Chapter 17: Cosmology

Chapter 1
How Science Works

  • The Scientific Method
  • Evidence
  • Measurements
  • Units and the Metric System
  • Measurement Errors
  • Estimation
  • Dimensions
  • Mass, Length, and Time
  • Observations and Uncertainty
  • Precision and Significant Figures
  • Errors and Statistics
  • Scientific Notation
  • Ways of Representing Data
  • Logic
  • Mathematics
  • Geometry
  • Algebra
  • Logarithms
  • Testing a Hypothesis
  • Case Study of Life on Mars
  • Theories
  • Systems of Knowledge
  • The Culture of Science
  • Computer Simulations
  • Modern Scientific Research
  • Astronomy
  • Astronomy as a Science
  • A Scale Model of Space
  • A Scale Model of Time
  • Questions
  • Chapter Quiz

Chapter 2
Early Astronomy

  • The Night Sky
  • Motions in the Sky
  • Navigation
  • Constellations and Seasons
  • The Seasons
  • The Magnitude System
  • Angular Size and Linear Size
  • Phases of the Moon
  • Eclipses
  • Aurora
  • Dividing Time
  • Solar Calendars
  • History of Astronomy
  • Stonehenge
  • Ancient Observatories
  • Counting and Measurement
  • Astrology
  • Greek Astronomy
  • Aristotle and Geocentric Cosmology
  • Aristarchus and Heliocentric Cosmology
  • The Dark Ages
  • Arab Astronomy
  • Indian Astronomy
  • Chinese Astronomy
  • Mayan Astronomy
  • Questions
  • Chapter Quiz

Chapter 3
The Copernican Revolution

  • Ptolemy and the Geocentric Model
  • The Renaissance
  • Copernicus and the Heliocentric Model
  • Tycho Brahe
  • Johannes Kepler
  • Elliptical Orbits
  • Kepler's Laws
  • Galileo Galilei
  • The Trial of Galileo
  • Isaac Newton
  • Newton's Law of Gravity
  • The Plurality of Worlds
  • The Birth of Modern Science
  • Layout of the Solar System
  • The Scale of the Solar System
  • The Idea of Space Exploration
  • Orbits
  • History of Space Exploration
  • Moon Landings
  • International Space Station
  • Manned versus Robotic Missions
  • Commercial Space Flight
  • Future of Space Exploration
  • Living in Space
  • Moon, Mars, and Beyond
  • Societies in Space
  • Questions
  • Chapter Quiz

Chapter 4
Matter and Energy in the Universe

  • Matter and Energy
  • Rutherford and Atomic Structure
  • Early Greek Physics
  • Dalton and Atoms
  • The Periodic Table
  • The Structure of the Atom
  • Energy
  • Heat and Temperature
  • Potential and Kinetic Energy
  • Conservation of Energy
  • Velocity of Gas Particles
  • States of Matter
  • Thermodynamics
  • Entropy
  • Laws of Thermodynamics
  • Heat Transfer
  • Thermal Radiation
  • Wien's Law
  • Radiation from Planets and Stars
  • Internal Heat in Planets and Stars
  • Periodic Processes
  • Random Processes
  • Questions
  • Chapter Quiz

Chapter 5
The Earth-Moon System

  • Earth and Moon
  • Early Estimates of Earth's Age
  • How the Earth Cooled
  • Ages Using Radioactivity
  • Radioactive Half-Life
  • Ages of the Earth and Moon
  • Geological Activity
  • Internal Structure of the Earth and Moon
  • Basic Rock Types
  • Layers of the Earth and Moon
  • Origin of Water on Earth
  • The Evolving Earth
  • Plate Tectonics
  • Volcanoes
  • Geological Processes
  • Impact Craters
  • The Geological Timescale
  • Mass Extinctions
  • Evolution and the Cosmic Environment
  • Earth's Atmosphere and Oceans
  • Weather Circulation
  • Environmental Change on Earth
  • The Earth-Moon System
  • Geological History of the Moon
  • Tidal Forces
  • Effects of Tidal Forces
  • Historical Studies of the Moon
  • Lunar Surface
  • Ice on the Moon
  • Origin of the Moon
  • Humans on the Moon
  • Questions
  • Chapter Quiz

Chapter 6
The Terrestrial Planets

  • Studying Other Planets
  • The Planets
  • The Terrestrial Planets
  • Mercury
  • Mercury's Orbit
  • Mercury's Surface
  • Venus
  • Volcanism on Venus
  • Venus and the Greenhouse Effect
  • Tectonics on Venus
  • Exploring Venus
  • Mars in Myth and Legend
  • Early Studies of Mars
  • A Close-Up View of Mars
  • Modern Views of Mars
  • Missions to Mars
  • Geology of Mars
  • Water on Mars
  • Polar Caps of Mars
  • Climate Change on Mars
  • Terraforming Mars
  • Life on Mars
  • The Moons of Mars
  • Martian Meteorites
  • Comparative Planetology
  • Incidence of Craters
  • Counting Craters
  • Counting Statistics
  • Internal Heat and Geological Activity
  • Magnetic Fields of the Terrestrial Planets
  • Mountains and Rifts
  • Radar Studies of Planetary Surfaces
  • Laser Ranging and Altimetry
  • Gravity and Atmospheres
  • Normal Atmospheric Composition
  • The Significance of Oxygen
  • Questions
  • Chapter Quiz

Chapter 7
The Giant Planets and Their Moons

  • The Gas Giant Planets
  • Atmospheres of the Gas Giant Planets
  • Clouds and Weather on Gas Giant Planets
  • Internal Structure of the Gas Giant Planets
  • Thermal Radiation from Gas Giant Planets
  • Life on Gas Giant Planets?
  • Why Giant Planets are Giant
  • Gas Laws
  • Ring Systems of the Giant Planets
  • Structure Within Ring Systems
  • The Origin of Ring Particles
  • The Roche Limit
  • Resonance and Harmonics
  • Tidal Forces in the Solar System
  • Moons of Gas Giant Planets
  • Geology of Large Moons
  • The Voyager Missions
  • Jupiter
  • Jupiter's Galilean Moons
  • Jupiter's Ganymede
  • Jupiter's Europa
  • Jupiter's Callisto
  • Jupiter's Io
  • Volcanoes on Io
  • Saturn
  • Cassini Mission to Saturn
  • Saturn's Titan
  • Saturn's Enceladus
  • The Discoveries of Uranus and Neptune
  • Uranus
  • Uranus' Miranda
  • Neptune
  • Neptune's Triton
  • Pluto
  • The Discovery of Pluto
  • Pluto as a Dwarf Planet
  • Dwarf Planets
  • Questions
  • Chapter Quiz

Chapter 8
Interplanetary Bodies

  • Interplanetary Bodies
  • Comets
  • Early Observations of Comets
  • Structure of the Comet Nucleus
  • Comet Chemistry
  • Oort Cloud and Kuiper Belt
  • Kuiper Belt
  • Comet Orbits
  • Life Story of Comets
  • The Largest Kuiper Belt Objects
  • Meteors and Meteor Showers
  • Gravitational Perturbations
  • Asteroids
  • Surveys for Earth Crossing Asteroids
  • Asteroid Shapes
  • Composition of Asteroids
  • Introduction to Meteorites
  • Origin of Meteorites
  • Types of Meteorites
  • The Tunguska Event
  • The Threat from Space
  • Probability and Impacts
  • Impact on Jupiter
  • Interplanetary Opportunity
  • Questions
  • Chapter Quiz

Chapter 9
How Planetary Systems Form

  • Formation of the Solar System
  • Early History of the Solar System
  • Conservation of Angular Momentum
  • Angular Momentum in a Collapsing Cloud
  • Helmholtz Contraction
  • Safronov and Planet Formation
  • Collapse of the Solar Nebula
  • Why the Solar System Collapsed
  • From Planetesimals to Planets
  • Accretion and Solar System Bodies
  • Differentiation
  • Planetary Magnetic Fields
  • The Origin of Satellites
  • Solar System Debris and Formation
  • Gradual Evolution and a Few Catastrophies
  • Chaos and Determinism
  • Extrasolar Planets
  • Discoveries of Extrasolar Planets
  • Doppler Detection of Extrasolar Planets
  • Transit Detection of Extrasolar Planets
  • The Kepler Mission
  • Direct Detection of Extrasolar Planets
  • Properties of Extrasolar Planets
  • Implications of Extrasolar Planet Surveys
  • Future Detection of Extrasolar Planets
  • Questions
  • Chapter Quiz

Chapter 10
Detecting Radiation from Space

  • Observing the Universe
  • Radiation and the Universe
  • The Nature of Light
  • The Electromagnetic Spectrum
  • Properties of Waves
  • Waves and Particles
  • How Radiation Travels
  • Properties of Electromagnetic Radiation
  • The Doppler Effect
  • Invisible Radiation
  • Thermal Spectra
  • The Quantum Theory
  • The Uncertainty Principle
  • Spectral Lines
  • Emission Lines and Bands
  • Absorption and Emission Spectra
  • Kirchoff's Laws
  • Astronomical Detection of Radiation
  • The Telescope
  • Optical Telescopes
  • Optical Detectors
  • Adaptive Optics
  • Image Processing
  • Digital Information
  • Radio Telescopes
  • Telescopes in Space
  • Hubble Space Telescope
  • Interferometry
  • Collecting Area and Resolution
  • Frontier Observatories
  • Questions
  • Chapter Quiz

Chapter 11
Our Sun: The Nearest Star

  • The Sun
  • The Nearest Star
  • Properties of the Sun
  • Kelvin and the Sun's Age
  • The Sun's Composition
  • Energy From Atomic Nuclei
  • Mass-Energy Conversion
  • Examples of Mass-Energy Conversion
  • Energy From Nuclear Fission
  • Energy From Nuclear Fusion
  • Nuclear Reactions in the Sun
  • The Sun's Interior
  • Energy Flow in the Sun
  • Collisions and Opacity
  • Solar Neutrinos
  • Solar Oscillations
  • The Sun's Atmosphere
  • Solar Chromosphere and Corona
  • Sunspots
  • The Solar Cycle
  • The Solar Wind
  • Effects of the Sun on the Earth
  • Cosmic Energy Sources
  • Questions
  • Chapter Quiz

Chapter 12
Properties of Stars

  • Stars
  • Star Names
  • Star Properties
  • The Distance to Stars
  • Apparent Brightness
  • Absolute Brightness
  • Measuring Star Distances
  • Stellar Parallax
  • Spectra of Stars
  • Spectral Classification
  • Temperature and Spectral Class
  • Stellar Composition
  • Stellar Motion
  • Stellar Luminosity
  • The Size of Stars
  • Stefan-Boltzmann Law
  • Stellar Mass
  • Hydrostatic Equilibrium
  • Stellar Classification
  • The Hertzsprung-Russell Diagram
  • Volume and Brightness Selected Samples
  • Stars of Different Sizes
  • Understanding the Main Sequence
  • Stellar Structure
  • Stellar Evolution
  • Questions
  • Chapter Quiz

Chapter 13
Star Birth and Death

  • Star Birth and Death
  • Understanding Star Birth and Death
  • Cosmic Abundance of Elements
  • Star Formation
  • Molecular Clouds
  • Young Stars
  • T Tauri Stars
  • Mass Limits for Stars
  • Brown Dwarfs
  • Young Star Clusters
  • Cauldron of the Elements
  • Main Sequence Stars
  • Nuclear Reactions in Main Sequence Stars
  • Main Sequence Lifetimes
  • Evolved Stars
  • Cycles of Star Life and Death
  • The Creation of Heavy Elements
  • Red Giants
  • Horizontal Branch and Asymptotic Giant Branch Stars
  • Variable Stars
  • Magnetic Stars
  • Stellar Mass Loss
  • White Dwarfs
  • Supernovae
  • Seeing the Death of a Star
  • Supernova 1987A
  • Neutron Stars and Pulsars
  • Special Theory of Relativity
  • General Theory of Relativity
  • Black Holes
  • Properties of Black Holes
  • Questions
  • Chapter Quiz

Chapter 14
The Milky Way

  • The Distribution of Stars in Space
  • Stellar Companions
  • Binary Star Systems
  • Binary and Multiple Stars
  • Mass Transfer in Binaries
  • Binaries and Stellar Mass
  • Nova and Supernova
  • Exotic Binary Systems
  • Gamma Ray Bursts
  • How Multiple Stars Form
  • Environments of Stars
  • The Interstellar Medium
  • Effects of Interstellar Material on Starlight
  • Structure of the Interstellar Medium
  • Dust Extinction and Reddening
  • Groups of Stars
  • Open Star Clusters
  • Globular Star Clusters
  • Distances to Groups of Stars
  • Ages of Groups of Stars
  • Layout of the Milky Way
  • William Herschel
  • Isotropy and Anisotropy
  • Mapping the Milky Way
  • Questions
  • Chapter Quiz

Chapter 15
Galaxies

  • The Milky Way Galaxy
  • Mapping the Galaxy Disk
  • Spiral Structure in Galaxies
  • Mass of the Milky Way
  • Dark Matter in the Milky Way
  • Galaxy Mass
  • The Galactic Center
  • Black Hole in the Galactic Center
  • Stellar Populations
  • Formation of the Milky Way
  • Galaxies
  • The Shapley-Curtis Debate
  • Edwin Hubble
  • Distances to Galaxies
  • Classifying Galaxies
  • Spiral Galaxies
  • Elliptical Galaxies
  • Lenticular Galaxies
  • Dwarf and Irregular Galaxies
  • Overview of Galaxy Structures
  • The Local Group
  • Light Travel Time
  • Galaxy Size and Luminosity
  • Mass to Light Ratios
  • Dark Matter in Galaxies
  • Gravity of Many Bodies
  • Galaxy Evolution
  • Galaxy Interactions
  • Galaxy Formation
  • Questions
  • Chapter Quiz

Chapter 16
The Expanding Universe

  • Galaxy Redshifts
  • The Expanding Universe
  • Cosmological Redshifts
  • The Hubble Relation
  • Relating Redshift and Distance
  • Galaxy Distance Indicators
  • Size and Age of the Universe
  • The Hubble Constant
  • Large Scale Structure
  • Galaxy Clustering
  • Clusters of Galaxies
  • Overview of Large Scale Structure
  • Dark Matter on the Largest Scales
  • The Most Distant Galaxies
  • Black Holes in Nearby Galaxies
  • Active Galaxies
  • Radio Galaxies
  • The Discovery of Quasars
  • Quasars
  • Gravitational Lensing
  • Properties of Quasars
  • The Quasar Power Source
  • Quasars as Probes of the Universe
  • Star Formation History of the Universe
  • Expansion History of the Universe
  • Questions
  • Chapter Quiz

Chapter 17
Cosmology

  • Cosmology
  • Early Cosmologies
  • Relativity and Cosmology
  • The Big Bang Model
  • The Cosmological Principle
  • Universal Expansion
  • Cosmic Nucleosynthesis
  • Cosmic Microwave Background Radiation
  • Discovery of the Microwave Background Radiation
  • Measuring Space Curvature
  • Cosmic Evolution
  • Evolution of Structure
  • Mean Cosmic Density
  • Critical Density
  • Dark Matter and Dark Energy
  • Age of the Universe
  • Precision Cosmology
  • Future of Astronomical Sources
  • Fate of the Universe
  • Alternatives to the Big Bang Model
  • Space-Time
  • Particles and Radiation
  • The Very Early Universe
  • Mass and Energy in the Early Universe
  • Matter and Antimatter
  • The Forces of Nature
  • Fine-Tuning in Cosmology
  • The Anthropic Principle in Cosmology
  • String Theory and Cosmology
  • The Multiverse
  • The Limits of Knowledge
  • Questions
  • Chapter Quiz

Chapter 18
Life On Earth

  • Nature of Life
  • Chemistry of Life
  • Molecules of Life
  • The Origin of Life on Earth
  • Origin of Complex Molecules
  • Miller-Urey Experiment
  • Pre-RNA World
  • RNA World
  • From Molecules to Cells
  • Metabolism
  • Anaerobes
  • Extremophiles
  • Thermophiles
  • Psychrophiles
  • Xerophiles
  • Halophiles
  • Barophiles
  • Acidophiles
  • Alkaliphiles
  • Radiation Resistant Biology
  • Importance of Water for Life
  • Hydrothermal Systems
  • Silicon versus Carbon
  • DNA and Heredity
  • Life as Digital Information
  • Synthetic Biology
  • Life in a Computer
  • Natural Selection
  • Tree Of Life
  • Evolution and Intelligence
  • Culture and Technology
  • The Gaia Hypothesis
  • Life and the Cosmic Environment
  • Chapter Quiz

Chapter 19
Life in the Universe

  • Life in the Universe
  • Astrobiology
  • Life Beyond Earth
  • Sites for Life
  • Complex Molecules in Space
  • Life in the Solar System
  • Lowell and Canals on Mars
  • Implications of Life on Mars
  • Extreme Environments in the Solar System
  • Rare Earth Hypothesis
  • Are We Alone?
  • Unidentified Flying Objects or UFOs
  • The Search for Extraterrestrial Intelligence
  • The Drake Equation
  • The History of SETI
  • Recent SETI Projects
  • Recognizing a Message
  • The Best Way to Communicate
  • The Fermi Question
  • The Anthropic Principle
  • Where Are They?
  • Chapter Quiz

Universal Expansion


The Hubble relation is our primary evidence for the expansion of the universe. When Einstein, Lemaitre, and others solved the equations of general relativity, they were able to describe how the size of the universe has changed with time. Astronomers use the symbol R to represent the scale or size of the universe at any time. You can think of R as the size of the universe, but more accurately it represents the distance between any two well-separated places. The cosmological principle says that any two points are moving apart at the same rate. Thus, the entire history of the universe is described by the way that R varies with time. Since the universe is expanding, R has been continuously increasing for billions of years. Remember that R describes the expansion of space that carries galaxies apart — the galaxies themselves are not expanding. Galaxies are just markers of expanding space.

 

The expansion of space provides a good way to define the cosmological redshift. If R is the scale of the universe at any time and R0 is the scale of the universe now, then the redshift is the ratio of the present scale to the previous scale, minus one. In equation form, z = (R0/R) - 1. We see regions near us in space as they are now, so R = R0 and z = 0. Remember that looking out in space corresponds to looking back in time. However the universe was smaller in the past, so a distant region of space has R < R0 and z > 0. Conceptually, light left distant objects when the universe was smaller and the waves have since been stretched by the expansion of space. We can now relate the expansion of the space to the redshifts of distant galaxies and quasars. The light from a distant galaxy might have been emitted when the universe was half its present size. Using the definition of redshift given above, R0 = 2R and z = 1. The light from the most distant quasar was emitted when the universe was one eighth of its present size. In this case, R0 = 8R and z = 7. Ancient light is light that has been reddened due to the expansion of space.

How are cosmological redshifts related to the Doppler effect? A redshift caused by the Doppler effect is defined as z = Δλ/λ, where Δλ is the difference between the wavelength observed and the wavelength emitted. A cosmological redshift is z = (R0 - R)/R = ΔR/R, where ΔR is the difference between the scale of the universe observed now and the scale of the universe when the light was emitted. However, there are crucial distinctions between Doppler redshifts and cosmological redshifts. The Doppler effect applies to waves of any kind traveling through a medium. The cosmological redshift is caused by the expansion of the medium itself. The Doppler effect relates the redshift to the speed of the waves; at low redshifts z = v/c. By contrast, the cosmological redshift is not related to the speed of light at all. The limitation imposed by special relativity — that nothing can go faster than the speed of light — does not apply on the global scale of the universe, which is governed by general relativity. As a result, there can be remote regions of the universe that are moving apart faster than the speed of light!

 

Until the mid 1990s, it took only two numbers to describe all the possible models for the expansion. The first is the current expansion rate, given by the Hubble constant. The second is the mean density of matter in the local universe. In expanding universes, the rate of expansion decelerates (slows down) with time, because galaxies are pulling on all other galaxies. The strength of the deceleration depends on the mean density of matter, where most of it is dark matter. The deceleration is also related to the curvature of space, which determines the fate of the universe. It is a fundamental consequence of general relativity that the structure, or curvature, of space is related to the amount of matter in the universe. This simple view had to be amended with the discovery of the acceleration of the universe and the implication of a component called dark energy that worked counter to gravity and was speeding up the expansion rate. For the rest of this article, we will just describe the behavior of universes containing only matter.

The expansion rate currently is the Hubble constant, H0. When the universe was denser and smaller, it had a higher expansion rate. If the universe had nothing in it, there would be no gravity to slow down the expansion. The result would be expansion at a constant rate. In an almost empty (i.e. low-density) universe, the deceleration is small, and R increases almost linearly with time. A low-density universe has negative space curvature in general relativity; it is called an open universe and it expands. At a certain critical density, the universe continues to expand to some maximum size at an ever-decelerating rate, taking an infinite amount of time to come to a halt. This special case has zero space curvature; it is called a flat universe. A universe in which the mean density is above the critical density has a positive curvature and is a closed universe. The mutual attraction of matter in such a universe is eventually enough to overcome the Hubble expansion. After R reaches a maximum value, the universe will collapse. As space begins to contract, all the galaxies will begin to rush toward each other and show blueshifts.

The critical density divides universes that will expand forever from universes that will eventually collapse. So astronomers characterize the big bang model by a density parameter0), which is the ratio of the observed density to the critical density. The density parameter is a dimensionless number. If Ω0 < 1, the universe is open and will expand forever. If Ω0 > 1, the universe is closed and will collapse. Remember that there are many possible values of the mean density that correspond to an open universe. Equally, there are many possible values of the mean density that correspond to a closed universe. However, the special case of a flat universe only occurs if the mean density equals the critical density, Ω0 = 1.

Consider the analogy of a rocket launched from the surface of the Earth. The escape velocity is about 11 km/s. A rocket launched with an initial velocity of less than 11 km/s will decelerate as it rises. The Earth's gravitational attraction will eventually overcome the upward velocity and force the rocket back to the planet's surface. On the other hand, a rocket with an initial velocity above 11 km/s will escape from the Earth forever. Of course, the rocket will continue to slow down since the planet's gravity has a long reach, but it will never reverse its direction and fall back to Earth. In our universe, the Hubble constant is analogous to the launch velocity of the rocket, and the mean density to the mass of the planet. For each possible launch velocity of a rocket, there is a mass of planet where that velocity will just equal the escape velocity. Conversely, for every planet there is a single velocity that will allow the rocket to just escape gravity's pull. Larger planets have larger escape velocities. By analogy, for every possible value of the Hubble constant, there is a mean density that will just be enough to stop the universal expansion and close the universe. A larger Hubble constant requires a larger mean density to close the universe.

The following shows how the density parameter relates to the curvature of space and the future of the universe:

• Flat universe: zero curvature, Ω0 = 1, fate is to expand to a maximum size

• Closed universe: positive curvature, Ω0 > 1, fate is to reach a maximum size and collapse

• Open universe: negative curvature, Ω0 < 1, fate is endless, decelerating expansion

• Empty universe: negative curvature, Ω0 = 0, fate is endless and constant expansion

An estimate of the age of the universe comes from tracing the expansion back to the time when all galaxies were on top of each other (R = 0). Space had zero size when the universe formed. A linear Hubble expansion leads to an age estimate of 1/H0. For the current best estimate of H0 = 71 km/s/Mpc, this age is roughly 13.7 billion years. Any expansion will have a deceleration, so the age estimate of 1/H0 is correct only in the artificial case of an empty universe. That is, 13.7 billion years is an upper limit to the age of the universe in the big bang model. Mathematically, it turns out that a flat universe has an age of ⅔(1/H0) or about 9 billion years. Therefore, the big bang model predicts that the universe will have an age between 9 and 13.7 billion years if the geometry is open, and less than 9 billion years if the geometry is closed. The inclusion of dark energy alters this calculation and leads to a slight increase in the calculated age of the universe, to 13.8 billion years.


Author: Chris Impey
Editor/Contributor: Erik Brogt