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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

还可能有dark mattar

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


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

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.

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



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

Isotropy: if we look in current in ffdirectionaldirect calrefilly

The same


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


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