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Chapter 26: Cosmology. Why is the sky dark? The expanding universe Beginning of the universe: The Big Bang Cosmic microwave background The early universe Shape of the universe The accelerating universe. Cosmology. What is cosmology? It is the study of the nature of the universe.
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Chapter 26: Cosmology • Why is the sky dark? • The expanding universe • Beginning of the universe: The Big Bang • Cosmic microwave background • The early universe • Shape of the universe • The accelerating universe
Cosmology • What is cosmology? It is the study of the nature of the universe. • How large is the universe? • What is the structure of the universe? • How long has the universe existed? • How has the universe changed over time?
Olber’s paradox: Why is the night sky dark? • Newton imagined the universe was infinite and static. • An infinite number of stars are scattered randomly throughout an infinitely large universe. • If it weren’t infinite then over time gravity would cause the universe to collapse. • If this were really true then everywhere we looked we would see a star and the night sky would be bright…
Einstein’s contributions • What does general relativity say about the universe as a whole? • Einstein’s calculations couldn’t produce a static universe. • He added a term called the cosmological constant to force a prediction of a static universe. • Einstein later said that was “the greatest blunder of my life.”
The expanding universe • Edwin Hubble found the first evidence that the universe was expanding. • Hubble law: v=H0d • This law states that remote galaxies are moving away from us with speeds proportional to their distance. • Because remote galaxies are getting farther and farther apart as time goes on, astronomers say that the universe is expanding.
Yet another redshift • Expansion explains why light from distant galaxies is redshifted. • Space expands as photons travel through it and the photon becomes “stretched.” • This is called a cosmological redshift. • It is NOT a Doppler shift.
Cosmological redshift • The cosmological redshift lets us calculate how much the universe has expanded since the light was emitted. • The factor 1+z indicates the amount of expansion.
Lookback time • An object’s redshift along with the Hubble law allow us to determine the distance to the object. • This gives us the lookback time to the object. • The distance measured in light years is equal to the lookback time in years. • To avoid uncertainties, astronomers typically describe the distance to an object in terms of its measured redshift.
The cosmological principle • The idea of the expanding universe demonstrates a central idea of cosmology. • Cosmological principle: The universe is homogenous and isotropic. • Homogeneous: all regions are the same • Isotropic: looks the same in every direction • Ultimately the cosmological principle means that we do not occupy a special location in the universe - they are all essentially the same.
The Big Bang • If you imagine time moving backward the Hubble flow will reverse direction. • If we look far enough into the past there must have been a time when the density of matter was inconceivably high. • An event, called the Big Bang, marks the “birth” of the universe. • I know it sounds crazy, but hold on because it turns out there is plenty of convincing evidence.
A resolution to Olber’s paradox: Part 2 • According to the Hubble law, the greater the distance to an object the greater its redshift. • Light from a galaxy nearly at the cosmic light horizon has a nearly infinite redshift. • This light has nearly no energy at all meaning the galaxies emitting the light are nearly invisible.
Evidence for the Big Bang • First, a dilemma: There is too much helium in the universe. Where did it come from and how can we explain it? • 65 years ago physicists first postulated that the early universe was at least as hot as the center of the Sun. • At this time, the universe was filled with many high-energy photons which should now have much longer wavelengths thanks to cosmological redshift. • Can we see them?
Cosmic microwave background • Wien’s law predicts that this radiation should have its peak in the microwave part of the spectrum. • The CMB was first detected in the 1960s by scientists working on communications systems. • Persistent noise in their system turned out to be the CMB.
Building blocks of the universe • Everything in the universe is either matter or radiation. • Matter: luminous and dark matter • Radiation: photons (majority are CMB photons) • Which plays a more important role in the universe? • The answer to this question depends on when you ask it. • We are interested in comparing the relative mass densities of matter and radiation.
Radiation mass density • We can combine E=mc2 with the Stefan-Boltzmann law to find the mass density of radiation in the universe: • For the present day T=2.75 K and rad=4.6x10-31 kg/m3
Matter mass density • To find the average matter mass density we must determine the amount of matter in a large volume of space. • m=M/V • Measurements of rich clusters we estimate that m=2.4x10-27 kg/m3. • Equivalent to about 1.5 H atoms per m3. • Luminous matter constitutes only about 17% of the total matter mass density of the universe.
Which wins? • The average density of matter is thousands of times larger than the mass density of radiation. • This is mainly because the CMB photons have such low energy. • There are actually 4.1x108 CMB photons per m3. • As we go back in time the universe gets smaller so both densities increase. • The photons become less redshifted (more energetic) and the total mass density of radiation increases rapidly.
Evolution of density • Transition happened about 24,000 years after Big Bang. • z=5200 • Using Wien’s law we can determine the radiation temperature at z=5200 to be 14,000 K.
Recombination • The photons that had been colliding with charged particles could now stream unimpeded through space. • These same photons are today the CMB photons. • Because the universe was opaque before z=1100 we can’t see further back into the past. • CMB photons are the most ancient photons we can observe.
Shape of the universe • We also want to know about the combined mass density of all forms of matter and energy. • We can do this by studying the shape of the universe. • Einstein tells us that gravity curves space. • Mass and energy are equivalent, so both can curve space. • Matter and energy scattered across space should give the universe an overall curvature. • Degree of curvature depends on combined mass density of energy and matter - called 0.
Density of the universe • A flat universe is a special case with a specific density. • Call this density the critical density or c. • Spherical: 0>c, • Flat: 0=c, • Hyperbolic: 0<c, • Alternatively, we define the curvature of the universe by the ratio of the combined average mass density to the critical density. • c
Can we measure the curvature? • If we could observe the paths of light from a distant source we could in principle measure the curvature of the universe. • We use the CMB photons. • The presence of CMB hot spots allows us to make the measurement. • Calculations indicate that these hot spots should have an angular size of about 1°.
Results of curvature measurements • We find that 0=1.0 with an uncertainty of 2%. • This says the universe is flat. (0=c) • Unfortunately, m is measured to be only about 24% of the critical density. • Radiation density is insignificant. • Radiation, matter and dark matter acount for 24% of the total density of the universe. What accounts for the rest? • Must be some form of energy we cannot detect gravitationally or electromagnetically. • Dark energy!
Dark energy • This is Einstein’s cosmological constant. • It is a form of energy that tends to make the universe expand. • It turn out that Einstein’s error was not introducing . The error was not making it big enough. • This is an extraordinary claim. Do we have any evidence to support it?
The future of the universe • If dark energy truly is a cosmological constant the universe will continue to expand forever. • In about 30 billion years only 1000 or so of the nearest galaxies will be visible. • Several models have been proposed describing a type of dark energy whose density slowly decreases as the universe expands. • This leads to predictions that the universe could either expand forever or eventually recollapse. • Future observations will help clarify these predictions.
