# D.5 Further Cosmology (HL)

## Further Cosmology

### Rotation curve & Dark mattar  ### Rotation curve

$$\frac{GMm}{r^2}=\frac{mv^2}{r}$$

$$v=\sqrt{\frac{GM}{r}}$$

$$M=\rho v=\rho\cdot\frac{4}{3}\pi r^3$$

$$v=\sqrt{\frac{4}{3}\pi G\rho}\cdot r$$

Density 可能是不均匀的

### Evidence for dark matter

• Rotation speed of galaxies is larger than expected at the outer region
• There must be more mass at the edges than is visually observable indicating the presence of dark mattar
• for v to stay constant for r greater than R, M has to be proportional to r

### Dark Matter

• Too cold, do not radiate, cannot be detected
• Examples
• MACHOs (MAssive Compact Halo Object)
• Baryonic (由夸克组成的)
• Examples:
• Black hole
• Brown dwarf 非常低温状态的白矮星
• WIMPs (Weakly Interacting Massive Particle):
• Non-baryonic
• Example:
• Neutrinos
• Forms a spherical halo around the galaxy, and accounts for tsame the "missing" mass of galaxies

### Critical density

$E_{ko}=\frac{1}{2}mv^2$

$E_{po}=-G\rho\cdot\frac{4}{3}\pi mr^3$

Critical denstiy: $E=E_{ko}+E_{po}=0$

$\rho_c=\frac{3H^2}{8\pi G}$

• E=0, $\rho=\rho_c$ (Zero curvature), the expansion will halt(stop) at infinity

• E>0, $\rho<\rho_c$ (Negative curvature), the expansion will continue at infinity

• E<0, $\rho>\rho_c$ (Positive curvature), the contraction will follow the expansion

The critical density is the density of flat, zero-curvature universe, resulting in universe expansion rate tending to zero.

38% maatargf

Creat applaued for ji]

68•

create empulse force that not only,put compacfing=e energy，哎是重点

Thewicn请，寄过

• Homogeniry on: On a large enough grbckground
• Isotropy:

Isotropy: if we look in current in ffdirectionaldirect calrefilly

The same

No-center/No-edigee

The cesronological priniple:

• Homogeneity: on a large enough scale, the universe looks

• Isotropy: If we look in different directions, we see essentially the same thing

• As the universe expands, the temperature drops.

• In the accelerating model, R increases faster and so theperature drops faster

Origin of Redshift

• The space in between us and galaxies is stretching R上升
• Wavelength strech up as well

CMB 这些人绘制测量的

• COBE
• WMAP
• The Planck space observatory

The variation in temperature

T=2.723

Delta T=0.00003K

The reus;t of variasion indensity of matter and energy in the universe.

=> Stars & galaxies will be formed

Geometry of the universe => flat/zero curvature universe