we see light from an object at a redshift three, we are looking at light emitted when the universe was a quarter of its present size. When we see light from the most distant objects at redshift six, that light was emitted when the universe was one-seventh of its present size. Cosmologists like to describe the universe in terms of a graph that plots the scale or scale factor of the universe verses cosmic time. Three characteristic curves can be seen on this kind of a diagram. In one, the open universe with negative curvature, the scale factor of the universe continues to increase although the line curves over indicating a deceleration. In the case of the flat universe the expansion continues and the scale increases, but it asymptotically heads to a maximum value of size. And in the closed case corresponding to positive space curvature, the universe reaches a maximum size, and then the curve reverses itself and falls back towards the origin.

Transcript: The big bang theory sounds as fantastic as the creation myths of many of the world cultures. How could you, and I, and the Earth, and sun, and Milky Way, and billions of galaxies have emerged from a tiny dense dot of energy and matter. There are three primary pieces of evidence. First, galaxies are all taking part in a universal expansion which manifests as a linear relationship between redshift and distance. If this expansion is traced backward it points to a time billions of years ago when galaxies were all in the same place, and the universe was much smaller than it is now. Second, the abundance of the light elements, in particular, helium, lithium, and deuterium, cannot be explained by normal fusion processes in stars but can be explained by fusion in the universe itself when it was hot young and dense. Third, space is filled with relic radiation leftover from the early hot phase which has been redshifted over the subsequent billions of years to microwaves.

Transcript: The man who first came up with the idea of the big bang was an unassuming Belgian priest called Georges Lemaitre. In 1929 he beat the giants of general relativity like Einstein to the punch by hypothesizing a universe derived from a cosmic singularity, “A day without a yesterday,” as he put it. This universe began infinitely small and infinitely curved and contained all matter and energy in a point, a singularity. Fred Hoyle, who supported the alternative theory of the steady state, disparaged this model and gave it the name big bang which stuck, and it’s used today to describe the current version of scientific belief in the origin of the universe. The big bang is based on the idea that the universe has not been the same but has evolved with time, and it’s also based on the idea of an origin event which forms a limit to our knowledge of the universe. Space and time both begin with the big bang.

Transcript: Many cultures around the world have creation myths based on the idea of cycles and time. Buddhist and Hindu legends measure the birth, death, and rebirth of the universe in units of four trillion years, a day in the life of Brahma. The Greeks Stoics imagined that the universe was created from fire, only to be destroyed by fire, and so on in endless cycles. Cycles of time also appear in the religions of the Mayans and the Aztecs. The Judeo-Christian religions set the stage for the discussion of origins with the idea of genesis, a time before which there was nothing. Modern cosmology includes the idea not only of an origin to space but an origin to time.

Transcript: Present day observations of the universe lead to speculation about its origin. There’s an extension of the cosmological principle called the perfect cosmological principal which holds that the universe is unchanging both in time and space, that the universe is not only the same in all directions and at all distances from the Milky Way but has been unchanging in time as well. This idea leads to the steady state model. The galaxies are all moving apart. In the steady state model of creation matter is slowly created in the vacuum between galaxies which leads to the formation of new stars and galaxies which participate in the expansion. An alternative is to view the cosmic Hubble expansion as the evidence of a large scale motion which can be traced backwards in time pointing to a time in the distant past when the universe was smaller, hotter, and denser than it is now. This is the big bang model.

Transcript: A very basic assumption about the universe which forms the basis for modern cosmology is called the cosmological principle, that the universe is isotropic and homogeneous. Isotropic means the same in all directions. This means that in any direction we look we tend to see the same structures and numbers of galaxies, and that is in fact confirmed by observation. It also means that the Hubble expansion is the same in every direction we look, that the expansion rate is smooth and not faster in one direction of the sky than in another direction, and this is also confirmed by observations. The second part of the cosmological principle, the homogeneity of space, is much more difficult to test because as we look out in space we look back in time. So when we view distant parts of the universe we are viewing parts of the universe as they were earlier when the universe was smaller, but we can basically test the idea by showing that the universe contains more or less the same structures everywhere we look and that on the largest scales, over a hundred megaparsecs or three hundred million light years, the average amount of material in any volume of space from one direction to the other is about the same. So the universe is indeed smooth on the very largest scales.

Transcript: It’s extremely difficult to conceptualize curved three dimensional space, so astronomers use analogies. The analogies are useful as long as we recognize that they all have limitations. The true situation is only described exactly by the equations and the mathematics of Einstein’s Theory of Relativity. The expanding universe and the big bang are not like an explosion with the galaxies flying apart like fragments or shrapnel through air because there is no air. Space itself is expanding, and the galaxies are being carried apart by the expansion. They are not flying through a medium. Astronomers also use the analogy of the curved surface of an inflating balloon. The analogy is fairly good. In a positively curved space the space is finite and bounded. A light wave sent out through a universe like this would indeed eventually return in the direction that it came from, but the universe is not like a balloon in the sense that there is no inside or outside the two dimensional space. The universe itself is the three dimensional curved space, and it’s not expanding into anything.

Transcript: According to the theory of general relativity, the universe and the space we live in may actually have a shape, and the shape need not be the flat infinite space described by Euclidean geometry. Infinite space will be flat, but curved space could be finite or infinite, bounded or unbounded. Consider for example the surface area of a sphere. A sphere is a curved surface. Its area is finite, four pi r squared, and yet it’s an unbounded surface. You can travel endlessly on the surface of a sphere without falling off. The universe has curvature that’s very subtle, and so the bending of light by gravity is only visible when viewed over very large distances, cosmological distances of billions of lightyears. It’s up to astronomers to make geometric measurements within the universe to decide what the curvature of space is, and it turns out that the universe we live in is very close to flat.

Transcript: It’s important to realize that the cosmological redshift, usually given by the symbol z, is not the same as a Doppler shift. The Doppler shift is a relative shift in the wavelength of waves passing through a medium. The cosmological redshift in the universe is caused by the expansion of space itself everywhere in the universe. The best analogy is a balloon with beads glued to the surface. It’s a two dimensional analogy for a three dimensional situation. The beads on the balloon as its inflated will all move apart from each other and the distance or speed of separation of the beads will increase with distance. This is the Hubble law. The situation seen from any bead will be the same. This is the cosmological principle; there’s no preferred location or galaxy within the universe. The beads themselves are not expanding. They’re held together by gravity as is the Milky Way and all other galaxies, but as space expands it carries the galaxies further and further apart. Finally a wiggly line to represent a wave drawn on the surface of the balloon will be stretched as the balloon is inflated corresponding to an increase in the wavelength of the wave or a redshift. This is the way that radiation stretches due to the expansion of space as it travels through the universe, and this is the cosmological redshift.

Transcript: When the equations of General Relativity are applied to the situation of the entire universe the solutions tend to be solutions of motion, either expansion or contraction. However, when Einstein visited Mt. Wilson Observatory in 1921 he asked the astronomers what their best view of the state of the universe was. Remember that this was before the discovery of the extragalactic distances to the nebulae and before Hubble’s discovery of the expansion. So the astronomers told Einstein that the universe was just one large Milky Way galaxy with the stars more or less in random motion. So Einstein was forced to solve the equations in such a way as to produce a static universe. To do so he added a term arbitrarily called the cosmological constant. He later called this the greatest blunder of his life. Because he was misinformed about the state of motion of the universe Einstein missed out on predicting the expansion.

Transcript: The ideas of geometry were invented by Euclid two thousand years ago, but in the nineteenth century Russian mathematicians and a few German mathematicians invented the mathematics of curved spaces. They also invented mathematics that would apply to geometries in more than three dimensions. When invented these mathematics were utterly hypothetical. No one had any idea that they might apply to the universe itself. In general these are called non-Euclidean geometries. There are three basic types of curvature in non-Euclidean geometry. If the curvature is in fact zero we have flat space; in two dimensions it would be like a sheet. This is the familiar geometry of Euclid where straight lines that are parallel never converge or move apart and where the angles in a triangle add up to a hundred and eighty degrees, but it’s also possible to have positively curved space or spherical geometry. The two dimensional analogy for this is a surface of a sphere. On the surface of a sphere parallel lines eventually converge, and angles in a triangle add up to more than a hundred and eighty degrees. The other sign of curvature is negative curvature which is called hyperbolic space. The two dimensional analogy is a saddle surface where parallel lines drawn on this surface diverge, and the angles in a triangle add up to less than a hundred and eighty degrees.

Transcript: The modern idea of cosmology is based on Einstein’s theory of General Relativity. Einstein realized in a thought experiment that acceleration due to gravity could not be distinguished from acceleration due to any other force. He also knew that mass and energy were equivalent according to E = mc2. The two ideas combine to lead to the fact that mass can bend light. In Newton’s idea of an infinite universe space and time flow smoothly, and never bend, and are linear at all distances from the Earth. In Einstein’s theory they are replaced by the idea of space-time: space that is supple according to gravity and the distribution of matter and time that is also supple in the situation of strong gravity. The equations of General Relativity apply to the intense gravity of a black hole, but they also apply to the universe as a whole.

Transcript: The solution to Olber’s paradox is subtle and involves three different concepts. The first is the redshift of light that occurs due to the expansion of the universe. This means that the light from distant objects is redshifted or reduced in energy, so as we move further out from the Earth or the Milky Way the light from successively larger and larger distances is reduced relative to the inverse square law of light. So the light does not pile up infinitely. Second, there is a distance beyond which we cannot see in the universe which corresponds to the distance that light can travel in the age of the universe. Third, the universe is so big that light has not had time to utterly fill the space between galaxies. The sum of all these factors leads to the fact that Olber’s paradox is not true, and the night sky is indeed dark.

Transcript: Newton’s theory of gravity set the stage for physical cosmology, a study of the universe based on the idea of laws of physics that applied everywhere throughout space, and it gave rise to the idea of a clockwork universe, although we now know the universe is so complex that it is far from deterministic. Newton imagined the universe as infinite and filled with stars in random motion. This is essentially a static universe. Newton’s rational was as follows. If the universe had an edge, then the stars near the edge would feel a greater force inside than outside where there are no stars, and so the stars would move inwards. Thus a universe with an edge would be forced to be in motion and collapse. The only way around this is to have an infinite universe filled with stars. Of course, an infinite universe has infinite gravity. This was a problem Newton couldn’t address within his theory, so Newtonian cosmology had problems that were known even to Newton at the time.

Transcript: The first scientific thinking about the universe dates back to the Greek philosophers of the fifth and sixth centuries B.C. They applied logic, they formed hypothesis, and they tried to test the hypothesis although this was a time two thousand years before the invention of the telescope, and there was a limit to what they could do with the naked eye. However, they made enormous strides. Aristarchus, for example, used logic and geometry to deduce a Sun-centered universe two thousand years before Copernicus, and in fact the biggest Greek universes that were calculated were many, many millions of miles across. They even came up with the idea of infinite space applying the mathematics of Euclid and realized the implications of an infinite universe. As Plato’s colleague Archytas put it, imagine you are at the edge of the universe, and you hurl a swift spear. Do you imagine that this spear hits something, finds a barrier, and bounces back, or should it travel forever? And if it should travel forever, what lies beyond the edge? The Greeks were thinking about the size of the universe, the implications of an infinite universe, and what an edge might mean two thousand years before scientists would address the problem with observations.

Transcript: The creation of the universe is described in the oldest writings that come down to us from cultures like the Babylonian, the Egyptian, the Greek, the Chinese, and the Indian. In Indian legend the universe is a giant egg which is brought forth from the void by the creator Prajapati. In Tahitian legend Ta'aroa creates the universe out of the immensity of pure space and forms the rocky substance of the Earth. In the Norse legend there’s nothing at all with frost to the north and fire to the south until the heat melts the frost, and from the liquid drops the giant Ymir grows who creates the world. These are examples of mythological cosmology, the description of the universe that ties cosmology to human cultures and to the stories that people have always told about the night sky.

Transcript: Cosmology is the study of the universe, its history, and everything in it. It comes from the Greek root of the word cosmos for order and harmony which reflected the Greek belief that the universe was a harmonious entity where everything worked in concert to produce a beautiful whole. The scientific method is challenged by the study of the entire universe. We only have one object to study. We cannot travel any distance in it, and we are trapped in time and space. In a sense it’s amazing that creatures as small and frail as humans can comprehend the cosmos at all, and the study of cosmology is one of the greatest human achievements.