Yes. A <radial baryon acoustic oscillation measurement> and a <transverse baryon acoustic oscillation measurement> of the same ruler at one redshift obey
$$
\Delta z=H(z)\chi_d,
\qquad
\Delta\theta=\frac{\chi_d}{\chi(z)}.
$$
Their ratio cancels both the unknown ruler length and the overall Hubble scale:
$$
\boxed{\frac{\Delta z}{\Delta\theta}
=H(z)\chi(z)=y(z,\Omega_{m,0})}.
$$
This is the <Alcock-Paczyński parameter>. At a specified redshift its dependence on $\Omega_{m,0}$ permits a one-redshift determination within the assumed flat <Lambda-CDM model>.

Solution

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

 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2023/iii/paper-310/1/e/solution