Lecture 32: The Early Universe




Pair Production and Annihilation

  • All types of particles have an anti-matter partner with the exact same mass but opposite charge.
  • When matter meets anti-matter, they destroy each other and create two gamma-ray photons with energy

    E = m c2

    where m is the mass of the particle
  • If a photon has energy higher than this threshold, it can create a particle-anti-particle pair.
  • As long as the temperature of the universe is above this energy threshold for the particle of interest, light can create pairs of the particle/anti-particle.
  • Below the threshold T, pair production ceases, and the particles annihilate their anti-particle partner.




Weak Nuclear Reactions

  • The weak nuclear reactions transform protons to neutrons and vice versa.
  • The two most important weak reactions are:
    1. n -> p + e + nu (neutron decay)
    2. p + e -> n + nu (electron capture)
  • When these reactions can both occur, we have about the same number of neutrons as protons in the universe.
  • The electron capture reaction is not favoured because the neutron is more massive than the proton.
  • In order to make electron capture occur, we need to supply energy

    E = (mn - mp)c2
  • Another problem is that we need to have lots of electrons around.
  • As long as T is higher than the threshold for creation of electron/positron pairs there will be lots of electrons.
  • Both energy thresholds correspond to approximately the same T.
  • When the universe cools below this T = 6 x 109 K no more neutrons are produced.
  • At this temperature, the abundances of particles are about 6 protons for every 1 neutron.




Big Bang Nucleosynthesis

  • Big Bang Nucleosynthesis is the creation of light elements from the protons and neutrons in the early universe.
  • Elements were formed by first creating the simplest possible nucleus and then adding particles to create more complicated nuclei.
  • The simplest nucleus is that of Deuterium ( D = 2H) composed of a neutron and a proton.
  • n + p -> D + light
  • This reaction can't take place if the universe is too hot.
  • If a photon has energy larger than
    E = ( mn + mp - mD)c2
    the photon will break the nucleus into its constituent particles (photodissociation).
  • This is called the Deuterium Bottleneck and occurs around T=1010 K.
  • When the universe cools below the Deuterium Bottleneck, Deuterium and heavier elements up to Helium-4 can be synthesized. (Small amounts of Lithium and Beryllium are also produced.)
  • The universe is cooling while this happens, so it becomes difficult to produce any element heavier than Be.
  • Nucleosynthesis stops at T below 109 K and the abundances of elements are frozen in.
  • The figure shows the predicted abundances of light elements.
  • These abundances are very similar to the abundances seen in Pop II stars.




Structure Forms after Big Bang Nucleosynthesis

  • After nucleosynthesis finishes the universe is filled with gas that's 75% H and 25% He by mass.
  • The density of the gas couldn't have been perfectly smooth.
  • Small density fluctuations must have existed.
  • Regions that are a little denser than average could collapse if the size of the region is larger than the Jeans length.
  • These collapsing regions were probably large enough to create the globular clusters, which then merged to form galaxies.
  • When we look at the Cosmic Microwave Background Radiation, we are see the fluctuations in temperature that existed at the time 300,000 years after the Big Bang.
  • Regions of lower than average temperature correspond to higher than average density that will collapse later to form globular clusters and galaxies.




Problems with the Big Bang Theory

  1. Why is the Cosmic Microwave Background Radiation so smooth?
    • This is called the Horizon Problem.
    • Regions in the sky separated by more than about 2 degrees were never in causal contact with each other.
    • Why is the temperature of these two regions the same within 1 part in 105?
  2. Why is the universe so nearly flat?
    • Observations seem to show that the universe has zero curvature.
    • But there are many possible values for the curvature, so why this special value?
    • This is called the Flatness Problem.




Inflation

  • The theory of inflation was proposed to solve these problems.
  • Around 10-34 s after t=0, a region of size
    r = c t = 3 x 10-26 m
    is in causal contact and can be at the same temperature.
  • The theory of inflation proposes that at this time a period of exponential expansion occurs lasting until t = 10-32 s.
  • During this time the universe increases in size by a factor of e100.
  • This causes the region of size 3 x 10-26 m to expand to the size 9 x 1017m.
  • This larger region can all be at the same temperature and evolve into the universe which we observe.
  • The rapid change in size also has the effect of making the curvature very close to zero.



The Initial Singularity

  • When the Universe was very young, the distances between things were very tiny.
  • Quantum mechanics is needed to describe very tiny distances.
  • For instance Heisenberg's uncertainty relation should apply here.
  • The equations describing cosmology come out of the theory of general relativity which does not include quantum mechanics.
  • The equations of general relativity are only valid when describing distances larger than 10-35m.
  • Or equivalently, general relativity only describes the universe when it is older than 10-44 s.
  • In order to describe the earliest times, a theory which combines gravity and quantum mechanics is needed (called quantum gravity).
  • One theory which might work is called Superstring Theory.
  • Superstring theory predicts that the universe is actually 10 dimensional, but that we only directly experience 3 dimensions.
  • Superstring theory may be able to describe the earliest times properly.
  • This is still unknown territory!