(On teaching cosmology: AAPT statement)

I awoke on Friday and because the universe is expanding it took me longer than usual to find my robe...

Woody Allen, in "Strung Out" The New Yorker, 18 Jul 2003.
 What is cosmology? The study of the evolution of the universe as a whole.
 Can we see galaxies move? The proper motion of M33, one of the closest ones, is 30 micro-arcseconds per year, 100 times slower than a snail on Mars as seen from Earth. Its real transverse velocity is large, but much more difficult to determine. Radial velocities instead are easier to measure, and related to the really big picture...

  Starting Points

  • The questions: How big is the universe? How old? What is its origin? Its fate?
  • Observation: Galaxy surveys; SDSS and 2dF have released data on more than 800,000 galaxies, out of about 10 billion potentially observable ones.
  • Other methods: Computer simulations, and theoretical models.
  • The assumptions: Homogeneity and isotropy (the Cosmological Principle); No center of the universe; No edge and "beyond"; Are they really valid?
  • A puzzle: Olbers' paradox (why is the sky dark at night?).
  • The beginning: Henrietta Leavitt's measurements on Cepheid stars.

Hubble's Law: How Are Galaxies Moving?

  • Facts: In the 1920s Edwin Hubble found that, except for some nearby ones, light from all galaxies is redshifted and the velocity v is proportional to the distance d, or v = H0 d, out to hundreds of millions of ly!
  • What is going on? Redshifts tell us that distances to galaxies are increasing, at a rate H0 of about 22 km/s for every Mly of distance. Although galaxies appear to be moving, the explanation of the redshift is not a real "motion" of the galaxies, but the stretching of space, the expansion of the universe; There is no "center", distances between all distant pairs of galaxies are increasing in the same way [but the galaxies themselves do not expand].
  • Comment: This implies that the distances to the farthest galaxies are increasing much faster than the speed of light! So if we accept the special theory of relativity, we cannot interpret the redshifts to mean that galaxies are actually moving away while space itself is unchanged.
  • Practical consequence: With the Hubble diagrams we have a new method to find distances to galaxies beyond distances where we can't see even supernovas; Just use the conversion factor H0 from a plot of Hubble's law.
  • How far can we see? The farthest known galaxy is about 15 Gly away (estimated actual distance); but the light actually traveled a much shorter distance, and a better way to indicate distance is the redshift or the "lookback time" [5 Gyr for z = 0.5, etc].

  • How big is the universe now? At least 156 billion light-years wide, based on the absence of patterns we would see if it was smaller; But we cannot see (the past of) all of it, only as far as the cosmological horizon.

  The Big Bang Model

  • When did it all begin? The universe cannot have been expanding like this forever, the expansion must have had a beginning, a "Big Bang" about 13.7 billion years ago.
  • What was the big bang? Not a normal explosion, but the beginning of the universe itself; Even around stars space changes and is curved, as Einstein's general relativity predicts; In cosmology, space evolves with the matter inside it.
  • Has it always expanded at the same rate? We can check by looking at the distance and velocity of the farthest supernovas; We would expect a departure from Hubble's law indicating that matter is slowing the expansion down, but in 1997 it was found that it is accelerating!

The Early Universe and Evidence for the Big Bang

  • The beginning: After an initial, very hot period of extremely fast expansion (inflation), which left the universe flat and smooth, particles and nuclei (mostly H, 25% He, etc, by 3 min) were formed.
  • Decoupling: At the end of the era of nuclei, when the universe was 300,000 years old and cooled to 3000 K, matter formed atoms and no longer affected photons (more energetic photons, like UV, would be absorbed by atoms, but there were not many such photons); The universe became transparent to light and matter could form the first gas clouds, that eventually led to galaxies by 1 Gyr.
  • Result/prediction: That light is still around, but very redshifted, as microwaves.
  • Do we have evidence? The 3 K cosmic microwave background, discovered in 1965 by Penzias and Wilson; The same in all directions, except for a blue/redshift in one direction, and small hotter patches, first detected in 1992.



What Will Happen in the Future?

  • Possibilities: Recollapse (a Big Crunch with "heat death"), or Eternal Expansion; In the standard model, if the universe recollapses it is closed and finite, if it does not recollapse it is infinite; which scenario is right depends on how much matter it contains.
  • What is the critical density? If H0 = 75 km/s/Mpc, 6 atoms/m3.
  • What do we know? The universe is very nearly flat, and ordinary matter is not even close to critical density; There are other forms of "dark" matter, but even then we reach less than 30%; And the acceleration of the expansion rate tells us that there must be a "dark energy" pushing outward...
  • Conclusion? If the universe is all like the part of it we can see, it will probably always keep expanding faster.
  • Summary: The main points of the Big Bang theory are correct, from redshifts, the cosmic microwave background and other observations, and Einstein's theory agrees. We know that there is dark matter from galaxy rotations, hot gas in galaxy clusters and gravitational lensing, and that there is dark energy from the accelerated expansion; But what are they made of?

page by luca bombelli <bombelli at>, modified 25 apr 2013