Lecture 21: Cosmology

Reading Assignment: Arny: Chapter 16 & 17, Cosmos: Chapter 10.

Big Bang Nucleosynthesis

Take the Universe back in time to when it was incredibly young, small, dense, and hot...

t < 10-35 seconds: Temperature extremely hot (T > 1028 K). Photons in equilibrium with subatomic particles and anti-particles.

10-32 s < t < 10-6 s: There was an excess of protons and neutrons created (1 extra p+ per every 109 proton-antiproton pair)

t 100 s: Nuclear fusion sets in (T 109 K) and Deuterium (hydrogen nucleus with one neutron) is formed. Then we get the reaction

1H2 + 2n 2He4 + e- + antineutrino
About 25% of the mass in hydrogen is converted into helium. There is also a little bit of 1H3, 2He3, and 3Li7.

No heavier elements form because density and temperature are not high enough. T 5 x 108 K after 10 minutes.

From the abundance of light elements now we can deduce the conditions of the early Universe (including its density and spacetime curvature).

Problem: 2He4 formed by stars also. Contaminates the primordial mix. Use deuterium instead. It is very sensitive to the density at early times.

If density is high for a long time the deuterium gets used up fast in the reaction 1H2 + n 2He3 + e- + antineutrino. High for a long time happens in an overdense Universe: M > 1. Leads to a low abundance of 1H2

We measure a high abundance of 1H2 in primordial gas clouds that lie between the galaxies. That means that M < 1. Current measurements of deuterium and other light elements suggest that density in Baryons (neutrons, protons) is about B 0.03.

Other measures of M which includes dark matter (gravitational lensing in clusters, etc.) suggest that M 0.3. Which again tells us that the dark matter makes up 90% of the mass of the Universe.

Big Bang Problems

There are a couple of problems that arise with the Standard Hot Big Bang Model.
  1. Why is the Universe (and in particular the CMB) so homogeneous and isotropic? If we calculate the angular size of the Particle Horizon on the sky at the time of the origin of the CMB (z ~ 1300) we find that regions of the CMB that are separated by more than 1° did not know about each other. So why do they have the same temperature and density?
  2. Why is the Universe so closed to being flat? If we run the expansion backward in time we find that it gets closer and closer to being flat. It's density would have needed to have been well tuned to produce a Universe so nearly flat some 10 billion years later.
A possible Solution came from an Astronomer in 1980 by the name of Alan Guth.


Suppose the Universe extremely rapidly for a while. The entire Observable Universe could have come from a tiny volume of uniform temperature and density. An expansion in size by a factor of 10100, A Googol! (10-30 cm - 1070 cm).

This is called Inflation.

The tiny volume was homogeneous and isotropic and so the observed Universe today also is.

All curvature flattened out because of the expansion. Locally the Universe is so flat because because the Radius of Curvature is so large. So 1 now, no matter what the initial conditions.

This inflationary expansion would have taken place between t = 10-35 s and t = 10-32 s.

Why did the inflation occur? : Look at Grand Unified Theories (GUTs). These are theories that attempt to unify the 4 fundamental forces of nature. Originally magnetic and electric forces were considered separately, but it was recognized that they were both aspects of the same interaction between charges. ---> Electromagnetic force. It has been discovered that the same is true of the weak nuclear force and the electromagnetic force. They have been combined in a single elctroweak force. A Grand Unified Theory would be one in which we could unify the electroweak with the strong nuclear force. A Theory of Everything (TOE) would also unify these forces with gravity.

Right after the Big Bang, the temperatures and densities are exceedingly high. Photons are in equilibrium with particle-antiparticle pairs. All the forces are unified (except perhaps gravity ???). They all behave the same and are indistinguishable from one another. Symmetric: unified.

As the Universe cooled below 1028 K (t = 10-35 s) the strong forces "freezes out", it becomes a different manifestation of the same unified force. Symmetry is broken because of a lower total Energy.

(Example the phase transition of water from liquid to solid when it drops below 0° C)

Suppose the Universe cooled below 1028 K and yet the strong force does not freeze out. The symmetry is not broken: SUPERCOOLED!

The Universe contains too much energy for its physical state (like liquid water below 0° C).

Creates an "Energy of a False Vacuum", which causes the Universe to expand impossibly fast --> Inflation.

Eventually the phase transition occurred (e.g. water --> ice) and energy is released which re-heats the Universe.

All of the matter in the Universe formed from the energy released by the symmetry breaking of the string nuclear force. After particles form there is no more inflation and a normal Hubble expansion continues.

Key Point: Observed Universe was only a tiny (smaller than a proton) homogeneous, isotropic volume before inflation. Expanded by a HUGE factor, Therefore the Universe now looks homogeneous, isotropic, and essentially flat.

Epicycles within epicycles anyone???

Origin of the Universe

From scientific tooth fairies to the completely absurd...

From where did the Universe come before inflation? (t < 10-35)

NOTE: it doesn't make any sense to ask what was going on before the Universe began. There was no time before time had begun. The question becomes meaningless.

Hold on for some rampant speculation..........

The Universe may have simply been a random fluctuation out of nothing!

Heisenberg's Uncertainty principle states that we cannot measure quantities simultaneously with arbitrary precision. For example if we no exactly where a particle is we have no idea what its momentum is. If we no exactly what the energy of a particle is we have no idea when it has that energy.

Positive energy can be created out of nothing for very short times. Something that has precisely zero total energy can live infinitely long. If the entire Universe (matter + radiation + gravity + cosmological constant) has an energy adding up to zero (the critical Universe). Then it can exist forever even though it came from NOTHING!

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