inflation and the early universe
DESCRIPTION
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 - PowerPoint PPT PresentationTRANSCRIPT
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?
