Lecture 31: Cosmology III: Geometry, CMB, and Inflation
Astronomy 101/103
Terry Herter, Cornell University
Course Home Page

Lecture
Topics
  • Expansion of the Universe
  • Geometry of the Universe
  • Fate of the Universe
  • The Cosmic Microwave Background
  • The Early universe
  • Problems with the Big Bang?
  • Inflation to the rescue

The Geometry
of Space
  • General Relativity predicts space will be "curved". [ p is not 3.1415926... ]
  • The curvature (geometry) of the universe depends on the value of Wk.
Universe
Wk
 Comment
Closed
< 0
Positive Curvature
Flat
= 0
Euclidean Space
Open
> 0
Negative Curvature

Closed
Universe

The Closed Universe

  • For Wk < 0, we have a closed universe, because space bends back on itself and makes the universe finite in size.
  • Space has positive curvature (like a sphere).
  • The volume is finite but there is no boundary!
  • Light shown in one direction would eventually return in the opposite direction.


Sphere
analogy
with a
Closed
Universe
Parallel straight lines cross!



Open Universe

The Open Universe

  • For Wk > 0, we have an open universe.
    • Space curves "outward".
    • Universe infinite in size.
  • Space has negative curvature (like a saddle).
  • Infinite volume


Saddle Analogy
with
Open Universe
Parallel straight lines diverge!


Spatial
Curvature

A flat plane has zero curvature, a sphere has positive curvature, and a hyperboloid has negative curvature.

This is illustrated in the 2-D analogies shown below, where a circle is cut out and place on a flat plane.


The Cosmic
Triangle
  • The Cosmic triangle shows in one diagram the possible dynamics and geometry of the Universe
  • It is a plot with three (!) axes: WM, WL, and Wk

Observational
Results
in the
Cosmic
Triangle
  • Showing the current observational data shows the best estimate of the geometry and fate of the universe.

Cosmic Triangle plots based on: N. A. Bahcall et. al, "The Cosmic Triangle: Assessing the State of the Universe", 1999, Science, 284, 1481.

Fate of the
Universe

  • The best estimates now yield
    • H0 = 71 km/sec/Mpc
    • WM = 0.27, WL = 0.73 => Wk = 0
    • Age of the Universe is then 13.67 Gyr.
  • This implies
    • The Universe is flat
    • It will go on expanding forever
    • Because L > 0, it will expand ever faster
  • The Universe will go on slowly cooling down.
    • All stars and star formation will die out.


Beginning of the
Universe
  • What about the origin of the universe?
  • If we extrapolate backwards in time, galaxies will be arbitrarily close together.
  • What happened back then?
  • How far back can we see?
  • The answer to this came in 1964 with the discovery of the Cosmic Microwave Background (CMB)

Cosmic Microwave
Background

  • Arno Penzias and Bob Wilson (Bell Labs)
  • In 1964, they conducted a study of radio emission from the MW to identify and eliminate interference to improve the telephone system!
  • Found a bothersome background "hiss" coming from everywhere.
  • This "hiss" turns out to be a "remnant" of the Big Bang.

The CMB
  • The Cosmic Microwave Background (CMB) has a blackbody spectral shape.
  • T = 2.73 K (As measured by COBE)
  • The universe is filled with "very cool" radiation!
  • Presently:
    • Matter density ~ 10-30 g/cm3
    • Radiation density ~ 5x10-34 g/cm3

Origin
of CMB
  • Where does the CMB come from?
  • As we extrapolate back in time, galaxies are closer together
  • And things get hotter
  • We eventually get to a time when galaxies did not exist
  • The universe at the time the CMB originated was a hot plasma (a mix of ions, mostly protons, and electrons)

Back to
the CMB
  • The CMB originated about 300,000 years after the Big Bang.
  • We cannon directly "see" beyond this period
  • We must rely on extrapolation based on our understanding of physics to go back further in time

 

  • COBE - The Cosmic Background Explorer mapped the sky at infrared and radio wavelengths
  • Its purpose was to study the CMB
  • COBE measured
    • The temperature of 2.73 K
    • A dipole moment due to the motion of the earth/sun/galaxy through the CMB
    • Fluctuations in the CMB which reflect the history of events in the early universe

CMB
Fluctuations
  • Fluctuations in the CMB tell us about
  • The geometry of the universe
  • The amount of matter in the universe
  • Whether the universe will expand forever or collapse
  • The expansion rate and age of the universe
  • The primordial seeds of galaxies and clusters

 

  • By looking at how the temperature varies on different angular scales astronomers perform a sort of Cosmic Ultrasound experiment to determine these properties of the universe.

Links on the CMB

Radiation and
Matter
  • Presently in the universe:
    • Matter density ~ 10-30 g/cm3 (w/ dark matter!)
    • Radiation density ~ 5x10-34 g/cm3 (CMB)
  • The matter density of the universe dominates at present.
  • But this wasn't always the case.

Early Universe

  • We now extrapolate back beyond where we can directly observe
  • As the universe evolved, both the matter and radiation densities decreased (to what we see today).
  • The radiation density changed faster!
  • Therefore, in the past the radiation density was much larger relative to the matter density.


Evolution of the
Universe



High Densities
and Temperatures
  • Not only was the density higher in the past, so was the temperature.
  • At that time radiation begins to dominate.
    • Universe ~ 20,000 times smaller.
    • The temperature of the CMB radiation was ~ 60,000 K.
  • The universe was extremely hot and dense at early times.

The Picture
So Far
  • About 13-14 billion years ago the Universe started
  • We don't know what triggered the Big Bang
  • We can extrapolated back to about ~10-43 seconds after the Big Bang.
    • Beyond this the physics is unknown.

Problems
with the
Big Bang
  • The Big Bang described thus far is very successful in may aspects, however there are two major problems that need to be addressed
  • Horizon Problem
    • Why is the CMB so uniform?
  • Flatness problem
    • Why are we so close to a flat universe?

The
Horizon
Problem
  • Looking at one part of the sky and looking in the opposite direction, radio telescopes measuring the CMB see the temperature to 1 part in 10,000.
  • Suppose the universe is 14 billion years old, then the two directions are separated by 28 billion lightyears.
  • Thus they should not be "causally connected"
    • That is, they should not know about each other
    • The two regions should not have the same temperature
  • In the past the situation was even worse
    • 100,000 years after the Big Bang the separation would be 10 million lightyears

The
Flatness
Problem
  • The Universe appears flat, that is, "just right".
  • However both the average density and the critical density change with time
  • In the past, right after the Big Bang if the average density were slightly larger or smaller we have and open or closed universe.
  • At the beginning the density would have to be very close to the critical value (1 part in 1015)
    • Otherwise a Big Crunch or Big Chill would have occurred long ago.

The
Answer
  • About 10-35 seconds after the Big Bang the Universe cooled to 1027 K!
  • This caused a "phase transition"
  • Like water changing into ice
  • This phase transition released a lot of energy
  • The strong force split from the other forces releasing tremendous amounts of energy
  • The universe expanded by a factor of 1050 in 10-33 seconds!

Inflation
  • This rapid expansion phase is called inflation.
  • Inflation solves the Horizon and Flatness problems
  • The parts of the Universe we see now were causally connected before inflation
    • Thus the CMB will be the same in all directions afterward
  • The Universe becomes flat
    • Because of the stretching of space

The "True
Picture"
  • The Universe expanded rapidly due to inflation after the Big Bang
  • This was followed by expansion and cooling
Course Home Page