How do we measure cosmic parameters?

 
There are four parameters that govern the universe expansion. First, the energy density of relativistic particles mostly is that of Cosmic Microwave Background photons. This quickly falls as the space scale-factor grows so contributes to the expansion very little. Second, at the moment of recombination, when electrons were captured by protons, the temperature of the CMB was higher in space regions where the density of photons was greater. The density did vary since fluctuations of primordial plasma density collapsed increasing the density and pressure of photons since those are coupled to charged particles via scattering. This resulted in outward longitudinal waves in the surrounding plasma, whose hotter crests propagated with the speed of sound. In plasma, this speed is of the order of the speed of light. Thus, before electrons decoupled from matter at the moment on recombination 380 thousand years later, the waves had traveled a distance of about 70 kiloparsecs. Since then the universe becomes transparent for photons so this distance just expanded by about two thousand times now forming a huge standard ruler for us. Regions of higher CMB temperature of that size subtend about one degree angle and have been observed by the COBE, WMAP and Hubble space missions. From the observation we conclude the universe curvature is negligibly small. Now, neglecting both the radiation and curvature contributions to the universe scale-factor evolution we are only left to choose between the matter and dark energy contributions. Fortunately the apparent brightness of distant supernovae depend on them differently for various distances to supernovae, i.e for various redshifts. Mathematically this gives independent simultaneous equations which can be solved for the two contributions being about 32 and 68 percents respectively.

Supernovae prove the accelerating expansion of the universe

Observing supernova brightness at high redshifts has also revealed acceleration of the universe expansion.

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