Chapter 26 Cosmology

26.1 The Universe on the Largest Scales

  • Therefore, the universe is homogenous (any 300-Mpc-square block appears much like any other) on scales greater than about 300 Mpc

  • The Universe also appears to be isotropic—the same in all directions

  • The cosmological principle includes the assumptions of isotropy and homogeneity

26.2 The Expanding Universe

  • Olber’s Paradox:

    • If the universe is homogenous, isotropic, infinite, and unchanging, the entire sky should be as bright as the surface of the Sun

  • So, why is it dark at night?

    • The universe is homogenous and isotropic—it must not be infinite or unchanging

    • We have already found that galaxies are moving faster away from us the father away they are:

      • recession velocity= H0 x distance

  • So, how long did it take the galaxies to get there?

    • time=distance/velocity

    • = distance/(H0 x distance)

    • = 1/H0

    • Using H0 =70km/s/Mpc, we find that time is about 14 billion years

  • Note that Hubble’s law is the same no matter who is making the measurements

  • If this expansion is extrapolated backwards in time, all galaxies are seen to originate from a single point in an event called the Big Bang

  • So, where was the Big Bang?

  • It was everywhere!

  • No matter where in the Universe we are, we will measure the same relation between recessional velocity and distance with the same Hubble constant

  • This can be demonstrated in two dimensions. Imagine with coins stuck to it. As we blow up the balloon, the coins all move father and father apart. There is, on surface of the balloon, no “center” of expansion

  • The same analogy can be used to explain the cosmological redshift

26.3 The Fate of the Cosmos

  • There are two possibilities for the Universe in the far future:

    1. It could keep expanding forever

    2. It could collapse

  • Assuming that the only relevant force is gravity, which way the Universe goes depends on its density

  • If the density is low, the universe will expand forever. If it is high, the universe will ultimately collapse

  • There is a critical density between collapse and expansion. At density the universe still expands forever, but the expansion speed goes asymptotically to zero as time goes on

  • Given the present value of the Hubble constant, that critical density is:

    • 9×10-27 kg/m³

  • This is about 5 hydrogen atoms per cubic meter

  • If space is homogenous, there are three possibilities for its overall structure:

    1. Closed— this is the geometry that leads to ultimate collapse

    2. Flat— this corresponds to the critical density

    3. Open—expands forever

26.4 The Geometry of Space

  • In a closed universe you can travel in a straight line and end up back where you started ( in the absence of time and budget constraints of course!)

More Precisely 26-1: Curved Space

  • The closed geometry is like the surface of a sphere

  • The flat one is flat

  • The open one geometry is like a saddle

26.5 Will the Universe Expand Forever?

  • The answer to this question lies in the actual density of the Universe

  • Measurements of luminous matter suggest that the actual density is only a few percent of the critical density

  • But we know there must be large amounts of dark matter

  • However, the best estimates for the amount of dark matter needed to bind galaxies in clusters, and to explain gravitational lensing, still only bring the observed density up to about 0.3 times the critical density, and it seems very unlikely that there could be enough dark matter to make the density critical

  • However when we look at data, we see that they correspond not a decelerating universe, but to an accelerating one

  • This acceleration cannot be explained by current theories of the Universe, although we do know it is not caused by either matter or radiation

  • Dark Energy: repulsive

  • Gravity: attractive

  • What else supports the “dark energy” theory?

    • In the very early life of the Universe, the geometry must be flat

    • The assumption of a constant expansion rate predicts the Universe to be younger than we observe.

26.6 Dark Energy and Cosmology

  • Given what we now know, the age of the universe works out to be 13.7 billion

  • This is consistent with ither observations, particularly of the age of globular clusters, and yields the following timeline

    • 14 billions years ago: Big Bang

    • 13 billion years ago: Quasars form

    • 10 billion years ago: First stars in our galaxy form

26.7 Cosmic Microwave Background

  • The cosmic microwave background was discovered fortuitously in 1964, as two researchers tried to get rid of the last bit of “noise” in their radio antenna

  • Instead they found that the “noise” came from all directions and at all times, and was always the same. They were detecting photons left over from the Big Bang

  • When these photons were created, it was inly one second after the Big Bang, and they were very highly energetic. The expansion of the universe has redshifted their wavelengths so that now they are in the radio spectrum, with a blackbody curve corresponding to about 3K

  • Since then, the cosmic background spectrum has been measured with great accuracy