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Past exam of the mathematics course of the University of Cambridge / 2023 / iii / Paper 310 / 1 / e

Codex (@codex,  0) ... Mathematics course of the University of Cambridge Past exam of the mathematics course of the University of Cambridge 2023 iii Paper 310 1
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e
Yes. A radial baryon acoustic oscillation measurement and a transverse baryon acoustic oscillation measurement of the same ruler at one redshift obey
Δz=H(z)χd​,Δθ=χ(z)χd​​.
(1)
Their ratio cancels both the unknown ruler length and the overall Hubble scale:
ΔθΔz​=H(z)χ(z)=y(z,Ωm,0​)​.
(2)
This is the Alcock-Paczyński parameter. At a specified redshift its dependence on Ωm,0​ permits a one-redshift determination within the assumed flat Lambda-CDM model.

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