1. Introduction to modern astronomy 27
島袋隼⼠(Hayato Shimabukuro)（云南⼤学、
SWIFAR）
©GETTYIMAGES

2. The fate of the cosmos
ρ > ρcr
ρ < ρcr
(a)The universe turns to shrink and is collapsed (Big Crunch). We do not know what happened.
(b)The universe expands forever.
What physics determines the evolution of the universe?

3. The geometry of space
•If the space is flat, the sum of a
triangle’s angles becomes 180∘
•If the space is opened, the sum of a
triangle’s angles becomes greater
than 180∘
•If the space is closed, the sum of a
triangle’s angles becomes less than
180∘

4. Rμν −
1
2
gμνR + Λgμν =
8πG
c4
Tμν
The geometry of space
Einstein equation
时空的扭曲 物质（能量）
时空的⼏何学
Open universe Closed universe Flat universe
In order to consider the evolution of the
universe, we need Einstein’s theory of
general relativity.

5. The geometry of space
What physics determines the evolution of the universe?
ρcr =
3H0
8πG
= 9 × 10−27
kg/m3
Remember the critical density
•If the density of the universe is greater
than , the universe becomes a closed
universe.
ρ
ρcr
Closed universe
•If the density of the universe is smaller than , the universe becomes an opened universe.
ρ ρcr
Open universe
•If the density of the universe is equal to
, the universe becomes a flat universe.
ρ
ρcr
Flat universe
How large is the density of the universe ?
ρ

6. The density of the universe
•Now we understand the density of the universe is important to determine the future of
the universe.
•Recent observations suggest the density of the universe is roughly equal to the critical density.
ρ ∼ ρcr Or Ω0 =
ρ
ρcr
∼ 1
This implies that our universe is almost flat.

7. But, we face another mystery.
The density of the universe
We find or . But, the content of the density is very strange.
ρ ∼ ρcr Ω0 =
ρ
ρcr
∼ 1
ρ = ?
Ordinal matter

8. But, we face another mystery.
The density of the universe
We find or . But, the content of the density is very strange.
ρ ∼ ρcr Ω0 =
ρ
ρcr
∼ 1
ρ = No! Ordinal matters such as galaxies,
and stars make up only a few percent of
the density of the universe.
?
Ordinal matter

9. But, we face another mystery.
The density of the universe
We find or . But, the content of the density is very strange.
ρ ∼ ρcr Ω0 =
ρ
ρcr
∼ 1
ρ = + ?
Ordinal matter Dark matter

10. But, we face another mystery.
The density of the universe
We find or . But, the content of the density is very strange.
ρ ∼ ρcr Ω0 =
ρ
ρcr
∼ 1
ρ = + ?
Ordinal matter Dark matter
No! Even if we include the density of dark matter, . does not become 1!!
Ω0 ∼ 0.25 Ω0

11. Supernova as a standard candle
Then, how can we achieve ??
Ω0 = 1
•As I told you before, measuring distance is important in astronomy.
We can measure the distance of a supernova by observing its brightness.
Fainter stars are more far away from us, brighter stars are closer to us.
Before I explain the answer, we focus on the Type Ia supernova observation.

12. Then, how can we achieve ??
Ω0 = 1
•As I told you before, measuring distance is important in astronomy.
Before I explain the answer, we focus on the Type Ia supernova observation.
Independent on the distance to the supernova, we can also measure the redshift of the supernova
by using its spectrum.
Supernova as a standard candle
z =
0
0

13. Supernova as a standard candle
Now we can obtain the supernova's distance and redshift independently.
By using the cosmological model (宇宙学的理论), we can associate the distance with redshift.
dL ≈
c
H0
z
(
1 +
1 − q0
2
z
)
acceleration parameter.
q0 :
•If , the expansion of the universe accelerates（加速） and distance becomes larger
for a given redshift
q0 < 0
•If , the expansion of the universe decelerates（减速） and distance becomes shorter
for a given redshift
q0 > 0

14. Accelerating cosmic expansion
•If , the expansion of the
universe accelerates（加速）
and distance becomes larger for a
given redshift
q0 < 0
•If , the expansion of the
universe decelerates（减速）
and distance becomes shorter for
a given redshift
q0 > 0
•The observation of supernova
indicates .
q0 < 0
The expansion of the
universe is accelerating!

15. Accelerating cosmic expansion
•If , the expansion of the
universe accelerates（加速）
and distance becomes larger for a
given redshift
q0 < 0
•If , the expansion of the
universe decelerates（减速）
and distance becomes shorter for
a given redshift
q0 > 0
•The observation of supernova
indicates .
q0 < 0
The expansion of the
universe is accelerating!

16. Dark energy and accelerating expansion
Ordinal matter or dark matter
Gravitational force attract each other
Dark energy
To let the expansion of the universe
accelerate, dark energy should
behave as the anti-gravitational
force!
Q. Why is the expansion of the universe accelerating?
A. We do not know the answer, but we assume dark energy causes it.

17. Dark energy and accelerating expansion
Q. Why is the expansion of the universe accelerating?
A. We do not know the answer, but we assume dark energy causes it.

18. The density of the universe
ρ = + +
Ordinal matter Dark matter Dark energy
= 1

19. The density of the universe
ρ = + +
Ordinal matter Dark matter Dark energy
= 1
Dark energy: ~70 %, Dark matter: ~25 %, Ordinal matter: ~5 %

20. The fate of the universe
The expansion of the universe is accelerating now,
but we do not know the future!

23. Summary
• Our universe is homogeneous and isotropic at large
scales
• Our universe is expanding and the future of the universe
depends on the density of the universe.
• According to supernova observations, the expansion of
the universe is accelerating. We assume this is caused by
dark energy.