How to calculate rate of the universe expansion?

The zero-zero component of the Einstein’s equations for gravity with the metric of the expending universe is called the Friedman equation. We use this differential equation to calculate the behavior of the expending space. The equation includes two unknown functions of time: the scale factor and energy density of the expanding universe. It’s solutions define how the scale-factor changes with time depending on both the energy density and curvature of the universe. Additionally, the energy density is linked to the scale factor by conservation of energy. The RHS of the equation consists of four terms each of which differently depends on time or, in other words, on the scale-factor. The curvature term is inversely proportional to the second power of the scale-factor while the energy density of dust and radiation are inversely proportional to the third and fourth power of the of scale-factor respectively. The density of dark energy presumably remains constant being considered as the vacuum energy. Thus as the scale factor grows the relative contribution of the constituents changes. For instance, the dark energy contribution dominates in future and already manifests itself by accelerating expansion now. Having known the rate of growing of the scale factor at present only allows us to conclude about today’s value of the sum of all those constituents of the equation. Thus we need additional arguments do decide how much each of them contributes these days. Unlike other constituents, the contribution of radiation is negligible, hundredth of percents of the total energy density. Now, judging by anisotropies of the cosmic microwave background we can estimate the curvature of space being equal two hundredth.

Variation of different contributions to the universe's energy

Assuming the curvature is zero, we can calculate the present energy density which appears to be several proton masses per a cubic meter.

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How to calculate rate of the universe expansion? — 1 Comment

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