1. More Big Bang
Big Bang Nucleosynthesis
Problems with the Big Bang

2. Big Bang Nucleosynthesis
Around 10-9 s, quarks froze out into protons and neutrons, note neutrons are unstable, but lifetime is long enough, 15 minutes.
When did nuclei form? Simplest nucleus is deuterium, D, consists of p+n. Energy to dissociate D is 2.2 MeV, which is 160,000 that needed to dissociate H atom, so temperature should be 1.61053000 K = 5108 K.
Nuclei started to form when temperature dropped below 5108 K.

3. Big Bang Nucleosynthesis
At this time, there were lots of p+n around, so it was easy to make nuclei by adding one p or n at time. For example:
p+n  D+, D+p  3He+, 3He+n  4He+
No stable nuclei with atomic number 5, this mostly stops nucleosynthesis at He.
Can make 4He+D  6Li+  and 4He+3H  7Li+ , but only small amounts because there is not much D or 3H.

4. Big Bang Nucleosynthesis
Measurement of ratios H : 4He : 6Li : 7Li in environments unaffected by any stellar nucleosynthesis are important tests of the Big Bang theory.

5. Problems with the Big Bang
The horizon problem
The flatness problem
How to fix the problems: inflation

6. Cosmic Microwave Background
The Universe glows at 2.7 K in every direction.
The temperature is the same to < 0.1%.

7. Observable Universe
We can only see the parts of the Universe from which light has had time to travel to us.

8. The Horizon

9. Horizon Problem CMB is 0.98lhorzion away
Two antipodal points of CMB are 1.96lhorzion away from each other, but at same temperature within 10-5.

10. Flatness Problem
In matter and radiation dominated eras, any deviation of  from 1 grows with time.
Friedman equation
Radiation era: a  t1/2 and H  t-1, so
Matter era: a  t2/3 and H  t-1, so

11. Scale factor versus time
Nuclei form at 3 minutes, radiation era ends at 47 kyr, flatness grows by 8109.
Matter dominated from 47 kyr to 9.8 Gyr. Deviation from flatness
grows by (9.8109/47,000)2/3 = 3500.
Now universe is flat to 0.02, at 3 minutes must have been flat to
0.02/(8109  3500) = 710-16

12. Flatness problem
Any tiny deviation from the critical density is amplified over time.

13. Inflation makes the Universe flat

14. Inflation is expansion driven by a cosmological constant
If duration of inflation era is long compared to Hubble time, 1/H, during inflation, then universe exponentially expands and is driven exponentially towards flatness.

15. Inflation Whole observable universe came from a tiny region. Size [cm]
Time [seconds]
Whole observable universe came from a tiny region.

16. Inflation in GUT
In Grand Unified Theories (GUT) there was an quantum mechanical field that caused inflation at s and lasted for ~100 e-foldings.
Starting with a strongly curved universe, this would drive the flatness to e-2100 ~
If inflation ended at s, then size of current CMB surface was 0.98lhora = 4 m (a = 810-27).
At start of inflation, now visible universe had a size of (4 m)e-100 ~ m. Horizon distance was m, much larger.

17. Inflation and cosmology
Inflation solves flatness problem by driving the Universe exponentially towards flatness.
Inflation solves the horizon problem because the whole universe originally came from a very small area. Thus, the different parts of the CMB were causally connected before inflation began.
Inflation still needs to be tested. NASA plans to fly a satellite to measure the polarization of the cosmic microwave background in order to test inflation.

18. Review questions
Why is it surprising that the microwave background has almost exactly the same temperature in all directions on the sky?
Why is it surprising that the geometry of the universe is so close to flat?
What is the best explanation to date of why the Universe is uniform and flat?