Layer 26
Cosmology & the Expanding Universe
Use FLRW expansion to connect redshift, cosmic temperature, distance, lookback time and the history of the universe.
interactivemodel assumptions visibleestablished science separated from analogy
Story step: Apply gravity, fields, matter and statistical physics to the universe as a whole: expansion changes wavelengths, temperatures and the growth of structure.
1 · Expansion history
In a homogeneous, isotropic FLRW cosmology, the expansion rate depends on the energy-density components.
H(z)/H₀ = √[Ωr(1+z)⁴ + Ωm(1+z)³ + Ωk(1+z)² + ΩΛ]
—Ωk
—approx. model age
—present acceleration sign
2 · Redshift stretches wavelengths
Cosmic expansion relates emitted and observed wavelengths through the scale factor.
1 + z = a₀/aemit = λobs/λemit
—observed wavelength
—scale factor a
—CMB temperature scaling
3 · Lookback time & distance
Redshift is not a simple distance ruler; converting it to distance depends on the cosmological model.
—lookback time
—line-of-sight comoving distance
—CMB T then
Numerical integral of the selected FLRW parameters; radiation density is fixed at Ωr = 9×10⁻⁵ for this teaching model.
4 · Cosmic timeline
Drag across logarithmic cosmic time. Milestones are approximate and represent broad epochs rather than sharp universal boundaries.
—nearby epoch
—time after Big Bang
13.8 Gyrcurrent best-fit age scale (approx.)
Scientific boundary: This lab uses homogeneous/isotropic FLRW cosmology and a simple density-parameter model. Precision cosmology requires full datasets, perturbation theory and parameter inference. Dark matter and dark energy are observationally motivated components whose microscopic nature remains open.