Pixel-art light wave stretching from blue to red as it travels from a spiral galaxy across expanding space, illustrating cosmological redshift

Is Cosmological Redshift a Doppler Shift? Stretching Light Explained

2026年11月10日

When astronomers spread the light of a distant galaxy into a spectrum, the familiar patterns of hydrogen, oxygen and other elements are all there, but shifted toward longer, redder wavelengths. The further away the galaxy, the bigger the shift. This is cosmological redshift, and it is the main evidence that the universe is expanding. This post builds on our explainer How Did the First Elements Form?, since the same expansion cooled the early universe enough for nuclei and atoms to form.

Formula plate in Pixelated Physics pixel style: Definition of redshift, 1 + z = λ_obs / λ_emit

What is redshift?

Redshift, written z, measures how much a wavelength has been stretched:

1 + z = λ_obs / λ_emit

where λ_emit is the wavelength when the light was emitted and λ_obs is the wavelength we observe, both in metres (or nanometres), and z has no units. Our worked example: if light leaves a galaxy at 500 nm (green) and arrives at 1,000 nm (infrared), then 1 + z = 2, so z = 1.

Formula plate in Pixelated Physics pixel style: Special-relativity Doppler shift, 1 + z = √((1 + β) / (1 − β)), β = v / c

Who discovered that galaxies are redshifted?

OpenStax Astronomy tells the story (OpenStax Astronomy, §26.5^[1]). Beginning in 1912, and over about 20 years, Vesto Slipher at Lowell Observatory photographed the spectra of more than 40 spiral nebulae and found that most were shifted to the red. In 1927 the Belgian priest and astronomer Georges Lemaître published a paper suggesting we live in an expanding universe and used Slipher’s data to estimate the rate of expansion. In 1929 Edwin Hubble published his relation between distance and radial velocity for galaxies (Hubble, 1929^[2]), now written v = H₀d and called the Hubble–Lemaître law.

What causes cosmological redshift?

In the standard model of cosmology, the distance between distant galaxies grows in proportion to a single number, the scale factor a(t), which is defined as 1 today. Light travelling between galaxies is stretched by exactly the same factor as everything else:

1 + z = a(t_obs) / a(t_emit)

where a(t_emit) is the scale factor when the light left and a(t_obs) is the scale factor when it arrives. So z = 1 means the universe has doubled in linear size since the light set out.

The cosmic microwave background is the extreme example. ESA explains that about 380,000 years after the Big Bang, the universe had cooled to around 3,000 kelvin and light could travel freely; because of the expansion, those photons have since been redshifted to wavelengths of roughly a millimetre and an effective temperature of about 2.7 K (ESA^[3]). Since a thermal glow’s temperature falls in step with the stretching, 1 + z ≈ 3,000 / 2.726 ≈ 1,100 (our calculation). Our post What Is the Cosmic Microwave Background? tells that story in full.

Pixel-style physics diagram: Redshift stretches every wavelength by 1 + z. 1 + z = λ_obs / λ_emit · a 500 nm line arrives at 1,000 nm (z = 1) and 1,500 nm (z = 2)

How is that different from a Doppler shift?

An ordinary Doppler shift happens when a source moves through space relative to you, like the falling pitch of a passing siren. For light, special relativity gives the shift for a source moving directly away at speed v:

1 + z = √((1 + β) / (1 − β)), β = v / c

where c = 299,792,458 m/s is the speed of light and β is the speed as a fraction of c. Solving it for our examples: z = 1 would mean β = 0.6, and z = 2 would mean β = 0.8. No matter how big z gets, β never reaches 1.

Applied to the whole universe, that formula gives the wrong answers. Tamara Davis and Charles Lineweaver compared it with the brightness of distant supernovae and report that the special-relativistic Doppler interpretation of cosmological redshifts is ruled out at a confidence level of 23 sigma (Davis & Lineweaver, 2004^[4]). They also show that we can see galaxies that have, and always have had, recession velocities greater than the speed of light.

Using the standard ΛCDM model with Planck’s 2018 values, H₀ = 67.4 km/s/Mpc and Ωₘ = 0.315 (Planck Collaboration, 2018^[5]), our own calculation gives the present recession speed for a galaxy at z = 1 as about 0.77c, and at z = 2 as about 1.19c, faster than light. The galaxy is not moving through space faster than light; the distance to it is growing that fast. Since 1998 we have also known that the expansion is accelerating (Riess et al., 1998^[6]), an effect attributed to dark energy, which our Void Whisperer tee personifies.

Pixel-style physics diagram: The Doppler formula vs the expanding universe. SR: 1 + z = √((1 + β)/(1 − β)) · ΛCDM present recession speed, H₀ = 67.4, Ωₘ = 0.315 (our calculation)

So is it a Doppler shift or not? An open debate

This is where we label an open point, because careful physicists disagree about the best description, not about the numbers.

The “stretching space” view. Redshift is the stretching of light by the growth of the scale factor, as in the formula above. This is how most textbooks put it.
The “many small Doppler shifts” view. Emory Bunn and David Hogg argue that the most natural interpretation is a Doppler shift, or rather the accumulation of many infinitesimal Doppler shifts, measured by a chain of observers along the light’s path (Bunn & Hogg, 2009^[7]). They say the stretching-of-space picture obscures a central idea of relativity: that locally, spacetime always looks like flat Minkowski space.

Both camps agree on the essential point: you cannot use the single special-relativity Doppler formula for the whole journey, and you must use the scale factor (or general relativity) to get the right numbers. Bunn and Hogg also show that a frequency shift can be described either as kinematic or as gravitational depending on which family of observers you imagine. The disagreement is about which words build better intuition.

Quick FAQ

What is cosmological redshift in simple terms?

The stretching of light’s wavelength by the expansion of the universe while the light is travelling.

What does z = 1 mean?

Wavelengths have doubled, and the universe has doubled in linear size since the light was emitted.