Cosmological Redshift and the Hubble Law

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cosmology redshift expansion

Core Idea

The redshift of distant galaxies—the stretching of wavelengths due to expansion of spacetime—is related to distance by the Hubble law: recession velocity is proportional to distance (v = H₀d). This relationship revealed that the universe is expanding uniformly and enabled the first measurements of the cosmic expansion rate (Hubble constant ~70 km/s/Mpc). Cosmological redshift differs fundamentally from Doppler redshift: it results from metric expansion, not motion through space.

Explainer

You are familiar with the Doppler effect: when a source of waves moves away from you, the waves get stretched and their wavelength increases. For light, this stretching shifts the spectrum toward the red end — a redshift. In the 1920s, Edwin Hubble observed that nearly all distant galaxies show redshifted spectra, and that the amount of redshift is proportional to the galaxy's distance. This pattern — now called the Hubble law — was the first observational evidence that the universe is expanding.

The Hubble law is expressed as v = H₀d, where v is the recession velocity of a galaxy, d is its distance from us, and H₀ is the Hubble constant, measured at approximately 70 km/s/Mpc (kilometers per second per megaparsec). This means a galaxy 100 Mpc away recedes at about 7,000 km/s, while one 200 Mpc away recedes at 14,000 km/s. The linear relationship tells us something profound: the universe is expanding uniformly. There is no special center — every point in the universe sees every other point receding, just as dots on a balloon all move apart from each other as the balloon inflates. The Hubble constant sets the rate of this expansion and, inverted, gives a rough estimate of the age of the universe (1/H₀ ≈ 14 billion years, close to the more precise value of 13.8 billion years from detailed cosmological models).

The critical conceptual distinction is between cosmological redshift and ordinary Doppler redshift. A Doppler shift occurs when a source moves through space — it is a kinematic effect. Cosmological redshift is fundamentally different: the galaxies are not flying apart through a pre-existing space; rather, the fabric of space itself is expanding, and the light waves traveling through it get stretched along with it. A photon emitted with a certain wavelength when the universe was smaller arrives with a longer wavelength because space has expanded during the photon's journey. The redshift parameter z is defined as the fractional change in wavelength: z = (λ_observed - λ_emitted) / λ_emitted. A galaxy at z = 1 means the universe has doubled in scale since that light was emitted.

This distinction matters because at large distances, the Doppler interpretation breaks down. Galaxies with redshifts z > 1 have recession velocities that formally exceed the speed of light, which would be impossible for motion through space but is perfectly consistent with metric expansion — space itself is not bound by the speed-of-light limit. The Hubble law in its simple form (v = H₀d) is an approximation valid for nearby galaxies; at cosmological distances, the full general-relativistic treatment replaces it with a relationship between redshift and the scale factor of the universe. Measuring the Hubble constant precisely remains one of the central challenges of modern cosmology, with different measurement methods currently yielding slightly discrepant values — the so-called Hubble tension — which may point to new physics beyond the standard cosmological model.

Practice Questions 5 questions

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Redshift and the Hubble Law

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