Cosmology The Origin and Future of the Universe Part I

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CosmologyThe Origin and Future of the
UniversePart I

• Olbers Paradox

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Remember?

• Hubbles distance measurements confirmed a model
  of the Universe in which stars are grouped into
  galaxies..
• .. and local clusters of galaxies were
  distributed uniformly in space..
• .. and that galaxies more than 500 million
  light-years away are generally too faint to be
  seen but this does not negate the possibility of
  this pattern continuing throughout the Universe

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So whats the problem?

• Well! Astronomers had established a cosmological
  model which was static, uniform and infinite
  just like Newton had perceived..
• until Heinrich Olbers came along

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Olbers Paradox

• If the Universe is infinite, it follows that
  there must be an infinite number of stars in all
  directions which, in turn, means that the sky
  should be equally bright in all directions and
  the sky would be exceedingly bright!
• We know that this is not so!

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Olbers Paradox

• If the Universe is static and not infinite then
  it would eventually collapse under its own
  gravitational forces!
• We know that this is not so!

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Olbers Paradox

• That the Universe must be infinite and yet can
  not be infinite is known as Olbers Paradox

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Olbers Paradox

• Newton and Olbers both believed that
• Space is infinite and extends in all directions
• The Universe is static
• And then Hubble came along!

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Hubbles Law

• Hubble discovered that the Universe is expanding
  and this negated the truths which were until
  then believed
• How did Hubble achieve this?

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Towards Hubbles Law

• Vesto Slipher had discovered that dark lines in
  the spectra produced by the light from other
  galaxies had shifted towards the red end of the
  spectrum
• These dark lines were otherwise easily
  identifiable as those representing particular
  elements

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Towards Hubbles Law

• These red-shifts were explained in terms of the
  Doppler Effect
• The bigger the red-shift, then larger the speed
  of recession viz. the greater the speed with
  which the galaxy and the Earth are moving apart

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The Doppler Effect

• If a source is emitting light of wavelength ?
  metres travelling at c metres per second then one
  wave will be emitted in a time of ?/c seconds
• If the source moves at v metres per second then
  it will have moved away (or towards) the observer
  a distance of v.?/c metres during the production
  of one wave
• This change in wavelength ?? is given by
• ?? v. ?/c

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The Doppler Effect

• This means that the fractional change in
  wavelength is calculable as shown
• ??/? v/c
• Remember - v speed of source and that c
  speed of light
• Remember this equation is only valid where v is
  small compared with c

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Hubbles Law

• Hubble discovered that there is a pattern between
  recessional speeds and the distance away of the
  galaxies
• The recessional speed of a galaxy is directly
  proportional to its distance from the Earth
• This is Hubbles Law and implies that the whole
  Universe is expanding

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Hubbles Law
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Hubbles Law

• Does this mean that the Earth is at the centre of
  the Universe if all cosmological bodies are
  moving away from the Earth?
• No it does not for the following reason..

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Hubbles Law

• If two galaxies are distance d apart then in a
  time ?t the galaxies move a distance of ?d
  further apart two galaxies a distance 2d apart
  would move a distance of 2?d further apart
• This would be true wherever you are in the
  Universe

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So what of Olbers Paradox?

• Owing to the fact that it was suggested now that
  the Universe is expanding and not static, a
  solution to Olbers Paradox exists..

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So what of a Big Bang?

• As it had been shown that galaxies are all moving
  apart from each other at speeds which are
  directly proportional to their distances apart,
  it suggests that there must have been a time when
  all of the galaxies in the Universe were in the
  same place..

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So what of a Big Bang?

• ..so the Universe must have started with a great
  explosion which we know as the Big Bang
• It is possible to calculate when this Big Bang
  occurred viz. if the recessional speed of a
  galaxy is 0.25 x speed of light and the distance
  away is 5 x 109 light years then the age of the
  Universe is equal to (5 x 109)/0.25 2 x 1010
  years

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The Hubble Constant

• Hubbles Law can be written as (speed of
  recession/distance) H0
• H0 is known as the Hubble Constant and is
  gradient of the graph linking recession speed to
  distance away of the galaxies it is also the
  inverse of the age of the Universe..
• Viz. 1/H0 age of the Universe

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The Age of the Universe

• The data obtained from the Hubble telescope,
  launched in the early 1990s, compared with other
  data has led to the general acceptance that the
  age of the Universe is around 12 (plus or minus
  2) billion years

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The Big Bang

• In 1965 Cosmic Microwave Background Radiation was
  discovered
• This was discovered as coming from all directions
  in space, at all hours of day and night and at
  the same strength (to within 0.01)

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The Big Bang

• The existence of this microwave radiation and the
  fact that it corresponded to a black body
  temperature of 2.7K supported the idea that the
  Universe started with a Big Bang

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The Big Bang

• When the Big Bang occurred the Universe would
  have been very hot and, therefore, there would
  have been a lot of radiation with very short
  wavelengths
• As the Universe expanded this radiation would
  have stretched to longer wavelengths and
  correspondingly lower energies

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The Big Bang

• It was predicted more than twenty years earlier
  that there should be microwave background
  radiation corresponding to a temperature just
  above absolute zero (0)K and the discovery of
  this radiation made the Big Bang theory more
  plausible

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The Big Bang

• The visible matter in the Universe is
  approximately 70 hydrogen and 27 helium
• Since the Universe has existed, hydrogen burning
  in the stars could not have converted more than
  23 of the hydrogen into helium

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The Big Bang

• There must have been a time when the temperature
  was so high that hydrogen-helium conversion
  (hydrogen burning) took place at a faster rate
  Big Bang
• The Big Bang theory thus became the standard
  model of the origin of the Universe