The Expansion of the Universe

Based on redshifts Vesto Slipher discovered, it appeared that many of the spiral nebulae are moving away from us.

• Hubble used these redshifts to derive distances to stars: redshift is proportional to distance. The more distant the stars, the greater the redshift.

• Planets, the solar system, our galaxy, etc. are not expanding because they are held together gravitationally. The expansion of empty space is a much smaller force compared to gravity.

• Starting about 10 million light years, objects sufficiently far apart begin to move away from one another.

Hubble’s Law #

Hubble’s Law (Hubble-Lemaitre Law)

• $v$ = velocity
• $H_0$ = Hubble constant: $71 \pm 3$ km/s/Mpc
  • Mpc = megaparsec = $32.6 \times 10^6$ light years
  • Currently contested
• $d$ = distance
• Hubble’s constant (or parameter) is constant throughout space, but not time. It has been seen to decrease over time.

How to measure distances using Hubble’s Law:

1. Use Doppler shift equation to get $z = \frac{\lambda - \lambda_0}{\lambda_0}$
2. Use $z = \frac{v}{c}$ to calculate velocity $v$
3. Use Hubble’s law $v = H_0 d$ to calculate distance

The more redshifted something is, the longer the lookback time. The lookback time is the amount of time light took for the object to reach us: for example, if the lookback time of an object is 2.5 billion years (0.2nm redshift), then that means we’re observing it as it was 2.5 billion years ago.

Most elliptical galaxies formed very early on. However, some formed recently due to the merging of two galaxies.

Active galaxies: have extremely luminous centers (by $L = 4 \pi d^2 b$) that are so bright that they cannot be caused by stars alone.

Accelerating Expansion and Dark Energy #

• Not only is the universe expanding, but the rate of expansion is accelerating.
  • The main conclusion of the studies of distant Type Ia supernovae is that the expansion of the Universe is now accelerating, rather than decelerating as expected. The acceleration implies that there must be gravitationally repulsive “dark energy” in the Universe.