Imagine a distant galaxy looks red in a photograph. Is that enough to announce that the Universe is expanding? Not yet. Colour also depends on its stars, dust and how the image was made. Astronomers need a much more precise pattern in the light—and a second, independent measurement.
On large scales, galaxies with greater independently determined distances have, on average, larger redshifts of their spectral lines. This relationship is described by an expanding Universe; the stretching of observed supernova light-curve durations supplies an additional check. Let us follow how two measurements lead to that conclusion.
Recognising lines rather than red paint
A spectrum is light separated by wavelength. It contains dark or bright lines associated with atomic transitions. Their laboratory wavelengths are known. A whole set of lines helps identify the emitter even when they have all shifted.
If recognised lines appear at longer wavelengths, we have a redshift. The name also applies when the light is outside the visible range. Astronomers compare line positions with a reference; they need not wait for a galaxy to move perceptibly across the sky. NASA/STScI explains this using galaxy spectroscopy.
The shift alone does not identify its cause. Relative motion also changes wavelength, and different gravitational conditions affect light’s frequency. To test a cosmic relationship we need a second column of data: distance.
Distance needs its own route to verification
Imagine a researcher first deriving distance from redshift by assuming expansion, then using those same numbers to prove a redshift–distance relationship. The argument has returned to its own assumption. Testing it requires distances calibrated another way.
For example, a Cepheid’s brightness-variation period helps estimate its intrinsic luminosity. Comparison with the observed flux gives distance after calibration and corrections. At larger scales, astronomers use other linked indicators, including type Ia supernovae. The cosmic distance ladder article explains those connections.
Comparing such distances with spectral shifts revealed an overall trend: farther away means, on average, a larger shift. Hubble’s original 1929 paper shows the relationship, the scatter and a discussion of galaxies’ peculiar motions. Its historical distance calibration was later revised; the numerical slope of that old plot does not supply today’s expansion rate.
The low-redshift relationship is called the Hubble–Lemaître law. In a simple approximation, the expansion contribution to recession is proportional to distance. Let us examine the arithmetic of that proportionality while explicitly keeping it separate from actual measurements.
One law, three hypothetical distances
Teaching model: H₀ = 70 km/s per Mpc
Hypothetical galaxy A
- Distance
- 20 Mpc
- Expansion contribution to recession
- 1400 km/s
Hypothetical galaxy B
- Distance
- 40 Mpc
- Expansion contribution to recession
- 2800 km/s
Hypothetical galaxy C
- Distance
- 60 Mpc
- Expansion contribution to recession
- 4200 km/s
Twice the distance → twice the expansion contribution.
What does expansion mean in the physical model?
In a large-scale cosmological model, the average matter distribution is approximately homogeneous. Distances between objects following the overall cosmic flow change with the scale factor. This number describes how the spatial scale has changed between two epochs.
As light travels between such objects, its wavelength increases with that change of scale too. We compare the wavelength emitted near the source with the wavelength observed near the receiver. No external space into which the Universe must inflate is required. The mathematical link between scale and redshift is given in the Particle Data Group cosmology review, Sections 22.1.1–22.1.2.
Our Galaxy need not occupy a special centre either. If all large distances increase by the same factor, another observer following the flow would find the same overall pattern around them. This describes the average cosmic scale, rather than every object’s size.
Distant galaxies’ recession and a change in the expansion rate over time are different questions. A slope in today’s distance–recession relationship does not by itself measure how that slope evolved throughout cosmic history.
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What can redshift be used to calculate?
Write the emitted wavelength as λ_(em) and the observed wavelength as λ_(obs). The dimensionless shift is:
z = (λ_(obs) − λ_(em))/(λ_(em)).
For a hypothetical 500 nm line observed at 505 nm:
z = (505 − 500)/(500) = 0.01.
Its wavelength has increased by 1%. For a purely cosmological redshift in a homogeneous model:
1 + z = (a_(obs))/(a_(em)).
Here a is the scale factor; the subscripts indicate the observation and emission epochs. Additional peculiar motions and gravitational shifts must be accounted for separately. At small z, with an appropriate peculiar-motion correction, the approximation is:
cz ≈ H_(0)d.
c is light speed, d the distance in this low-redshift approximation, and H_(0) the present expansion parameter. Choose a hypothetical H_(0) = 70 km/s per megaparsec; a megaparsec is a million parsecs. For z = 0.01, we get cz ≈ 2998 km/s and d ≈ 42.8 Mpc. This illustrates using the law after testing it, rather than independently proving that same law.
At large z, simply calling cz a velocity and inserting it into the same elementary formula is unjustified: a cosmological relationship between redshift and the chosen distance definition is needed.
Testing an event's duration as well as its light
Expansion makes another testable prediction. If successive signals arrive at longer intervals, the observed brightness evolution of a distant supernova should take longer according to its redshift. For the same duration in the source frame, the factor is 1 + z: a hypothetical 20 days at z = 1 would be observed as 40 days.
Supernovae are not identical stopwatches. Their intrinsic diversity must be allowed for, and corresponding spectral ranges in the source frame must be compared. A 2024 Dark Energy Survey analysis tested the time dependence using 1504 type Ia supernovae after data-quality selection; the result agrees with the expected 1 + z stretching.
An explanation must therefore account for both wavelength changes and the pace of events. The simple idea that a photon merely loses energy along the way, without changing time intervals, fails this test. This is additional support for the physical interpretation of redshift, rather than another distance calculation using the same number.
An individual galaxy can approach us
Each galaxy also participates in local gravitational motion. In our nearby surroundings, this can outweigh the small contribution of overall expansion. Individual negative redshifts and scatter around the average relationship are therefore expected. A sufficiently large sample is important, with observer motion, uncertainties and matter flows taken into account.
Check your inference: would one nearby blueshifted galaxy refute the whole trend? No: it could have enough peculiar motion towards us. In contrast, the absence of the overall relationship in a large, correctly calibrated sample would pose a serious problem for this description.
Bound systems do not simply scale with the cosmic flow either: planetary orbits and galaxies are held together by their internal dynamics. The general recession trend therefore does not mean that Earth or a ruler grows in that same proportion every day. Astronomer Ned Wright’s cosmology FAQ discusses this limit separately.
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Why do different analyses obtain different H₀ values?
Detecting expansion and establishing its exact present rate are tasks of different difficulty. For orientation, consider two specific analyses checked as of 30 October 2026.
The H₀ Distance Network, published in 2026, obtained 73.50 ± 0.81 km/s per Mpc from a network of local distance indicators, accounting for shared uncertainties and calibration correlations. The Planck 2018 analysis, published in 2020, instead inferred 67.4 ± 0.5 km/s per Mpc from the cosmic microwave background assuming the standard spatially flat six-parameter ΛCDM model.
The second route uses a model to connect the early Universe to the present; it is not a direct measurement of galaxies’ present recession. Disagreement between such determinations is called the Hubble tension. These two numbers do not cover all methods and do not by themselves establish any particular new physics. Further checks of systematics, calibrations and model assumptions are needed.
We deliberately kept the round number 70 in the teaching diagram. It makes the proportion transparent without presenting one real result as the final answer.
The conclusion rests on agreement between tests
Spectral lines supply redshift; separately calibrated indicators supply distance. Their systematic relationship and distant supernovae’s temporal evolution agree with an expanding Universe. Peculiar motions explain why an individual galaxy can depart from the average trend.
Expansion alone does not establish every detail of the Universe’s beginning, contents or future. A hot past requires additional evidence. To examine the most vulnerable step of today’s explanation more closely, return to independent cosmic distance measurements: without them, two columns of observations can easily be confused with one assumption.