Chapter 1 Introduction

Basic Ideas

Isotropic & Homogeneous

• Counts of faint galaxies in different directions

• CMB ( 99% of photons in the universe ) - low fluctuations ( $10^{-5} \mathrm{K}$ )

Expansion

• Hubble (1929) redshift-distance relation

  $$z=\frac{H_0}{c}d,\ v=H_0d$$
• Scatter of galaxies - peculiar motions

Cosmic distance ladder

• Cepheids

• Ia SN

Fundamental Observers

• Fluid (Plasma)

• Substratum (相对宇宙静止)——comoving

• We are not fundamental observers! (velocity relative to the sun, the Galactic center, M31, Virgo Cluster…) - subtract all the relative velocity - confirmed by highly isotropic CMB

Distances

• 1 AU = 1.5e13 cm

• 1 Parsec = 3.26 ly, mostly kpc or Mpc (8.7 kpc away from the Galactic center)

• Radius of the Observable Universe (Inside the horizon) $\sim$ 4450 Mpc ( $c/H_0$ )

Masses

• Solar mass $M_\odot$ = 2e33 g

• Milky Way

  • Stellar mass $\sim$ 1e11 $M_\odot$

  • Total mass $\sim$ 1e12 $M_\odot$

Luminosity and Magnitudes

• For flux $F$ and apparent magnitude $m$

$$F_1/F_2=10^{0.4(m_2-m_1)}$$

• Absolute magnitude $M$ - a distance of 10 pc

$$m-M=2.5\lg\left(\frac{d\ \mathrm{(pc)}}{10}\right)^2=5\lg d-5$$

Cosmological Principle

• Homogeneous - each point is ordinary

• Isotropic - each direction is ordinary

• Copernican Principle - humans, on the Earth or in the Solar System, are not privileged observers of the universe

• Universal cosmic time

Redshifts

$$z=\frac{\lambda_{obs}-\lambda_0}{\lambda_0},\mathrm{or}\ 1+z=\frac{\lambda_{obs}}{\lambda_0}$$

• Doppler Redshift is associated with a speed of recession

  $$v=cz,\ v\ll c\\ 1+z=\sqrt{\frac{1+\beta}{1-\beta}},\ \text{in general}$$

  The SR case is used when, for example, measuring the ejection velocity of gas clouds ejected from AGNs

• We will prove that

  $$1+z=\frac{\lambda_{obs}}{\lambda_0}=\frac{a_{obs}}{a_{em}}$$

  where $a$ is the scale factor of the universe，$em$ stands for emission

Universal Expansion

• 1929 Hubble Law - observing Cepheids

$$v=H_0d\\ H_0\approx 70\ \mathrm{km/s/Mpc}=100\cdot h\ \mathrm{km/s/Mpc}$$

• Today - Ia SN

• Hubble time

$$t_H\equiv \frac{1}{H_0}\sim14\ \mathrm{Gyr}$$

Components of the Universe

$$E_{tot}=\sqrt{m^2c^4+p^2c^2}$$

• Non-relativistic $pc\ll mc^2$

$$E_{tot}\approx mc^2+\frac{p^2}{2m}$$

Baryons

• Proton + Neutron + Electron

  • None relativistic

  • 0.5% stars

  • 4% Hydrogen/Helium

  • 0.03% heavy elements

0.3% Neutrinos

• mass > 0

• Relativistic

Radiation

• $E=h\nu=hc/\lambda$, 0 mass

21% Dark Matter

• Evidence

  • Rotation velocity of galaxies

  • Cluster

  • Gravitational lensing

74% Dark Energy

• Accelerate universal expansion after z = 1

Critical Density

$$\rho_c=\frac{3H_0^2}{8\pi G}=1.36\times 10^{11}\ M_\odot/\text{Mpc}$$