Hubble’s law is the observational fact that “the farther away a galaxy is, the faster it recedes,” leading to the discovery of cosmic expansion and estimates of the age of the universe.
Basic Knowledge
In 1929, Edwin Hubble observed galaxy spectra and discovered that the farther a galaxy recedes, the greater its redshift (the phenomenon in which the wavelength of light shifts toward longer wavelengths). The relationship between recession velocity v and distance d is:
v = H₀ × d
This is called Hubble’s law. H₀ is the Hubble constant, and modern measurements give about 70 km/s/Mpc (values from 67 to 73 km/s/Mpc differ depending on the measurement method = the Hubble tension).
Estimate of the age of the universe: 1/H₀ ≈ 14 billion years (an approximate upper limit for the age of the universe). The modern value obtained using detailed cosmological models is about 13.8 billion years.
Redshift z is defined as λobserved/λrest − 1, and z = 1 means that the light reaching us was emitted when the size of the universe was half its present size.
Redshift (the stretching of a light wave’s wavelength as a galaxy recedes; v/c ≈ z)
Hubble’s law (v = H₀d; the proportional relationship between recession velocity and distance)
Hubble constant(H₀) (the rate of cosmic expansion; about 70 km/s/Mpc. Its reciprocal gives an estimate of the age of the universe)
Age of the universe (about 13.8 billion years; the time since the Big Bang)
Hubble tension (an unresolved problem in which H₀ values obtained by the CMB method and supernova method disagree)
Accelerating cosmic expansion (discovered in 1998 through observations of Type Ia supernovae; attributed to dark energy)
Further Study (Background and Significance)
Hubble’s law means that space itself is expanding, not that galaxies are moving away from the center of the universe. From any galaxy, all other galaxies appear to recede (the raisin-bread analogy).
In 1998, observations of Type Ia supernovae revealed that cosmic expansion is accelerating (Perlmutter, Riess, and Schmidt received the Nobel Prize). The unknown energy causing this acceleration is dark energy, which accounts for about 68% of the universe’s energy density.
The standard model of modern cosmology is called the ΛCDM model (Λ = cosmological constant, CDM = cold dark matter). It describes the universe as consisting of about 5% ordinary matter, 27% dark matter, and 68% dark energy.
- Hubble’s law: v = H₀d (1929)
- H₀ ≈ 70 km/s/Mpc
- Age of the universe ≈ 13.8 billion years ≈ 1/H₀
- Cosmic expansion = expansion of space itself
- 1998: discovery of accelerating cosmic expansion (Nobel Prize 2011)
- ΛCDM model: ordinary matter 5%, DM 27%, DE 68%
- Hubble tension remains unresolved
Points of Caution (Easily Confused)
① Cosmic expansion means that space is expanding, not simply that galaxies are moving. ② Distinguish redshift (receding → wavelength lengthens) from blueshift (approaching → wavelength shortens). The Andromeda Galaxy is blueshifted because it is approaching us. ③ The reciprocal of the Hubble constant gives an approximate age of the universe. ④ Dark energy (the cause of accelerating expansion) and dark matter (the cause of additional gravity) are different.
Practice
- Express Hubble’s law as an equation and state the meaning of the variables.
- What is the approximate value of the Hubble constant in km/s/Mpc?
- What aspect of cosmic expansion was discovered in 1998?