Answer to question 1

1
Radius of Observable Universe and Expansion Rate
vs time, k 0
Radiation dominated
r 0
1018c
R 10 cm
10-15c
R 3 x 10-33 cm
2

• How did we get the range of fluctuations on the
  angular scales we see today in the CMB?
• The answer is we started out with a very simple
  same power on all scales that then evolved and
  vibrated in our cosmic plasma until the brick
  wall became transparent (in jargon we say the H
  de-coupled from the light).

3

• This set of conditions is called the
  Harrison-Zeldovich spectrum.
• Inflation generates this spectrum naturally
• All the interesting length scales (in todays
  scale factor terms) of 1 to 3000 Mpc separate
  from causal contact with each other well before
  inflation ended.
• The key is WELL BEFORE
• Net size of fluctuations did not have time to
  adjust to a complex set of conditions.

4
Perturbations

• Then these lead to predictions of our seeing the
  ripples we see in the CMB at about the correct
  angular scales!

5
Now the hard part Baryogenesis

• What is the problem?
• The answer is that physics types like symmetry.
  So, why wasnt the Universe exactly symmetric in
  terms of matter and anti-matter.
• With inflation plus additions all the particles
  and anti-particles collide, and turn into pure
  energy.
• gt What are these additions?

6
Baryogenesis

• Need 3 things

• Baryon non-conservation.

• The cosmic expansion goes so fast that reaction
  takes place before equilibrium is reached.
  Inflation solves this.

• Sub-atomic particles must know the arrow of
  time! Since they need to know the direction of
  cosmic expansion. The arrow of time relates to
  the CPT theorem. More on this later.

7
Baryogenesis, cont.

• Baryon non-conservation.

Need this so when baryons and anti-baryons
collide, we get some left over. Since, remember,
we started with EXACTLY the same amount of each.
Assume there is process that starts from our dark
energy and makes more baryons than anti-baryons.
Creating an excess of baryons, starting from
zero, means we made baryons which is the same as
non-baryon conservation.
8
Baryogenesis, cont.

• The cosmic expansion goes so fast that reaction
  takes place before equilibrium is reached.

Otherwise, even with an imbalance, the numbers
would even out over time . Inflation handles
this by just finishing inflation (expanding very
rapidly) when the universe makes transition from
pure vacuum energy to matter.
9

Sub-atomic particles must know the arrow of
time! Since they need to know the direction of
cosmic expansion. The arrow of time relates to
the CPT theorem.

• Need 3 things

On the scale of people, we can understand aging
and the arrow of time. For sub-atomic particles,
it is not obvious that they can sense a direction
to time.
The concept we need to consider time reversal
invariance.
10
Time Reversal Invariance

• On a sub-atomic scale, most all reactions have
  the same probability of occurring if the time
  assigned is positive or negative.
• This concept does not apply to clearly
  non-reversible processes such as a neutron
  decaying. A proton, electron and (anti) neutrino
  are not just casually going come together.

11
Time Reversal Invariance

• A reversible process does get the idea across
  better. The motion of pendulum (assuming no
  friction) looks the same whether we count time as
  positive or negative.
• All BUT one particle reaction we know about seems
  to follow this rule, so if we calculate the rate
  of neutron decay, it doesnt matter if we use
  positive or negative time.

12
Time Reversal Invariance

• The ONE effect weve seen only indirectly implies
  a non-time reversal process. But that it happens
  seems to imply this can happen elsewhere. This
  means we arent crazy to make this hypothesis
  for the early Universe.
• The indirect inference is based on a particle
  decay process and the CPT theorem. C stands for
  charge, P for parity, and T for time. More
  later. First a little more on the effect of
  sensing the arrow of time.

13
Time Reversal Invariance

• We want to explain why we didnt have the same
  exact number of baryons and anti-baryons so that
  they would have ALL met up with each other,
  annihilated and we wouldnt be here!
• Assume we start, just as inflation ends and the
  vacuum energy converts into matter, with some
  particle (X) and anti-particles (X) in equal
  numbers. Then assume the X decays slightly
  differently into baryons from the rate that X
  decays into anti-baryons.

14
Time Reversal Invariance

• Then when the slightly different amounts of
  baryon/anti-baryons meet up, we end up with with
  just a small (about 1 part in 109) of excess of
  baryons. Just enough to explain the current ratio
  of photons to baryons. And the process is hot by
  definition of having so many more photons.
  gtAnnihilation of baryons and anti-baryons
  (almost completely) leads to a hot Big Bang.

15
Time Reversal Invariance

• When X and X particles decay the X decays faster
  to produce MORE baryons when going forward in
  time than the X particles, and vice versa.
  Therefore, as the Universe expands as time
  increase (runs forward), we end up with our
  imbalance.

16
CPT Theory and Observations

• The CPT theorem says if I do a calculation of a
  particle collision probability and I (flip the
  positive charges to negative and vice versa plus
  change all the lefty particles to righty
  particles and vice versa, and change the sign on
  the time I use, I will get the same answer.
• This means if I observe a reaction in which I
  change charge and parity (description of
  left/right handiness)

17
CPT Theory and Observations

• And I see a difference. Then assuming CPT holds (
  and it better!), then this means sub-atomic
  particles can sense the arrow of time.
• Such a CP violating reaction was detected in
  the laboratory. gt
• This makes it plausible that a much higher energy
  CP violating and hence T violating reaction did
  occur in the early Universe.

18
CPT Theory

• In mathematical terms, C x P x T 1 means CPT is
  not violated. But if CP is violated this means by
  convention C x P -1, but this then means T
  better -1 (means T invariance is violated) so
  as to get C x P x T and keep CPT true.
• This is why we say CP - 1 implies T -1, or
  we have a reaction that is not invariant under
  time reversal or in other words can sense the
  direction of time.

This is truly a remarkable concept