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

Inflation: the horizon problem and its solution

Review: expansion dynamics and light propagation

Inflation: problems

Inflation: predictions for flatness and large scale structure

Cosmology 101

a

Energy conservation

Fundamental equation:

Example 1 - ordinary matter

Example 2 - cosmological constant Λ

Acceleration!

Dark Energy:

log a

matter: log ρ∼

Λ: log ρ

-3 log a

log t

log a ∼ log t2

3

log a ∼ t

Scale factor a(t)

x=0 x=2x=1

x=0 x=1 x=2

time=t

time = t’

distance = a(t)Δx

distance = a(t’)Δx

Photons travel at speed of light c :

a(t) dx = c dt

dx = c dt a(t)

a(t) dx =∫Horizon = a(t)∫∫∫

c dt’ a(t’)t

tearly

= 3 c t (1 - )tearly

t

1/3

1/3

∼ 3 c t a3/2∝Contrast:

Physical distance btw. galaxies ∝ a

log a

log(hor.)∼ log a32

log(phys. dist.)

∼log a

Horizon problem!

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:

c t

r

last scatter

big bang

log t

log a ∼ log t2

3

log a ∼ t

log t

log a ∼ log t2

3

log a ∼ t

earlyt

tv. early

inflation

a(t) dx =∫Horizon = a(t)∫c dt’ a(t’)t

tv. early

= a(t) ∫v. earlyt

tearly

c dt’ a(t’)+ a(t)∫c dt’ a(t’)t

tearly

= a(t)

a(t )v. early

cH

+ 3 c t

Note: a(t’) ∝ e a(t’) ∝ t’

Ht’ 2/3

t < t’ < t v. early early t < t’early

log a

log(hor.)∼ log a32

log(phys. dist.)

∼log a

Horizon problem solved!

Inflation’s prediction for flatness

Energy conservationa a -

= E. 2 GM1

2 a

M = 4πρa /33

1 - = 2GMaa.2

2Ea.2 0

Data tell us |2E/a | < 0.03.

.2

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.

log a

log(c a/ a)

log(phys. dist.)

∼log a

.

inflation

quantum fluctuation

log a

matter: log ρ∼

Λ: log ρ

-3 log ainflation ρ

Inflation: problems

Problems of inflation:

Why is the ρ associated with inflationso constant? Why did inflation stop?Why did inflation start?