Inflation and the Early Universe

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

4. Cosmology 101 a Energy conservation

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

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

7. log a ∼ t 2 log a ∼ log t 3 log t

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

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

11. 3 log(hor.)∼ log a 2 log(phys. dist.) ∼log a 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 last scatter r big bang

16. log a ∼ t 2 log a ∼ log t 3 log t

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

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

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

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

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

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

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