1. Hi Marcus, when it best suits you , could you start your tutorial from here

From Marcus's GR primer:   can be calculated ..

Is it possible to explain how k is calculated, what are its units, and what does it mean that namely, curvature G is 2*10^-48/43 times the energy tensor T?

Can you also explain how an why , assuming the Cosmological principle, the equation becomes: and how that becomes : and most of all: what is the relation between the curvature of spacetime G, ds^2 and Hubble parameter H^2 ?

Matter/energy curves spacetime, how does this determine the expansion of space H?
What is the relation between curvature of spacetime and radius of curvature of U and radius of the U, is it the same thing?

The best way to make a student understand is to consider current parameters:
H0 = 2.2*10 ^-18, M 10^56g , R 46.6 Gly, M/V density= 4*10^-31, critical density 10^-29 g/cm^3, rho_c/rho= 0.04

and show how it works in concrete, do you start with Mass, detrmine rho and this tells you the curvature of spacetime, the radius of the U , the expansion rate and the age of U?

Since the content of matter does not change, whereas the volume is always increasing, density is rapidly decreasing, should the curvature decrease?  2.

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