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lecture26
The document discusses key concepts in cosmology, including: 1) The universe appears homogeneous and isotropic at large scales, with only small fluctuations in density. 2) Olbers' paradox explains why the night sky is dark if the universe is assumed to be infinite and unchanging, which may be incorrect assumptions. 3) The expanding universe model provides a solution to Olbers' paradox, as the universe had a hot, dense beginning and a finite age, limiting the number of observable stars. 4) The fate of the universe depends on its total density - if density exceeds a critical threshold, the universe will eventually collapse, while a lower density means continued expansion.
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lecture26
- 1. Introduction to modernastronomy 26 島袋隼⼠(Hayato Shimabukuro)（云南⼤学、 SWIFAR） ©GETTYIMAGES
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- 3. The Cosmic principle（宇宙原理） Theproperties of the universe •Homogeneous（均匀的） •Isotropic（各向同性的） The cosmic principle(宇宙原理) “Our universe does not have any special region” Really?? •Our solar system seems to be special. The earth is a special place! “Our universe does not have any special region at large scales” The fluctuations in number density are small.
- 4. 9 persons 8persons 8 persons 8 persons 8 persons 8 persons •The average number density is roughly ~8 persons. In many regions, the number density is 8. But, a region has 9 people. This is fluctuation. •Same situation happens at large scales in the universe. The number density in the universe is almost the same as the average value everywhere at large scales.
- 5. The Cosmic principle（宇宙原理） •Ifwe observe the universe at small scales, we can find galaxies, galaxy clusters, and large-scale structures of the universe. Thus, the universe is not isotropic and homogeneous. •But, when we average the number density at large scales (~10Mpc), the number density fluctuations are very small (the number density everywhere has almost average value). The universe is very smooth. The universe has no center!
- 6. Olbers’s paradox（佯谬） •In additionthat the universe is homogeneous and isotropic, we assume the universe is infinite(⽆限) in spatial extent and unchanging in time. r L F = L 4πr2 :Brightness depends on the distance to the stars •The number of stars ( ) also depends on n r2 •Thus, the total brightness in the sky can be expressed by Ftotal ∝ ∫ ∞ 0 L 4πr2 ⋅ r2 dr = ∞
- 7. Olbers’s paradox（佯谬） Ftotal ∝ ∫ ∞ 0 L 4πr2 ⋅r2 dr = ∞ The sky should be too bright! •But, we know the actual sky is not bright. Olbers’s paradox Why is it dark in the night sky? Our assumption The universe is… •Infinite in spatial extent. •Unchanged in time. These assumptions may be incorrect
- 8. Olbers’s paradox（佯谬） Ftotal ∝ ∫ ∞ 0 L 4πr2 ⋅r2 dr = ∞ The sky should be too bright! •But, we know the actual sky is not bright. Olbers’s paradox Why is it dark in the night sky? Our assumption The universe is… •Infinite in spatial extent. •Unchanged in time. These assumptions may be incorrect
- 9. The expanding universe（膨胀宇宙） •Inorder to solve Olbers’s paradox, we first start Hubble’s law. t = v r = 1 H (Velocity)=(constant) (distance) × time = distance velocity •The inverse of the Hubble constant roughly provides the age of the universe. •Hubble constant is roughly 70km/s/Mpc. This indicates the age of the universe is roughly 14 billion years(140亿年) The age of the universe is finite! Age of the universe
- 10. The expanding universe（膨胀宇宙） Theage of the universe is finite! The number of stars (galaxies) is also finite. The age of the universe is finite, which means that the number of galaxies that can be observed is finite and their ages are shorter than the age of the universe. There are not enough stars (galaxies) in the universe to brighten the night sky. This is an answer to Olbers’s paradox. The night sky is not too bright.
- 11. The expanding universe（膨胀宇宙） t= v r = 1 H •The age of the universe is 14 billion years. •The universe is expanding. These facts suggest that our universe was small in the past. •Smaller universe is hotter. •The beginning of the universe was a hot and dense fireball! This universe is called Big Bang •Big Bang happened everywhere. Big Bang was not an explosion of the universe.
- 12. Big Bang isnot an explosion!
- 13. Big Bang happenseverywhere and Big Bang does not have a center. The universe was hot and dense everywhere
- 14. The expanding universe（膨胀宇宙） •Thebehavior of the expansion is like a balloon and galaxies are located on the balloon. Galaxies themselves do not expand.
- 15. The expanding universe（膨胀宇宙） •Thebehavior of the expansion is like a balloon and galaxies are located on the balloon. Galaxies themselves do not expand.
- 16. •We often use“redshift(红移)” to express distant or past（过去） universe. Redshift Redshift Due to the expansion of the universe, the wavelength of the distant or past universe extends. z = 0 0 Original wavelength Extended wavelength z=0: present universe z=0.1: 1.4 Gyr ago z=1: 7.8 Gyr ago z=10: 13.2 Gyr ago z=20: 13.7 Gyr ago G:Giga, 10亿年
- 17. The fate ofthe cosmos What happened in the universe's future? Will the universe expand forever? (Big question in cosmology) Let’s begin with another analogy. Rocket escaping from the earth Expanding universe Physics is similar!
- 18. The fate ofthe cosmos Scenario 1 •A rocket leaving the Earth with a speed greater than the Earth’s escape speed escapes from the earth.
- 19. The fate ofthe cosmos •If the launch speed of the rocket is less than the escape speed, the rocket eventually goes back to the earth and falls. Scenario 2
- 20. The fate ofthe cosmos •The expansion of the universe also behaves like a rocket. •The distance between two galaxies as a function of time. •The distance between two galaxies expands forever or eventually collapses. Expand forever Eventually collapse
- 21. The fate ofthe cosmos •In the case of a rocket, the speed of the rocket determines the fate of the rocket. What determines the fate of the universe? Remember that gravity pulls material. The universe •According to Einstein’s theory, gravity is caused by material (energy, mass). Thus, the fate of the universe depends on the density of mass in the universe. Critical density ρcr = 3H0 8πG = 9 × 10−27 kg/m3
- 22. The fate ofthe cosmos •In the case of a rocket, the speed of the rocket determines the fate of the rocket. What determines the fate of the universe? Remember that gravity pulls material. Gravity also pulls the universe itself. The universe •According to Einstein’s theory, gravity is caused by material (energy, mass). Thus, the fate of the universe depends on the density of mass in the universe. Critical density ρcr = 3H0 8πG = 9 × 10−27 kg/m3
- 23. The fate ofthe 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.