Lam Hui - Inflation And The Early Universe

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

1 2 GM a˙ − =E 2 a

1 2 GM For simplicity set E = 0 : a˙ = 2 a

Fundamental equation:

1 2 GM a˙ = 2 a

Example 1 - ordinary matter 1 ρ∝ 3 a

(M = constant)

4π 3 where M = aρ 3

1 =⇒ a˙ ∝ a 2

Therefore : a˙ ↓⇐⇒ a ↑

Example 2 - cosmological constant Λ ρ = constant =⇒ a˙ 2 ∝ a2 Therefore : a˙ ↑⇐⇒ a ↑

Dark

Acceleration!

1 Energy: ρ drops slower than a2 i.e. ρ ∝ a−3(1+w) with w < −1/3

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

∫∫ t Horizon =a(t)dx = a(t) c dt’ a(t’) ∫ ∫t dx = c dt a(t)

1/3

early

tearly = 3 c t (1 - 1/3 ) t 3/2 3ct a Contrast: Physical distance btw. galaxies

a

log(hor.)

3 log a 2 log(phys. dist.) log a

Horizon problem!

log a

Sloan Digital Sky Survey

scale ∼ 10

26

cm

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

t early

log t

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 early t v. early

∫

∫

∫ ∫

a(t) c +3ct = a(t v. early) H Ht’

2/3

Note: a(t’) e a(t’) t’ tv. early< t’ < t early tearly< t’

log(hor.)

3 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 = E 2 a 3 M = 4πρa /3 2E 1 - 2GM = . . 2 2 aa a

. 2 Data tell us |2E/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

quantum fluctuation

log(phys. dist.) log a

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?