Expanding Universe and Friedmann Models
The universe is expanding: distant galaxies recede with velocities proportional to their distance, a behaviour captured by the Friedmann models of general relativity that describe a homogeneous, isotropic cosmos whose scale grows with time.
Definition
The expanding universe is described by a homogeneous and isotropic spacetime whose Friedmann-Lemaitre-Robertson-Walker metric has a time-dependent scale factor; the Friedmann equations relate the expansion rate to the energy content and spatial curvature, and the Hubble-Lemaitre law expresses the observed proportionality between recession velocity and distance.
Scope
This area covers the dynamical framework of modern cosmology: the Hubble-Lemaitre velocity-distance law and the interpretation of redshift as cosmic expansion, the Friedmann-Lemaitre-Robertson-Walker metric and the Friedmann equations that govern the scale factor for matter-, radiation-, and dark-energy-dominated eras, the spatial geometry and density parameters of the universe, the cosmic distance ladder used to measure the Hubble constant, and the role of general relativity as the governing theory of cosmic dynamics.
Sub-topics
Core questions
- Why do nearly all galaxies recede from us, and what does this tell us about the universe?
- How do the Friedmann equations link the expansion rate to the contents of the cosmos?
- What is the spatial geometry of the universe and how is it measured?
- How is the Hubble constant determined, and why do different methods disagree?
Key concepts
- Scale factor
- Redshift
- Hubble constant
- FLRW metric
- Critical density
- Density parameter
- Spatial curvature
- Comoving distance
Key theories
- FLRW cosmological models
- A homogeneous and isotropic universe is described by the Friedmann-Lemaitre-Robertson-Walker metric with a single time-dependent scale factor and a curvature constant, providing the geometric backbone for all standard cosmological models.
- Friedmann equations
- Applying Einstein's field equations to the FLRW metric yields the Friedmann equations, which relate the expansion rate and acceleration of the scale factor to the energy density, pressure, and spatial curvature of the universe.
- Hubble-Lemaitre law
- The recession velocity of a distant galaxy is proportional to its distance, with the constant of proportionality being the Hubble parameter; this empirical relation established that the universe is expanding rather than static.
Clinical relevance
The expanding-universe framework underpins the entire Big Bang model: it sets the age and size of the observable universe, fixes the relation between redshift and look-back time used to interpret every cosmological observation, and provides the dynamical stage on which nucleosynthesis, recombination, and structure formation unfold.
History
Friedmann derived expanding and contracting solutions of general relativity in 1922, and Lemaitre independently linked them to galaxy redshifts in 1927; Hubble's 1929 distance-velocity relation provided observational confirmation, and the Robertson-Walker metric formalized the homogeneous isotropic geometry, together establishing the expanding universe as the foundation of modern cosmology.
Debates
- The Hubble tension
- Measurements of the Hubble constant from the local distance ladder are systematically higher than the value inferred from the cosmic microwave background within the standard model, a discrepancy of several standard deviations that may signal new physics or unrecognized systematics.
Key figures
- Edwin Hubble
- Georges Lemaitre
- Alexander Friedmann
- Howard Robertson
- Arthur Walker
Related topics
Seminal works
- friedmann1922
- hubble1929
Frequently asked questions
- Is the universe expanding into something?
- No: the expansion describes space itself stretching, so distances between distant galaxies grow over time. There is no external space the universe expands into; the Friedmann models describe the geometry intrinsically without reference to any outside.
- Does cosmic expansion mean galaxies move faster than light?
- Sufficiently distant galaxies do recede faster than light, but this is allowed because it is the expansion of space rather than motion through space; special relativity's speed limit applies only to local motion, not to the growth of cosmological distances.