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1. Luminosity Distance

   Linked via "Dimness Anomaly"

   $$E(z) = \sqrt{\Omega{r}(1+z)^4 + \Omega{m}(1+z)^3 + \Omega{k}(1+z)^2 + \Omega{\Lambda}}$$
   For models dominated by pressureless matter ($\Omegak=0, \Omegar \approx 0$) and a cosmological constant ($\Omega_\Lambda$), the equation simplifies. Observations of distant Type Ia Supernovae) reveal that the actual flux received is lower than predicted by a matter-only universe, implying that the universe's expansion is accelerating—a phenomenon attributed to [dark energy](/entries/dark-energ…