- #36
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OK, Ned Wright's calculator does not give us some of the information in Morgan's output, but we can compute the additional information from what Ned Wright gives us and some standard equations.
If we add the following eq's
[tex]
D_{then} =\frac{D_{now}}{z+1}
[/tex]
[tex]
H = \frac{\dot{a}}{a}
[/tex]
clarification: [itex]H_{then} = H [/itex] evaluated at [itex] a = \frac{1}{z+1}[/itex]
[tex]
V_{then} = H_{then} D_{then}
[/tex]
to Ned Wright's form of the Friedmann eq, i.e.
[tex]\dot{a} = H_0 \sqrt{\frac{\Omega_m}{a} + \frac{\Omega_r}{a^2} + \Omega_v a^2 + (1-\Omega_t)}
[/tex]
we have everything we need to calculate the additional information. (I have not repeated the information on how to calculate [itex]D_{now}[/itex], just added the information needed to calculate the 'extra' quantities that Morgan's calculator gives and Ned Wright's does not.)
We can safely set [itex]\Omega_r=0[/itex] as discussed for anything we can see (i.e. the equations will work to z=1100 and as an added bonus a fair ways beyond).
The results we get by doing this appear to agree with Morgan's results for the test case.
[add]The main motive for writing this out is that Morgan's calculator gives answers, but does not have an explanatory page for the formulas used. Ned Wright's calculator has such an explanatory page, but does not calculate everything that Morgan's calculator calculates. Thus it is useful to document the formulas needed to calculate the extra quantities.
If we add the following eq's
[tex]
D_{then} =\frac{D_{now}}{z+1}
[/tex]
[tex]
H = \frac{\dot{a}}{a}
[/tex]
clarification: [itex]H_{then} = H [/itex] evaluated at [itex] a = \frac{1}{z+1}[/itex]
[tex]
V_{then} = H_{then} D_{then}
[/tex]
to Ned Wright's form of the Friedmann eq, i.e.
[tex]\dot{a} = H_0 \sqrt{\frac{\Omega_m}{a} + \frac{\Omega_r}{a^2} + \Omega_v a^2 + (1-\Omega_t)}
[/tex]
we have everything we need to calculate the additional information. (I have not repeated the information on how to calculate [itex]D_{now}[/itex], just added the information needed to calculate the 'extra' quantities that Morgan's calculator gives and Ned Wright's does not.)
We can safely set [itex]\Omega_r=0[/itex] as discussed for anything we can see (i.e. the equations will work to z=1100 and as an added bonus a fair ways beyond).
The results we get by doing this appear to agree with Morgan's results for the test case.
[add]The main motive for writing this out is that Morgan's calculator gives answers, but does not have an explanatory page for the formulas used. Ned Wright's calculator has such an explanatory page, but does not calculate everything that Morgan's calculator calculates. Thus it is useful to document the formulas needed to calculate the extra quantities.
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