23. The Big Bang, Inflation, and General Cosmology 2

Transcript: Throughout most of the history of the universe structures have been forming under the action of gravity. Remember that the visible parts of galaxies just represent the tip of an iceberg of mostly dark matter. The way in which structure forms depends on the detailed properties of dark matter. If dark matter is cold, which to a physicist means that the particles that form the dark matter were not relativistic at the time of recombination when neutral hydrogen occurred and the microwave background photons were released, then structure forms in what’s called a bottom up way. Galaxies form first, then clusters, then even larger structures. On the other hand, if dark matter is hot, which means it was moving relativistically at the time of recombination, then structure forms in what’s called a top down way. Structure on galaxy scales is erased, and the largest structures form first. Astronomers believe there’s good evidence that the universe shows structure consistent with cold dark matter and not hot dark matter. Hot dark matter particles produce too much structure on large scales, more than is observed. Also there are no good candidates for a hot dark matter particle. Neutrinos have a tiny amount of mass but are insufficient in their mass to account for cosmic structure.

Transcript: As we trace events in the universe back toward the big bang, the first important epoch reached is a time about three hundred thousand years after the big bang. The universe by this time has cooled to a temperature of about three thousand Kelvin like the photosphere of a cool star. The density of matter and radiation has become low enough that photons no longer routinely interact with the charged particles that are there, protons and electrons. This has two fundamental consequences for the universe. First, the photons start to travel freely without interacting with matter. This is the era of decoupling. Photons decouple from matter, and it’s the era at which we see the cosmic microwave background radiation. Those photons have been flowing freely through the universe for eleven billion years since. The universe becomes transparent at this point. The second consequence is that protons and electrons combine to form stable neutral hydrogen atoms. This is called recombination. The two physical processes are connected.

Transcript: Inflation is an extraordinary idea. What is the evidence in favor of it, and is it even possible to test something that happened so long ago? First, space is observed to be close to flat, and recent observations show that it’s extremely close to flat, within a few percent. This confirms a prediction of inflation but of course was one of the motivations for the idea of inflation in the first place, so it’s not really an independent test of the idea. Second, the fluctuations of the cosmic microwave background radiation have a particular random character and fit a distribution in the amplitudes that follows a power law. This could not have been the case, and it is in fact a close prediction of a quantum process to produce such a distribution of fluctuations. So the microwave background radiation is consistent in detail with the inflationary idea. As for the nature of the force that drove this exponential expansion, that’s still poorly understood, and in fact the energy scale involved is beyond that that is reachable with ground based accelerators or even any accelerator on the drawing board. The only way we can test the inflationary idea is with observations of the early universe itself.

Transcript: How does the idea of inflation explain some of the problems of the standard big bang model? First, by stretching space by an enormous degree, the universe is predicted to be flat. Imagine a tiny curved balloon that is rapidly inflated to a huge size. Someone observing one small piece of the balloon will see it to be flat or very close to flat. Flatness of space is a prediction of inflation. The same expansion also causes space to be smooth. Regions that we currently observe to be far apart on the sky were once in very close contact. Regions for example twenty or thirty billion lightyears apart now were once only a few meters apart. Thus we can explain the perfect thermal spectrum of the big bang radiation because it reflects the fact that it originated from a region which was in close thermal and causal contact. The expansion also produces a dispersal of defects, topological defects and monopoles, such that we would not expect to observe any in our universe, matching observation. Inflation in a fundamental way predicts that the physical universe must be enormously larger than the observable universe. It could in fact be infinite. The final and staggering implication of the inflationary model is that inflation took regions of space that were quantum fluctuations and inflated them to the size of galaxies where they became the seeds for large scale structure that we observe in the universe. Thus if inflation is correct, when you observe galaxies we are observing quantum fluctuations in the first iotas from the big bang.

Transcript: In 1981, MIT physicist Alan Guth was looking for possible explanations for the smoothness and flatness of the universe when he came up with the idea of cosmic inflation. Inflationary cosmology is an adjustment to the standard big bang model wherein the universe went through a period of extremely rapid or exponential expansion at a time ten to the minus thirty-five to ten to the minus thirty-three seconds after the big bang; that’s a billion-billion-billion-billionth of a second after the big bang. In this tiny iota of time the universe expanded by forty orders of magnitude from smaller than an atomic nucleus to the size of about a grapefruit. The cause of inflation was the energy derived from a phase transition, such as that occurs when ice turns into water, which is associated with the unification of three of the fundamental forces of nature: the weak nuclear force, the strong nuclear force, and the electromagnetic force.

Transcript: One of the very difficult things to explain in standard cosmology is the flatness of space. Remember that the early universe was small and dense, and space-time was actually curved and knotted in the quantum era so the current flatness of space is an unusual condition. In standard cosmologies with no vacuum energy, flat space corresponds to a critical energy density, and in the expansion dynamics of the universe it’s an equal amount of energy in kinetic energy of the expansion and in the potential energy of all the gravity in the universe. The best analogy for this strange situation is to imagine throwing something up into the air. If you give it some particular random speed it’s likely to fall back down to your feet, but if you give it the very special velocity of the escape velocity, the object will just leave the gravity of the Earth. If you give it much larger than the escape velocity, the object will sail off into space and travel forever. The universe itself is poised between re-collapse and endless expansion. The flat space condition is a very particular condition corresponding to equal amounts of potential and kinetic energy. It’s as if the odds of throwing something up into the air and having it at exactly the escape velocity were very small. The fine tuning of the universe is the closeness of the space-time shape to being flat. The fact that space-time is this close to being flat now means that the initial parameters of the big bang expansion must have been very finely tuned early in the universe.

Transcript: The big bang model has considerable predictive and explanatory power, but there’s some fundamental questions about the nature of our universe that it leaves unanswered. Why is the universe so smooth and isotropic? The reason this question is important to ask comes from a consideration of the early expansion. In the early big bang, regions of space were separating at larger than the velocity of light, yet the microwave background radiation shows an almost perfect black body or thermal spectrum. This can only occur when the entirety of space is in thermal equilibrium, and yet the superluminal expansion implies that there’s no way that light signals could have passed between different regions of space. So how did space come to a complete perfect temperature everywhere and throughout? Why is the universe so close to being flat? There is nothing about the standard big bang model that says that space should be utterly flat as opposed to curved. This becomes a mystery in the standard big bang model. Also, in the early universe there are many esoteric particles and defects of space time, and in the standard big bang model it’s a mystery as to why we do not see these, either topological defects or monopoles. None have been observed with telescopes or in particle physics detectors, and yet the big bang predicts that they should exist in space. Since we do not see these defects we need another explanation for their absence.

Transcript: The big bang model provides a good description of the current universe which is large and cold and mostly empty. It implies that the early phase was hot and dense. The big bang model is supported by the observation of galaxy recession, by the light element abundance which is consistent with cosmic nucleosynthesis in the early hot big bang, and by the presence of cosmic microwave background radiation, smooth and isotropic suffusing space as leftover radiation from the big bang itself. This is a great success of the scientific method, but how far can we push the big bang model? Spurred by its success, theorists have been driven to speculate about the earliest moments of the universe’s existence. Some of this is pure speculation, but other ideas are based on well understood laboratory physics as physicists and astronomers combine to talk about the first fractions of a second of creation after the big bang.

Transcript: The fact that the early universe had a phase of superluminal or faster than light expansion means that it is not trivial to calculate the size of the observable universe. In other words the following simple idea does not work. The universe is eleven or twelve billion years old, so we might imagine that it must be eleven or twelve billion lightyears across. That’s not true because the early expansion was so rapid. Galaxies early in the expansion were being carried apart faster than the speed of light. Later on they were moving apart less rapidly, and eventually the light became able to reach us. So depending exactly on the cosmological model, the size of the observable universe is twenty-five to thirty billion lightyears across. The observable universe represents the horizon, the distance we can see or the distance within which light has had time to reach us in the history of the universe and the cosmic expansion. Given that we think that the universe is now accelerating, the future of the observable universe is very interesting. Acceleration, if it continues, will gradually take galaxies out of our horizon and away from being visible. So over long periods of time the accelerating universe will remove objects from our view. Over a time scale of many billions of years there will actually be less and less to study. Observational astronomy will not last forever. In the end, the acceleration will cause the only galaxies to be visible to be those that are bound to the Milky Way itself.

Transcript: Astronomers make a distinction between the physical universe, all that there is, and the observable universe, all that we can see. The distinction comes about because early in the cosmic expansion any two points in space were separating at faster than the velocity of light. This sounds like a violation of relativity. Special relativity however, which says that the velocity of light is the maximum speed for any signal applies, only to local reference frames. General relativity is the theory that governs the cosmic expansion, and general relativity places no speed limit on the expansion of the big bang. The time when points were moving apart faster than the velocity of light was a time about five billion years ago when the universe was forty percent of its current size or redshift of 1.25. Back much further, three hundred thousand years after the big bang at the time of the microwave background radiation, points in space were moving apart at forty times the velocity of light. Thus there are regions of physical space that we have never seen in the history of the universe, implying that the physical universe is potentially much larger than the observable universe.

Transcript: Space-time diagrams are a way of graphically representing space and time. Remember that the universe we live in is made up of three dimensions of space and one of time, also called the space-time continuum. To represent this in a graphical form we have to collapse the three dimensions of space to one dimension; this becomes the x-axis. The other dimension is time, and that’s the y-axis. By convention the slope of a line at forty-five degrees corresponds to the fastest speed that anything can move in the universe, the velocity of light, three hundred thousand kilometers per second. Any other objects other than radiation most move at the speed of light or slower speeds. On the page, therefore, we form a triangle with the point of origin of the events at the apex. The triangle can sweep out a cone, and this is called a light cone in two dimensions. Essentially the light cone defines all the regions within a space-time that are in causal connection or can communicate with each other by electromagnetic radiation or any other means. In a space-time diagram true events that have their origin on the x-axis emit light cones going upward. Unless these light cones overlap, the two regions are not in communication with each other. Space-time diagrams are therefore used to show which regions of a universe or a space-time are in communication with each other and which regions are isolated from each other.

Transcript: Events take place in both space and time. This is fairly obvious if we consider some every day examples. To make an appointment you have to be at the right place and the right time. The two ways you might miss an appointment are by going to the right place but on the wrong day or by going on the right day but going to the wrong place. You might for instance be in a baseball game trying to catch a fly ball. To be in the position and the time to catch the fly ball is a decision in both time and space. If you miss the fly ball it could be because you got to the right place but too late, or perhaps you got there on time but were slightly to the wrong side of where the ball landed. These trivial examples illustrate that time and space are connected. In physics and astronomy it’s routine to talk about space-time as connected entities whether we’re discussing the behavior of microscopic particles in the physics lab or objects in the universe. In the theory of relativity, time and space are formally coupled and linked mathematically. The distortions of relativity caused by motions close to the speed of light apply equally to space and time.

Transcript: There may be a profound connection between entropy in the universe and the arrow of time, the pervasive since that time moves only in one direction. Remember that the microscopic laws of physics have no arrow of time. However, in any statistical system of particles there’s a tendency for it to move to its most probable state. Entropy is disorder or chaos, but it’s also related to the number of possible states in a system. Imagine the shuffling of a deck of cards as an analogy for the evolution of the universe. Our universe has a relatively low entropy or low degree of disorder, especially compared to a situation where the universe was filled with black holes; the entropy would be millions of times higher. This corresponds to a highly ordered deck of cards. As the deck is shuffled, objects interact in the universe. The order becomes less. The entropy increases. The arrow of time is obvious in this. Interactions will always tend to produce more disorder. However, if the disorder was high to start with, a high degree of entropy at the beginning of the universe, a well shuffled deck of cards, then as the deck is shuffled again there is no change as the deck is shuffled over and over. So high entropy initial state produces no sense of the arrow of time.

Transcript: The entropy of the universe is a measure of its disorder or chaos. If the laws of thermodynamics apply to the universe as a whole as they do to individual objects or systems within the universe, then the fate of the universe must be to increase in entropy. This is obvious in the case where the universe re-collapses in a big crunch because there all structures are erased in the heat death, but in the big chill it’s is not as obvious. However, entropy of the universe continues to increase in the expansion when it continues forever. Black holes contain a hundred million times more entropy than a normal star of the same mass, so as matter goes into stellar remnants in black holes there’s a huge increase in entropy. As normal matter decays into a sea of radiation, the unstructured radiation also has a large amount of entropy. For example, the microwave background contains much of the entropy of the universe currently. In an open universe the eventual increase in entropy over its life time is a factor of ten to the power twenty-three.

Transcript: In the big bang model the universe does not necessarily have an edge in space, but it does have an edge in time. The age is measured to be about eleven or twelve billion years. There is a distance, therefore, beyond which light could not have reached us in the time since the big bang. This is called a cosmic horizon. We can’t see beyond it. The observable universe grows slightly everyday as light from more and more distant regions reaches us for the first time. Early in the cosmic expansion, the expansion rate was actually faster than the speed of light, so there are points in space that early on were moving away faster than the speed of light from each other but have since slowed down and could communicate with light signals. We know therefore in the big bang model that the physical universe, all that there is, is larger than the observable universe, all that we can see.

Transcript: In standard big bang models the curvature of the universe and its fate are related. In a high density universe where the density of matter exceeds the critical density, the universe will reach a maximum size and then re-collapse. The strong force of gravity causes the expansion to be overcome. The result is a reversal of the big bang called the big crunch. Our universe appears to have insufficient matter to match the critical density and so will likely expand forever. Extra evidence for this is the existence of vacuum energy or cosmological constant. The fate of our universe is therefore going to be the big chill. In this outcome, the cycle of star birth and death eventually is broken within galaxies as all the gas is used up. After about ten to the thirteen years, ten trillion years, most of galaxies will just contain white dwarfs, black holes, and other dark or dim stellar remnants. Galaxies essentially will switch off slowly with time. After ten to the thirty-five years fundamental particles will decay, and after ten to the power eighty years, although the number is uncertain, black holes within galaxies, even at their nuclei, will evaporate. The eventual result is a uniform sea of electrons, positrons, neutrinos, and low energy photons.

Transcript: It’s easy to forget, since the night sky is so dark, that the universe is filled with radiation. The cosmic microwave background represents photons from the big bang stretched by the expansion of space with their energy reduced to microwaves. There are vastly more photons in the microwave background radiation than there are particles in the universe, a hundred million photons for every hydrogen atom, so the total in the universe is ten to the power eighty-eight photons. What is the equivalent mass of this huge amount of energy? Using Einstein’s E = mc2 it’s possible to calculate it, and the result is an exceedingly low amount of equivalent mass. The energy of these photons is very low. The radiation density of the universe corresponds to twenty thousand times less than the critical density, far lower than the mass density of dark matter or even normal baryonic material. Even though the universe is flooded with photons, matter governs the behavior of this universe.

Transcript: In general, light in the universe is a poor tracer of mass. Galaxies are bright markers of space, however, they poorly represent the distribution of dark matter. The different distribution of galaxies with respect to dark matter is called bias, and it’s a fundamental part of any theory of galaxy formation to explain how and why galaxies cluster the way they do and how it relates to the dark matter distribution. Even if galaxies do not trace the distribution of dark matter, they must move in response to the gravity of dark matter. Those motions can be measured by astronomers with spectrographs, and this allows astronomers to infer the dark matter distribution from galaxy surveys. In addition to the cosmic expansion that affects all galaxies, they have departures from Hubble flow which are called peculiar velocities imprinted by the gravitational interaction with dark matter acting over billions of years. Careful analyses of large surveys of thousands of galaxies enables a fairly accurate measurement of the cosmic density of dark matter leading to the conclusion that it’s about one-third of the critical density.

Transcript: There’s a basic problem in cosmology. Astronomers measure the light emitted by different objects, but they really want to detect or measure the mass. So the measurement of the mass is indirect. Some galaxies for example are so diffuse that their light level falls below the sky brightness, and so they are missing from galaxy catalogs yet they may contain much dark matter. The intergalactic medium is so diffuse that it cannot be seen in optical light. It is hot and should emit x-rays or ultraviolet radiation, but this has not been directly detected yet. So astronomers must use a variety of techniques to infer the mass density of the universe from the light emission.

Transcript: Another way to look at the mass density of the universe is in terms of the cosmic mass to light ratio. Mass to light ratio is defined as the ratio of the mass, in solar units, to the luminosity, in solar units, so for the Sun by definition M over L is one. In general, low mass stars have mass to light ratios greater than one, and high mass stars have ratios less than one. We know that the stellar populations typical of normal galaxies give overall mass to light ratios in the range of three to ten. This means that anywhere in the universe on larger scales where we infer mass to light ratios much above ten we must be looking at dark matter. The halos in galaxies through dynamical measurements have mass to light ratios in the range ten to fifty, groups of galaxies in the range thirty to two hundred, clusters of galaxies in the range one hundred to four hundred, and the Local Supercluster, through a very uncertain measurement, has a mass to light ratio in the range three hundred to five hundred. On all these large scales most of the mass is coming from dark matter. However, the mass to light ratio in the standard cosmology corresponding to critical mass density is one thousand five hundred. So even on the largest scales there’s not sufficient dark matter to account for a critical density; it’s a factor of three short.

Transcript: The big bang model cannot be properly described without a measurement of the dark matter density in the universe. Observations of individual galaxies, either their rotation curves or velocity dispersions, and observations of clusters of galaxies show that ninety to ninety-five percent of the matter in the universe is dark. We don’t yet know what it is, but it’s almost certainly in the form of microscopic particles not yet detected in labs on the Earth. A variety of techniques are used by astronomers to measure dark matter on different scales. They show that galaxies are imbedded in dark matter, that there’s a large amount of dark matter in clusters, and that even in the space between galaxies there is dark matter. The cosmic density of dark matter with the current best measurements is about thirty percent of the critical density; omega equals 0.3. Even with the baryonic material added, dark matter does not have sufficient density to close the universe or overcome the cosmic expansion.

Transcript: There are two fundamentally different types of matter in the universe. Baryons is the term that refers to normal matter: the stuff that we’re made of; our world, the Earth, the Sun, most of the universe we’re familiar with. It’s the normal material of matter, protons, neutrons, and electrons, although electrons being nearly two thousand times lighter than protons or neutrons do not weigh much in the census. The baryon density is the cosmic density of all this material. To calculate it, astronomers sum up the matter contained in all the galaxies in the universe including their stars, their gas, and their dust, that’s ten to the power twenty galaxies, a hundred billion, billion galaxies, also the material in the intergalactic medium which at early epochs was a majority of the material which has since flowed into galaxies. The sum of the census is ten to the power eighty baryons or microscopic particles. As huge as this number is, it’s only 0.3 percent of the critical density. If there was nothing more than baryonic matter in the universe, it would not nearly be sufficient to close the universe.

Transcript: In simple big bang models, that is models without a cosmological constant, the critical density of matter is the density needed to just overcome the expansion so that the universe continues to expand but at an ever decreasing rate. It’s defined mathematically as three times the Hubble constant squared divided by eight times pi times the gravitational constant. Since the critical density is proportional to the Hubble constant squared, this implies that a faster expansion rate requires more matter to overcome the expansion. The value of the critical density given current measurement of the Hubble constant is at about ten to the power minus twenty-eight kilograms per cubic meter. This fantastically small number corresponds to only five hydrogen atoms per cubic meters of space or about one hydrogen atom in the volume occupied by a TV set. The dynamics of the expansion are determined by the matter density of the universe. If the matter density equals the critical density, space is flat, and the universe coasts to a maximum size, taking an infinite amount of time to do so. If the density is less than the critical density, the universe has negative curvature and will expand forever at a decreasing rate or deceleration. If the density is larger than the critical density, the universe will reach a maximum size and re-collapse, and space has a positive curvature. All of these statements are modified in the presence of vacuum energy or a cosmological constant.

Transcript: The big bang model predicts that the universe is evolving, that it was smaller, hotter, and denser in the past. Astronomers would like to test this basic prediction. One test involves spectral lines in distant quasi-stellar objects or quasars where the cosmic microwave background radiation excites the line. Observations and comparisons at different redshifts show that the temperature of the microwave background radiation, which is currently 2.7 Kelvin, was indeed hotter in the past, varying as one plus the redshift as predicted by the big bang model. Also, there are many observations to show that galaxies themselves have evolved, being smaller and having been assembled from pieces so they grow bigger and brighter with time and redshift to the present day. The universe is indeed evolving.

Transcript: Tracing the expansion rate back in time gives the age of the universe in a big bang model. Cosmological parameters, when they’re measured, can be used to predict the age of the universe. Based on the accurate measurements of the WMAP satellite, the age of the universe is between eleven and twelve billion years. Note that any universe where there is vacuum energy and a cosmological constant has an older age than a universe without such vacuum energy because the cosmological constant acts to accelerate the expansion and give an older age. The fundamental test of the big bang model is to look for the oldest objects where the age is measured using an astrophysical technique. In astronomy we use globular clusters, the oldest known stellar systems in the Milky Way galaxy. Their ages are measured by comparison of theories of stellar evolution with observations of the globular cluster. This technique is called isochrone fitting. These careful observations and the theories of stars that go with them show that the oldest globular clusters in the Milky Way galaxy have ages of about ten to eleven billion years allowing enough time for them to have formed along with the Milky Way. Thus, the big bang passes a critical test; it contains no objects older than the universe itself.

Transcript: An important test of the big bang model is some sort of verification of the reality of cosmic expansion. It’s possible that redshift may be non-cosmological in origin caused by some other phenomenon or property of light. The best test of the cosmological expansion, the reality of expanding space, is the prediction that the surface brightness of an object goes as one plus the redshift to the fourth power. Surface brightness is defined as the flux per unit area of an extended object like a galaxy. This means that in the big bang model galaxies should dim according to one plus z to the fourth power. Two of the factors of one plus z come from the area effect. Another factor of one plus z comes from time dilation in the arrival rate of photons from distant regions, and the fourth factor of one plus z is the redshift itself. It’s a difficult measurement once again because galaxies do not have sharp edges and are not very good standard candles in their properties. However, in the past decade astronomers have indeed confirmed that light from distant objects diminishes according to one plus z to the fourth and that the cosmic expansion is real.

Transcript: The current expansion rate of the universe is given by the Hubble constant. Measurement of the Hubble constant was subject to an enormous effort over the past forty years culminating in the Hubble Space Telescope key project. In this huge collaboration involving hundreds of orbits with that precious facility, a series of measurements of the local universe involving Cepheid variables was used to derive the expansion rate. The answer was seventy kilometers per second per megaparsec with an error of only ten percent on that measurement. It’s still one of the most accurately measured numbers in cosmology. The expansion was shown to be isotropic, that is the same in different directions in the sky. The velocity of any galaxy predicted by the smooth expansion is called Hubble flow. However galaxies do not usually have exactly the velocity predicted by Hubble flow because gravitational interactions between galaxies cause them to depart from a smooth flow. The amount by which they depart is called a peculiar velocity. The average amount of peculiar velocities of galaxies in the local universe is about a hundred to a hundred and fifty kilometers per second.

Transcript: The most sensitive test of the curvature of space uses the cosmic microwave background radiation. These microwaves were released three hundred thousand years after the big bang. The fluctuations in the microwave background were imprinted with a certain angular size, and depending on the shape of the universe, the fluctuations are either magnified or demagnified as they travel through billions of lightyears of space and billions of years of time to reach us. The universe therefore can act as an enormous lens. Careful observations of the fluctuations with NASA’s WMAP satellite shows that there is no space curvature. There is no magnification or demagnification of the fluctuations traveling through vast amounts of cosmic time. The universe therefore is very close to being flat.

Transcript: General relativity relates the dynamics of the expanding universe to the curvature of space. Thus space curvature is one of the most important things to measure about our universe, but it’s an extremely difficult measurement because the curvature is so subtle. In principle it would be possible to measure space curvature if there were objects of a fixed linear size in space. We could then measure how their apparent size varied with distance or redshift. But galaxies do not have fixed sides or edges, and their size actually evolves with cosmic time. So the size of galaxies cannot be used for this test. It also might be possible to measure the number of objects in equal volumes with distance or redshift to see what the space curvature was. In flat space, the number of objects per unit volume goes as the cube of the distance. In positively curved space, since the volume of the universe is smaller, the number of objects goes as a lower power than the third of radius, and in negatively curved universes where the volume is larger, it goes as a higher than the third power of distance. But this is a difficult measurement too because the objects we are counting, galaxies, both merge and change their properties with cosmic time.

Transcript: The big bang model is described by a small number of cosmological parameters. Astronomers talk about a world model, but in fact they’re talking about a description of the entire universe. If these parameters are measured, the entire history of the universe, past, present, and future, can be described although the detailed behavior of objects within the universe is too complex to be described in this way. Cosmological parameters require difficult observations, work at the limit of ground-based and space-based telescopes. Scientists need independent measurements using different techniques, and even then there are limitations imposed by the fact that we only have one universe to study. The basic cosmological parameters are the current expansion rate or the Hubble constant, the baryon content of the universe, that is normal matter, the dark matter content of the universe, the cosmological constant, and the age of the universe. Different types of observations are required to measure each of these quantities.