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What is the difference between FRW and LCDM models
 
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Noble P Abraham



Joined: 31 Jul 2008
Posts: 9
Affiliation: School of Pure and Applied Physics, Mahatma Gandhi University, Kottayam

PostPosted: March 05 2010  Reply with quote

Please help me, what is the difference between the following dL relations

1. FRW model
d_L=5 \mbox{log} \left( (1+z) \frac{c}{H_0} |\Omega_k|^{-1/2}\ \mbox{Sinn} \left[ \ |\Omega_k|^{1/2} \int _{0}^{z} [(1+z^{\prime })^{2}(1+\Omega_{m}z^{\prime})-z^{\prime}(2+z^{\prime} )(\Omega _{\Lambda})]^{-1/2}\;  dz^{\prime} \right] \right)
where
Ωk = 1 − Ωm − ΩΛ
Sinn(x) = Sin(x) for Ωm + ΩΛ > 1
Sinn(x) = Sinh(x) for Ωm + ΩΛ < 0
and
Sinn(x) = x for Ωm + ΩΛ = 1
(From Moncy & Narlikar, astro-ph/0111122, Drell et. al., astro-ph/9905027)

2. ΛCDM model
d_L=5 \mbox{log} \left( (1+z) \frac{c}{H_0} |\Omega_k|^{-1/2}\ \mbox{Sinn} \left[ \ |\Omega_k|^{1/2} \int _{0}^{z} [\Omega_m (1+z^{\prime }) ^3+\Omega_k (1+z^{\prime })^2+\Omega_\Lambda]^{-1/2}\;  dz^{\prime} \right] \right)

where
\Omega_k=\frac{k}{H_0 ^2}
Sinn(x) = Sin(x) for k > 0
Sinn(x) = Sinh(x) for k < 0
and
Sinn(x) = x for k = 0

(From Szydlowski and Godlowski, astro-ph/0509415)

Can I put Ωk = 1 − Ωm − ΩΛ in the second case (ΛCDM) as well?

Kindly treat me as a beginner and correct me.
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Ben Gold



Joined: 25 Sep 2004
Posts: 97
Affiliation: University of Minnesota

PostPosted: March 06 2010  Reply with quote

Quote:
Can I put Ωk = 1 − Ωm − ΩΛ in the second case (ΛCDM) as well?


Yes, if you do that and perform some algebra you should find that they're exactly the same equation.
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