1. Inflation and the Early Universe 早期宇宙之加速膨脹 Lam Hui 許林 Columbia University

2. This is the third in a series of 3 talks. July 5: Dark energy and the homogeneous universe July 11: Dark matter and the large scale structure of the universe Today: Inflation and the early universe

3. Outline Inflation: the horizon problem and its solution Review: expansion dynamics and light propagation Inflation: problems Inflation: predictions for flatness and large scale structure

4. Cosmology 101 a Energy conservation

5. Fundamental equation: Example 1 - ordinary matter Example 2 - cosmological constant Λ Acceleration! Dark Energy:

6. log a matter: log ρ ∼ Λ: log ρ -3 log a

7. log t log a ∼ log t 2 3 log a ∼ t

9. Scale factor a(t) x=0x=2x=1 x=0x=1x=2 time=t time = t’ distance = a(t) Δx distance = a(t’) Δx

10. Photons travel at speed of light c : a(t) dx = c dt dx = c dta(t) a(t) dx = ∫ Horizon =a(t) ∫ ∫ ∫ c dt’ a(t’) t t early = 3 c t (1 - ) t early t 1/3 ∼ 3 c ta 3/2 ∝ Contrast: Physical distance btw. galaxies ∝ a

11. log a log(hor.) ∼ log a 3 2 log(phys. dist.) ∼ log a Horizon problem!

12. Sloan Digital Sky Survey

13. Horizon problem: 2 sides of the same coin - On the scale of typical galaxy separations: how did the early universe know the density should be fairly similar? - On the scale of typical galaxy separations: how did the early universe know the density should differ by a small amount?

15. Another way to view the horizon problem: c t r last scatter big bang

16. log t log a ∼ log t 2 3 log a ∼ t

17. log t log a ∼ log t 2 3 log a ∼ t early t t v. early inflation

18. a(t) dx = ∫ Horizon =a(t) ∫ c dt’ a(t’) t t v. early = a(t) ∫ v. early t t early c dt’ a(t’)+ a(t) ∫ c dt’ a(t’) t t early = a(t) v. early c H + 3 c t Note: a(t’) ∝ e a(t’) ∝ t’ Ht’ 2/3 t < t’ < t v. earlyearly t < t’ early

19. log a log(hor.) ∼ log a 3 2 log(phys. dist.) ∼ log a Horizon problem solved!

20. Inflation’s prediction for flatness Energy conservation a a - = E. 2 GM1 2a M = 4 πρ a /3 3 1 - = 2GM aa. 2 2E a. 2 0 Data tell us |2E/a | < 0.03.. 2

21. Inflation’s prediction for large scale structure ‘Hawking’ radiation from inflation seeds structure formation. Inflation predicts nearly equal power on all scales: amplitude of fluctuations ∝ scale. n-1 Data tell us n ∼ 0.95 ± 0.02.

22. log a log(c a/ a) log(phys. dist.) ∼ log a. inflation quantum fluctuation

23. log a matter: log ρ ∼ Λ: log ρ -3 log a inflation ρ Inflation: problems

24. Problems of inflation: Why is the ρ associated with inflation so constant? Why did inflation stop? Why did inflation start?