Hubble’s Law and Cosmic Expansion Study Pack
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Last updated May 27, 2026
Hubble’s Law and Cosmic Expansion Study Guide
Trace the evidence behind cosmic expansion from galactic redshift and Hubble's Law (v = H₀ × d) to the Big Bang model, covering the Hubble constant, stretching spacetime, and the cosmic microwave background.
Key Takeaways
- •Hubble's Law states that a galaxy's recession velocity is directly proportional to its distance from Earth, expressed as v = H₀ × d, where H₀ is the Hubble constant.
- •The observed redshift of galaxy spectra provides the empirical evidence that the universe is expanding, with more distant galaxies showing greater redshift.
- •Cosmic expansion does not mean galaxies move through space from a central point; rather, space itself stretches, carrying galaxies apart in every direction simultaneously.
- •The Hubble constant (H₀) is currently estimated at approximately 70 km/s/Mpc, though ongoing measurements using different methods produce slightly different values — a discrepancy researchers are actively investigating.
- •Running cosmic expansion backward in time leads to the Big Bang model, in which all matter, energy, space, and time originated from an extremely hot, dense state approximately 13.8 billion years ago.
- •The cosmic microwave background radiation — a faint, nearly uniform glow of microwave energy permeating the entire sky — is direct observational evidence of the hot early universe predicted by the Big Bang.
Hubble's Law: Velocity, Distance, and the Expanding Universe
Hubble's Law is the foundational mathematical relationship describing how the universe expands, connecting a galaxy's distance from Earth to the speed at which that galaxy appears to be moving away.
The Mathematical Relationship
- •Hubble's Law is written as v = H₀ × d, where v is the recession velocity of a galaxy, d is its distance from Earth, and H₀ is the Hubble constant.
- •This linear relationship means a galaxy twice as far away recedes twice as fast — the proportionality holds across enormous cosmic scales.
- •Edwin Hubble published this relationship in 1929 based on measurements of nearby galaxies, building on earlier velocity data compiled by Vesto Slipher.
The Hubble Constant (H₀)
- •H₀ quantifies the current rate of cosmic expansion and carries units of kilometers per second per megaparsec (km/s/Mpc), meaning for every megaparsec of distance, recession velocity increases by H₀ km/s.
- •Modern estimates place H₀ at roughly 68–73 km/s/Mpc, but measurements derived from the cosmic microwave background and those derived from local distance indicators (like Cepheid variable stars and Type Ia supernovae) yield slightly different values.
- •Researchers refer to this discrepancy as the Hubble tension — it remains an open problem that may point to new physics or unresolved systematic errors in measurement techniques.
Redshift as Evidence for Cosmic Expansion
The primary observational tool astronomers use to measure galaxy recession velocities is the redshift of light — a shift in spectral lines toward longer wavelengths caused by the stretching of space between the source and the observer.
How Redshift Arises from Expansion
- •When space expands while light is traveling through it, the wavelength of that light stretches along with space, shifting it toward the red end of the electromagnetic spectrum.
- •This cosmological redshift is distinct from the Doppler redshift caused by motion through a static medium, though both produce similar spectral shifts at low velocities.
- •Astronomers measure redshift (denoted z) by comparing the observed wavelength of known spectral lines — such as the hydrogen Balmer series — to their laboratory-measured rest wavelengths.
Interpreting Galaxy Spectra
- •A higher z value indicates greater recession velocity and, through Hubble's Law, greater distance from Earth.
- •Galaxies in every direction of the sky show redshift rather than blueshift (with a few gravitationally bound exceptions like Andromeda), confirming that expansion is occurring uniformly in all directions.
- •The most distant observed objects, including quasars and early galaxies detected by instruments like the James Webb Space Telescope, have redshift values greater than z = 10, meaning their light has been stretched to more than eleven times its original wavelength.
The Geometry of Expansion: What Is Actually Moving
A common misconception about Hubble's Law is that galaxies are flying apart through pre-existing space like shrapnel from an explosion; the correct picture is that space itself is expanding, and galaxies are largely carried along with it.
Expansion of Space, Not Motion Through Space
- •General relativity describes spacetime as a dynamic, stretchable fabric; cosmic expansion is a property of that fabric increasing in scale over time.
- •There is no center of the expansion — every observer in any galaxy sees all other galaxies receding, just as every point on the surface of an inflating balloon moves away from every other point simultaneously.
- •The recession of very distant galaxies can appear to exceed the speed of light because it is space expanding, not matter moving through space; special relativity's speed-of-light limit applies to motion through space, not to the expansion of space itself.
Gravitationally Bound Systems and Local Exceptions
- •On scales smaller than galaxy clusters, gravity overwhelms cosmic expansion, which is why planets, stars, galaxies, and the Local Group of galaxies are not themselves expanding.
- •The Andromeda Galaxy (M31) is blueshifted because its gravitational interaction with the Milky Way produces an approach velocity that exceeds the small recession velocity expected at its distance of ~2.5 million light-years.
- •Cosmic expansion becomes the dominant effect only at distances beyond a few tens of millions of light-years, where galaxies are not gravitationally bound to one another.
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Hubble's Law
Explain Hubble's Law in your own words. What does the equation v = H₀ × d tell us about the relationship between a galaxy's distance and its motion, and what does this reveal about the universe as a whole?
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