Hope I'm in the right section for this question! In the big bang model, the expansion of the universe is slowed down by gravity. If there is enough matter in the universe, then the expansion can be overcome and the universe will collapse in the future. The density of matter that is just sufficient to eventually halt the expansion is called the critical density. The equation for the critical density is(adsbygoogle = window.adsbygoogle || []).push({});

ρcrit = 3H₀²/ 8πG

You can see that the critical density is proportional to the square of the Hubble constant — a faster expansion requires a higher density to overcome the expansion.

We can calculate ρcrit by inserting the gravitational constant, G = 6.67 × 10-11 Nm2 / kg2, and adopting H0= 70 km/s/Mpc. We first convert the Hubble constant to metric units, H0= 2 × 10-18s-1. Now we can solve to get ρcrit = 3 × (2.1 × 10-18)2 / 8 × 3.14 × 6.7 × 10-11 = 7.9 × 10-27 kg/m3 ≈ 10-26 kg/m3. Equal to about five hydrogen atoms per cubic meter.

With all that being said, can anyone tell me why;

8π x G? Or why 3 × H²?

In other words, I'm looking for an explanation as to why we are using particular numbers like 8π or 3H² to achieve density?

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# Critical density: question correction

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