Cosmological Redshift and Distance
As the universe expands, light from distant sources is stretched to longer wavelengths, the cosmological redshift, and the very notion of distance splits into several distinct, expansion-dependent measures.
Definition
Cosmological redshift is the increase in the wavelength of light by the factor by which the scale factor has grown during its travel, and cosmological distances are observer- and method-dependent quantities (comoving, luminosity, angular-diameter) that reduce to a single Euclidean distance only in the nearby, low-redshift limit.
Scope
This topic covers the cosmological redshift as a stretching of wavelengths by the growth of the scale factor, its distinction from the Doppler and gravitational redshifts, and the family of distance measures, comoving, proper, luminosity, and angular-diameter, that arise in an expanding spacetime, together with how each relates to redshift and the expansion history.
Core questions
- Why is cosmological redshift not simply a Doppler shift?
- How does redshift relate to the expansion history of the universe?
- Why are there several different definitions of distance in cosmology?
Key concepts
- Cosmological redshift
- Scale factor at emission
- Comoving distance
- Luminosity distance
- Angular-diameter distance
- Standard candles and rulers
Key theories
- Redshift from scale-factor growth
- The observed wavelength of light is stretched in proportion to how much the scale factor has grown since emission, so redshift directly measures the relative expansion of the universe between emission and observation rather than a local velocity.
- Multiple distance measures
- In an expanding universe, luminosity distance (from observed brightness) and angular-diameter distance (from observed size) differ from each other and from comoving distance, all related through redshift and the expansion history, so the distance one infers depends on what is measured.
Clinical relevance
These relations turn observations into cosmology: measuring the brightness of standard-candle supernovae against their redshift reveals the accelerating expansion, and angular-diameter distances to the cosmic microwave background and to galaxy clustering features constrain the geometry and contents of the universe.
History
Slipher measured the first galaxy redshifts in the 1910s, and Hubble in 1929 combined redshifts with distance estimates to reveal the linear redshift-distance relation; understanding these shifts as cosmological expansion rather than ordinary motion followed from the Friedmann-Lemaitre interpretation of general relativity.
Key figures
- Edwin Hubble
- Georges Lemaitre
- Vesto Slipher
Related topics
Seminal works
- weinberg2008
- hogg1999
Frequently asked questions
- Are galaxies redshifted because they move away from us?
- At cosmological scales the redshift arises from the expansion of space stretching the light in transit, not from motion through space; nearby it can be approximated as a recession velocity, but at high redshift the expansion interpretation is essential and recession 'speeds' can even exceed c without violating relativity.
- Why can a more distant object appear larger in some cases?
- Because the angular-diameter distance in an expanding universe reaches a maximum and then decreases at high redshift, very distant objects can subtend a larger angle than somewhat closer ones, a counterintuitive effect absent from everyday Euclidean geometry.