In the Wikipedia article https://en.wikipedia.org/wiki/Accelerating_universe#Evidence_for_acceleration the following equation(adsbygoogle = window.adsbygoogle || []).push({});

(1)

[where the four currently hypothesized contributors to the energy density of the universe are curvature, matter, radiation and dark energy]

is given without any derivation from the previous equations

(2)

(3)

(4)

I have several question about these equations.

(a) I assume that in (2) K is -1, 0, +1 respectively for the space being hyperbolic, flat, or spherical. Then R would be the radius of curvature of the universe at time t. Is that correct?

(b) How is (1) derived form (2), (3), and (4)?

(c) Is the sum of the four Omegas in (1) supposed to equal the Omega in (4)?

(d) In the Einstein equations, isn't Lambda a constant density, independent of a?

(e) Isn't Omega[DE] = Lambda/rho[sub-c] and Lambda a constant independent of a?

(f) If e is correct, then

Omega[DE] = Lambda * (8*pi*G/3) * (a/adot)^2

OK, if that's right, where does the exponent with w in the coefficient of Omega[DE] come from?

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# Equation involving H and a re Accerlerating Universe

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