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Radius of Observable Universe and Expansion Rate vs time, k = 0 = 0 Radiation dominated R = 3 x 10 -33 cm R = 10 cm R. =10 18 c 10 -15 c

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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).

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This set of conditions is called the Harrison- Zel’dovich spectrum. Inflation generates this spectrum “naturally” All the interesting length scales (in today’s 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.

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Perturbations Then these lead to predictions of our seeing the ripples we see in the CMB at about the correct angular scales! Brick Wall, 15 billionlt yrs

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Now the hard part: Baryogenesis What is the problem? The answer is that physics types like “symmetry.” So, why wasn’t 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. => What are these additions?

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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.

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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.

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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.

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Need 3 things: 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. 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.”

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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.

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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 doesn’t matter if we use positive or negative time.

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Time Reversal Invariance The ONE effect we’ve seen only indirectly implies a non-time reversal process. But that it happens seems to imply this can happen elsewhere. This means we aren’t “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.

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Time Reversal Invariance We want to explain why we didn’t have the same exact number of baryons and anti-baryons so that they would have ALL met up with each other, annihilated and we wouldn’t 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.

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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 10 9 ) 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. =>Annihilation of baryons and anti-baryons (almost completely) leads to a hot Big Bang.

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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.

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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)

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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. => This makes it plausible that a much higher energy CP violating and hence T violating reaction did occur in the early Universe.

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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.

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