I try to calculate the age of the universe with the FLRW model: H(a)=H0√ΩR,0(a0a)4+ΩM,0(a0a)3+(1−ΩT,0)(a0a)2+ΩΛ,0.
I set ΩM,0=0.317 (matter density) and ΩΛ,0=0.683 (dark energy), as delivered by Planck 2013; ΩT,0=1.02 (space curvature), according to this site; and ΩR,0=4.8×10−5 (radiation density), according to this document.
For the time t(a) I take the scale factor a and divide it through the integrated recessional velocity t(a)=a∫a0H(a′)a′ da′/(a−0) and finally simplify to t(a)=a2∫a0H(a′)a′ da′.
But the problem is, I then get about 8×109 years for the age of the universe, but it should be around 12×109 years (which I get when I set ΩR,0 to zero):
ΩR,0=4.8×10−5:
ΩR,0=0→0.00001:
Do I have to use some other models than FLRW/ΛCDM, or is one of my parameters outdated?
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