Trying to Implement Friedmann Calc., But Can't

1. Jan 29, 2013

FF2013

I have no background in physics. I began to read a discusson regarding cosmology, and thought that I might be able to practically implement the Friedmann equation in a real world effort to trace the volume of the universe from the present backward through time. I take the mass of the universe to be 10^53 kg/m^3. I presume the universe is presently roughly 14 billion years old. I presume that the volume of the universe at present is approximately 3.3 x 10^80 m^3. I take the universe to be 70 percent cos. constant and 30 percent mass. I presume that the following is a valid presentation of the Friedmann Equation:

(a'/a)^2 = 8(pi)G(Summation of rho's for pos. and neg. energy)/3 - k(c^2)/(a^2).

A few issues immediately confront me.

1. How do I convert "a" into "Runi", or at least correlate them?
2. If the universe has been spatially "flat" during most of its life (in the context of the a time frame that can easily stop at 100 million years after the "big bang"), can I then take "k" to be zero? If so, is the following a reasonable Gaussian algorithm?

delta_a = ((8(pi)G(Summation of rho's for pos. and negative energies)/3)^0.5)delta_t ?

How do I correlate "Summation of rho's for pos. and neg. energies" at any point in time with the value of "a" via the value of Runi, the radius of the universe, its corresponding volume (directly affecting the summation of energy densities)?

(I've seen "Runi = ax" and "R'uni = a'x", but I need some direction with regard to how to apply these equations to the preceding question.)

Internet discussions of the topic insist that using the Friedmann Equation should be a piece of cake. I'd appreciate responses that can help me to trace the scale of the universe back to 100 million years after the "big bang". An few sample iterations would be very useful, if anyone has the time to illustrate a working approach.

Thank you.