Astronomy 101 Lecture 27, May 5 2003

The structure of the universe – (Chapter 26 in text)

We saw last time that measurements of the matter and energy in the universe gave the results: about 4% of the critical density is tied up in atoms (in stars, clouds, dead stars, etc), another 23% is dark matter. A very surprising new development is that there is a component called ‘dark energy’ that is more dominant than the matter and adds about the right amount to make the whole sum equal to the critical density. That means the universe is just on the edge of being bound or unbound (expand forever or recollapse to a Big Crunch).

0 = ratio of density of all matter and energy in universe to the critical density

0 = matter + dark energy

There is another way to get at the matter density of the universe besides just counting up what is out there.

The distribution of galaxies – the number of them in some volume of space – depends on how much mass there is in the universe. The more mass there is, the greater the tendency for matter to accumulate in clumps, pulled by gravity.

The tendency to clump will grow as bigger clusters and superclusters form, attracting still more matter to them.

The analysis of the clumpiness of the universe seems to confirm the measurements we discussed last time. The total matter (visible matter of atoms in stars etc. and dark matter) gives about the same value for the density: matter ≈ 0.25

Map of the galaxies in a region of space; clusters and filaments reveal the overall pattern of mass.

These data allow us see the acceleration of the universe, from which we infer the presence of ‘Dark Energy’.

d = v t, so in a distance vs. time plot, the slope is the velocity.

Steeper slope = larger velocity.

SN study shows smaller velocity in past – accelerating expansion.

The Supernova Project (see lecture 26):

Measure velocity and distance to supernova Ia events in the past; determine if universe is accelerating or decelerating (is velocity increasing or decreasing?)

One possibility for the Dark Energy:

In 1917, Einstein was puzzled by why his general relativity predicted that the universe would change its size with time. At the time, neither he nor anyone knew that the universe was expanding. He added a term to his equations of general relativity, called the cosmological constant that fixed this ‘problem’.

When Hubble discovered the expanding universe, the situation changed and the cosmological constant seemed not to be needed.

Einstein called the introduction of the cosmological constant ‘the biggest blunder of my scientific career’.

Now, having observed dark energy, it seems that the cosmological term could again be needed! The data are consistent with it, but there are other alternatives. HOWEVER, we now know much more about the vacuum and the particles that swim in it – and the natural size predicted for would be 120 orders of magnitude larger than what is needed for dark energy.

So, dark energy is still a huge problem!

Revisit the age of the universe – when was the Big Bang?

In matter dominated universes, gravity slows down the expansion – recollapses if > 1 (purple curve), expands forever if < 1 (blue curve).

The black line is for an empty universe, where there is no gravitational slowing of the Hubble expansion, and the age is just 1/H0.

The green curve incorporates the cosmological constant,. In the past this universe takes longer to get to the present epoch, and later on, starts expanding faster.

With H0 = 71 (km/s)/Mpc now:

Age (empty universe) = 13x109 years

Age(critical density) = 9x109 years

Age(only matter, no dark energy) = 11x109 years

Age(including dark energy ) = 13.7x109 years

A little wrinkle on the age determinations:

Astronomers believe that the oldest globular clusters are 10 – 12 billion years old. And the oldest quasars seem to be 13 billion years old.

It seems wrong (!) to have some stars or galaxies older than the universe itself !

So, if these estimates are right, they rule out the shorter ages of the universe obtained without the dark energy term.

The curvature of space:

We learned that in general relativity, the presence of matter warps space. Particles or light travel on geodesics which are curved in the neighborhood of matter.

The same is true for the universe at large. The CURVATURE of the universe is determined by the total density of matter and energy, .

For > 1, the universe has positive curvature and is ‘closed’ in topology – in analogy with a sphere in 2 dimensions

For < 1, the universe has negative curvature and is ‘open’ in topology – in analogy with a saddle in 2 dimensions

For = 1, the universe has no curvture and is ‘flat’ or Euclidean – analogy with a plane in 2 dim.

It is hard for us to imagine curvature of three-dimensional space, but its easy to imagine curvature of two-dimensional space and the analogy works pretty well.

Positive curvature == closed geometry (sphere) Parallel lines (e.g. lines of longitude, parallel at the equator, meet at the N and S Poles). The interior angles of a triangle sum to > 180O + + > 180O

Zero curvature = flat geometry (plane) Parallel lines never meet but remain parallel. Sum of interior angles of triangle = 180O (Euclidean geometry)

Negative curvature = open geometry (saddle) Parallel lines never meet and diverge. Sum of interior angles of triangle < 180O.

Curvature on two dimensional universes:

Imagine an alien with two laser guns that she fires along parallel lines.

If she shoots them in flat space (Euclidean) they go off and never meet.

If she lives in a closed universe, her laser beams will cross somewhere (like the lines of longitude on the closed 2-dim surface of the earth). They will also circle the universe and come back to hit her from behind.

If she lives in an open universe, the beams on the saddle shape diverge and never meet.

Testing the curvature of space, and thus the density of mass/energy

The Cosmic Microwave BackgroundAs the early universe expanded from the Big Bang ‘singularity’, it also cooled off, and went through several distinct epochs (see next lecture). Up until about 380,000 years from the Big Bang, the temperature was hot enough to keep the (mostly Hydrogen) atoms ionized (electrons freed from the nucleus). At these times, there was a bath of photons being absorbed and emitted as the electrons were alternately stripped and captured. These photons formed a Blackbody distribution appropriate to the temperature of the matter in the universe at that time.

At 380,000 years when the universe had T=3000K, the atoms could no longer be ionized, and neutral atoms formed. The photons left at this time no longer interacted with the matter and went off freely in all directions.

We say that photons and matter ‘decoupled’.

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History of the universe

At 380,000 years the photons formed a blackbody distribution that peaked in the visible light region.

wavelength

Since then, the universe has expanded by a factor of about 1000, and thus the wavelength of the photons has stretched with it. Today, the expansion makes the blackbody photons peak in the radio or microwave region, with a temperature of 2.7K

(The two epoch’s distributions are related by Wien’s law T = constant – if increases, T decreases.)

In 1964, Penzias and Wilson discovered a radio hiss in their radio antenna that was always present, no matter what direction they pointed.

The discovery of this ‘Cosmic Microwave Background’ (CMB) was the first experimental indication that the Big Bang had occurred.

In the last decade, the measurements of the cosmic microwave background have improved enormously.

1989 – COBE satellite

1998 – BOOMERANG balloon circling the South Pole

2003 Wilkinson Microwave Anisotropy Probe (satellite)

These measurements are made outside the Earth’s background radiation, and show a nearly perfect blackbody radiation with T = 2.73 K coming from space. It is slightly distorted by the Earth’s motion through space, but this can be corrected.

Once the microwaves from the disk of our galaxy are removed, and a correction is made for the motion of Earth’s motion through space, the temperature seen for the CMB is remarkably uniform – constant T to within 1 part in 100,000. These figures show the very small fluctuations in Temperature in false color – these represent density fluctuations in the early universe that evolved eventually into the clumpings of matter that made galaxies.

WMAP satellite, 2003

COBE satellite, 1989

The details of the map give us much information about the early universe. WMAP data are enormously more sharply focused than COBE.

The baby pictures indicate the improvement in resolution.

Comparison of observations (upper) with simulations (below) tells us that space is flat!

Thus they tell us that = 1 to within a percent or so.

The characteristic spacing of the small Temperature fluctuations tell us about the curvature of space – just as the shape of triangles did for our 2-dimensional curved surfaces.

The small temperature fluctuations have a characteristic size of about 1O . It is the size of the fluctuations that tells us that the density of the matter and energy is just the critical value. The radiation fluctuations are connected to the fluctuations of the protons and electrons at the time – radiation and particles interact with each other up until the decoupling. So the CMB tells us about the fluctuations in matter that will later evolve into the proto-galaxies.But the dark matter does not interact with the radiation, and may have had larger density fluctuations. We will return to this in the next lecture.

The cosmic background radiation gives us a way to look back to near the beginning of the universe, and is a powerful tool to understand the curvature of space and the seeds of galaxies.

The supernovae told us about the acceleration of the universe and thus the difference of dark energy and matter. (Dark energy pushes out, matter pulls inward). The CMB results tell us that the sum = dark energy + matter = 1.

Taking the two measurements together gives us the values of dark

energy and matter separately.

Dark Energy = 73%

Dark Matter = 23%

Atoms in stars, clouds = 4%

Summary: the contents of the universe:

Two problems raised by the CMB observations:

1. At the time photons decoupled, the universe was young enough that no light or information could have yet reached opposite sides of the universe. Now we observe them to have the same properties – temperature and density fluctuations.

How did one side know how to be the same as the other? HORIZON PROBLEM

2. We see that = 1 now and the universe is flat. Of all the possible densities that the universe could have had, it chose the critical density that makes space flat. That seems like too big an accident, and we suspect there should be some underlying reason for this. FLATNESS PROBLEM

Universe at 380,000 yearsA

B No signal could have reached B from A yet; the distance from A to B was larger than 380,000 light years. So why are these regions so similar?

Even a tiny variation from = 1 back at the decoupling time would have been magnified to a much larger difference now. So, the universe must have started out as flat, which needs explaining since it would not seem to be necessarily true.