Cosmology Toolbox.
Distances, ages and the CMB, to more significant figures than the data justify.
Cosmology
Input
Dark energy uses w(a) = w₀ + wa(1 − a). Neutrinos are treated as massless radiation, so fold any ν mass into Ωm. Formulas follow Hogg (1999).
Uses the cosmology from the calculator above.
Time-delay cosmography: wait months for one supernova to explode several times, then argue about the mass model for years.
Tension between two measurements
Asymmetric error bars are symmetrised and stat and sys errors are added in quadrature. Gaussians are assumed throughout, as is tradition. Required reading: xkcd 2516.
Conversions
v = H₀d is fine for z ≲ 0.05. Beyond that, use the calculator. Peculiar velocities (~300 km/s) apply at all distances and do not care about your error budget.
Fit H₀ to your own data
Click the map to read a temperature.
The points are the power spectrum measured from this one map, and the error bars are cosmic variance. You only get one sky. You can't ask for a second one, so the scatter at low ℓ stays.
v is the special-relativistic Doppler velocity. For cosmological redshifts it is a convention, not a speed, and it doesn't break any speed limits. Please don't email. Optical lines use air wavelengths, UV lines use vacuum wavelengths.
CODATA 2018, IAU 2012 (au) and IAU 2015 nominal solar values. Click a row to copy the number. G only has six significant figures because gravity has never liked being measured.