The Standard Model of Cosmology

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The Standard Model of Cosmology

• Chad A. Middleton, Ph.D.
• Mesa State College
• October 11, 2007
• The most incomprehensible thing about the world
  is that it is comprehensible.
• -A. Einstein

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Cosmology

• is the scientific study of the large scale
  properties of the Universe as a whole.
• addresses questions like
• Is the Universe (in)finite in spatial extent?
• Is the Universe (in)finite in temporal extent?
• What are the possible geometries of the Universe?
• What is the fate of the Universe?

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Ancient Greek Worldview A Geocentric Cosmos

• Rotating spheres carry the moon, sun, planets,
  stars around a stationary Earth
• Perfect, eternal unchanging celestial region
• Universe is finite

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Keplerian Orbits

• Based on Tycho Brahes astronomical measurements
• Copernican circular Heliocentric orbits must be
  abandoned

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Keplers 3 Laws of Planetary Motion

• The planets move in elliptical orbits with the
  Sun at one focus.
• A line drawn from the Sun to any planet sweeps
  out equal areas in equal time intervals.
• The square of the period of a planet is
  proportional to the cube of the semi-major axis
  of its orbit.

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Olbers Paradox
If the Universe in infinite, unchanging, and
everywhere the same, shouldnt the entire night
sky be bright?

• Kepler believed
• space must be finite
• of stars must be finite
• space surrounded by some kind of dark wall

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Newtons Universal Law of Gravitation

• Successes
• Described the motion of massive bodies
• on earth
• in the heavens

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So what keeps the stars fixed?

• Newtons view of the Cosmos
  a perfect balance?
• Newton envisioned
• an infinitely large universe
• stars were placed at just the right distances so
  their attractions cancelled.

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In 1915, Einstein gives the world his General
Theory of Relativity

• describes the curvature of space
• describes the matter energy

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Space is not an empty void but rather a dynamical
structure whose shape is determined by the
presence of matter and energy.

• Matter tells space how to curve
• Space tells matter how to move

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Einsteins Static Universe

• General Relativity does NOT allow for a
  static cosmological model
• ? Einstein introduces a Cosmological Constant
• ? Static Universe if

vacuum energy
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In 1929, Edwin Hubble discovers that the Universe
is expanding!
Einstein calls ? the greatest blunder of his
life!
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Doppler Shift allows for determining the velocity
of approaching/receding galaxies!
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Cosmological Principle

• On sufficiently large distance scales, the
  Universe is
• 1. Isotropic
• 2. Homogeneous
• ? Maximally Symmetric Space

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For a Homogeneous Isotropic Universe 3
possible Geometries
Recent data indicates that the Universe is flat
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Friedmann-Robertson-Walker (FRW) Cosmology
Choose the Robertson-Walker metric
3 non-interacting components

• pressureless matter
• radiation
• vacuum

the Robertson-Walker metric describes a
spatially homogeneous, isotropic Universe
evolving in time
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The FRW Equations are

• density (?) pressure (p) of the Universe
  determine the evolution of the scale factor (a)

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Solutions for the scale factor when ? 0

• Radiation dominated
• Matter dominated
• Vacuum dominated

NOTICE As t? 0, a(t) ? 0
Solutions for a non-static Universe an
abstract theoretical curiosity?
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Georges Lemaître suggests the Universe had a
temporal beginning..

• Belgian Astrophysicist/
  Catholic Priest
• 1927 paper in Annals of the
  Brussels Scientific
  Society
• Lemaître
• showed that the universe had to be either
  contracting or expanding.
• suggested that the Universe had a definite
  beginning in which all its matter and energy were
  concentrated at one point.

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Did the Universe begin with a Big
Bang??
The Big Bang ...

• is not an explosion that happened at one point
  in space

• occurred at every place in space _at_ one moment in
  time

Big Bang - a time of infinite density, infinite
temperature, and infinite spacetime curvature
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In the early 1960s, the Princeton group in
gravitational physics

• finds that the Universe should be uniformly
  bathed in a background microwave radiation
• predicts a blackbody spectrum of the background
  radiation w/ T 10K

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In 1965, observational evidence for the Big Bang!!

• Arno Penzias Robert Wilson
• Bell Lab Physicists calibrating the Bell Labs
  microwave antenna designed for satellite
  communications
• Awarded the 1978 Nobel Prize in physics for
  discovery of the Cosmic Microwave Background
  Radiation

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Yeah, but does this microwave background
radiation have a Blackbody Spectrum?

• In Nov 89, NASA launches the Cosmic Background
  Explorer (COBE) to measure
• the spectrum
• the anisotropies
• of the cosmic background radiation.

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Spectrum of the
Cosmic Microwave Background Radiation
John Mather George Smoot Awarded the 2006
Nobel Prize in physics for their discovery of
the blackbody form and anisotropy discovery of
the CMB

• The excellent agreement with Plancks law is the
  best fit ever measured!

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COBE image of the Cosmic Microwave Background
Radiation

• Light from when the Universe was 380,000 years
  old
• Map of ?K anisotropies

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Conclusions

• Theory observational evidence indicate that
• the Universe is infinite in spatial extent
• the Universe began w/ a Big Bang 13.7
  billion years ago
• the Universe is flat
• the Universe will continue to expand indefinitely

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Models of the Expansion of the Universe
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An AlternativeSteady State Cosmology

• Proposed by Hoyle, Bondi, Gold
• Perfect Cosmological Principle
• - Universe is not only homogeneous in space
  but also in time
• Universe has NO beginning or end to time
• new matter is continuously being created as
  Universe expands
• Expansion rate is constant

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Steady State vs Big Bang

• Big Bang
• Predicts the correct abundance of H (75) He
  (25)
• Universe only few Billion years old?
• Steady State
• Space Time treated symmetrically
• What about Olbers Paradox?

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Inflation

• Why is the Universe so
• spatially flat
• homogeneous isotropic
• Where did the temperature anisotropies come from?

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The Standard Model of Cosmology

• Chad A. Middleton, Ph.D.
• Mesa State College
• October 11, 2007
• The most incomprehensible thing about the world
  is that it is comprehensible.
• -A. Einstein