Big Bang Model of the Universe
Earth and Space

Cosmology

Lesson for 16-19

Cosmology is the study of the Universe, its origins, history and possible future.

Ancient cosmologies took the Earth (and humanity) as central; as our understanding has advanced, the Earth and its inhabitants seem more and more insignificant.

Here you will be dealing with some of the big questions of science, questions that people have raised for millennia.

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Preparation for cosmology topic

Earth and Space

Episode 703: Preparation for cosmology topic

Teaching Guidance for 16-19

This is an area in which there is still a ferment of conflicting ideas. It is useful if you can get some of this across to your students, rather than presenting them with a neat, no-loose-ends version of the scientific truth.

It is worth making an effort to keep up-to-date by reading magazines such as New Scientist, Scientific American etc. Encourage your students to do the same.

Main aims of this topic

Cosmology


Students will:

  • describe the evidence for the expansion of the Universe
  • relate this to other evidence that the universe originated in a hot big bang

Prior knowledge

Students should know that light from astronomical objects is often red-shifted, and that this can be interpreted in terms of movement of the source.

Where this leads

Even if your students are not going to become professional cosmologists, this is a topic that many will want to read about in the future, so you will be doing them a great favour if you can kindle their interest at this stage.

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The expanding universe

Expansion of the Universe
Earth and Space

Episode 704: The expanding universe

Lesson for 16-19

The universe is expanding; don’t confuse this with the big bang (see episode 705: Cosmology).

Lesson Summary

  • Student activity: Looking at a galaxy (20 minutes)
  • Discussion: The scale of the universe (10 minutes)
  • Discussion: Hubble’s observations (10 minutes)
  • Demonstrations: Expanding universe (20 minutes)
  • Student activity: Modelling Hubble’s law (20 minutes)
  • Discussion: Cosmological red shift (10 minutes)
  • Student questions: Red shift of quasars (30 minutes)

Student activity: Looking at a galaxy

In 1925 Hubble showed that the Andromeda nebula was a collection of stars (i.e. a galaxy) outside and quite distinct from our own Milky Way galaxy. Students can look for Andromeda using binoculars.

Episode 704-1: Two million-year-old light: Seeing the Andromeda nebula (Word, 60 KB)


Discussion: The scale of the universe

Discuss the different ways in which astronomers determine distances in space, and the units used.

Episode 704-8: The ladder of astronomical distances (Word, 106 KB)


1 light-year (1 ly) = 9.46 × 1015 m

1 parsec (1 pc) = 3.09 × 1016 m

1 Mpc = 3.09 × 1022 m

Episode 704-2: Distances in light travel time (Word, 42 KB)


Discussion: Hubble’s observations

Hubble measured 24 galaxies. 22 had red shifted light. He plotted recession speed v against distance d.

Speed was much easier to measure (from the Doppler shift) than distance. There are real problems in setting a length scale. Different methods are used at the ever increasing distances, each overlapping to allow a (hopefully) consistent calibration.

Hubble found v  ∝  d; for each increase in distance of 1 Mpc the recessional speed of galaxies increases by 70 km s-1. This is the H0 . The bigger H0 the faster the universe expands (and thus the younger it is) and vice versa.

This gives us an idea of the age of the universe:

H0 in km s-1 per km = 70 km s-13.09 × 1019 km

H0 = 2.26 × 10-18 s-1;

Age of universe = 12.26 × 10-18 s-1

Age of universe = 4.4 × 1017 s

So 15 My, more or less.

Episode 704-3: Hubble’s law and the age of the universe (Word, 200 KB)


Demonstration: Expanding universe

It is useful to show that, although the whole of the universe is expanding, this does not imply that there is a single centre of expansion.

Inflate a balloon with sticky paper dots attached to it, representing galaxies. Note that the galaxies move apart, but they do not themselves get bigger (because gravity holds them together).

Episode 704-4: Relativity and the expanding universe (Word, 140 KB)


Draw up two OHP sheets, each with a matrix of dots. They have the same pattern, but one has a greater spacing. Overlay second OHP sheet – whichever dot on the bottom sheet you use as the origin to match to a dot on the second sheet, all the other dots move away from the chosen dot. There is no centre from which all dots move away from.

Student activity: Modelling Hubble’s law

Students could use a length cut from a wide rubber band. Mark dots to represent galaxies. Identify a home galaxy. Stretch the rubber. A dot twice as far from the home galaxy moves twice the distance; this is the Hubble Law.

The Hubble law thus implies that the universe is expanding.

What’s it expanding into? Nothing! Space (or rather space-time) is being created as the universe expands.

If universe is expanding, why don’t we see it locally – e.g. in the solar system? Is it too small an effect? Yes; the expansion is overcome by gravity.

Discussion: Cosmological red shift

The so called cosmological red shift is not due to relative speeds as such – it’s due to the expansion of space itself, stretching the wavelength of light because space(time) is expanding but the resulting formula for red shift is the same.

A red shift of 1 corresponds to 7 × 109 years ago, i.e. the light was emitted when the universe was half as old as it is now. Red shifts > 5 have been observed.

Episode 704-5: Red shift (Word, 199 KB)


Episode 704-6: Red shifts of galactic spectra (Word, 156 KB)


Student questions: Red shift of quasars

Students can tackle some questions about the red shifts of quasars.

Episode 704-7: Red shifts of quasars (Word, 37 KB)


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Cosmology

Big Bang Model of the Universe
Earth and Space

Episode 705: Cosmology

Lesson for 16-19

Cosmology is the study of the origins, history and future of the universe. The currently favoured model is the big bang.

Lesson Summary

  • Discussion: The hot big bang (10 minutes)
  • Discussion: How old is the universe? (10 minutes)
  • Student questions: The age of the universe (20 minutes)
  • Discussion: Cosmic microwave background (10 minutes)
  • Discussion: The future of the universe (10 minutes)
  • Student questions: Critical density (20 minutes)
  • Discussion: Missing mass and dark energy (10 minutes)
  • Student activity: Olbers’ paradox (20 minutes)

Discussion: The hot big bang

Imagine running a film of the universe backwards – all matter and energy were originally in a very, very dense state. All exploded outwards: the big bang (Fred Hoyle coined this name, intending it to be derisive).

What happened before the big bang? Space-time was created at the big bang; so many cosmologists argue that the question has no physical meaning.

At the present time (2005) the overwhelming weight of evidence favours the Hot Big Bang theory. There are 3 independent pieces of evidence:

  • The observed expansion of the universe
  • The Cosmic Microwave Background (CMB) radiation
  • The cosmic relative abundance of the light elements (created by the big bang, rather than subsequently in stars or supernovae)

Discussion: How old is the universe?

Episode 704-3: Hubble’s law and the age of the universe (Word, 200 KB)


As discussed above, the Hubble constant gives us a means of estimating the age of the universe. It is ~ 14 billion years old.

Episode 705-1: The age of the universe (Word, 102 KB)


Thus the size of the visible universe is set by how far a light beam has travelled since the big bang, which is c  ×  age of universe.

size of the visible universe = 14 × 109 light years or 1.3 × 1026 m.

Student questions: The age of the universe

Students can look at a number of estimates of the age of the universe.

Episode 705-2: Calculating the age of the universe (Word, 59 KB)


Episode 705-3 The parsec (Word, 50 KB)


Discussion: Cosmic microwave background (CMB)

Space is filled with the cosmic microwave background radiation. This allows an estimate of how much the universe has stretched since it was emitted.

Episode 705-4: The cosmic microwave background radiation (Word, 198 KB)


Discussion: The future of the universe

This is a topic that is still the focus of research and debate.

If there is enough mass in the universe then its gravitational attraction will eventually overcome the expansion. The universe will stop expanding and then collapse to an eventual big crunch (cf. throwing an object upwards with less than the escape velocity). This is called a closed universe .

If the quantity of mass is just right then the expansion slows to zero at infinity. This is called a flat universe.

If there is not enough mass for its gravitation effect to overcome the expansion, the universe will continue to expand forever. This is called an open universe .

A closed universe might rebound forever – a big bang eventually resulting in a big crunch which rebounds into a big bang and so on. The whole universe may be a gigantic oscillator!

The critical density is the demarcation between an open and closed universe.

Student questions: Critical density

Observation has yet to pin down the actual density with sufficient precision to decide if our universe has a density larger or smaller than the predicted critical density r0 .

Episode 705-5: Critical density (Word, 36 KB)


Discussion: Missing mass and dark energy

According to the standard cosmological model, the universe consists of three categories of mass/energy. Dark matter (25%), dark energy (70%) and a smattering of normal matter (5%).

Dark matter was invented to account for the observed rotational shape of galaxies. Dark energy has been invented more recently to account for the latest red shift data. (As of 2005) at the highest red shifts the universe seems to be accelerating!

Student activity: Olbers’ paradox

To exemplify the depth of ideas that can come from thinking about a simple observation – that the sky is dark at night – students can read about Olbers’ paradox. They could report their thoughts to the class.

Episode 705-6: The sky is dark at night (Word, 46 KB)


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