Inflation and the Early Universe Lam Hui Columbia

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

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

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

Cosmology 101 a Energy conservation

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

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

log a ∼ t 2 log a ∼ log t 3 log t

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

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

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

Sloan Digital Sky Survey

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?

Another way to view the horizon problem: ct last scatter big bang r

log a ∼ t 2 log a ∼ log t 3 log t

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

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

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

Inflation’s prediction for flatness a Energy conservation 1. a 2 - GM = Ea 2 3 M = 4πρa /3 2 E 1 - 2 GM =. . 2 2 aa a 2. Data tell us |2 E/a | < 0. 03. 0

Inflation’s prediction for large scale structure ‘Hawking’ radiation from inflation seeds structure formation. Inflation predicts nearly equal power on all n-1 scales: amplitude of fluctuations ∝ scale. Data tell us n ∼ 0. 95 ± 0. 02.

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

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

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