BAO and RSD

The connection between BAO and RSD

• 1. The BAO and RSD analyses are often performed together Bautista et al. (2021).
• 2. The RSD analysis can be thought of as an enhanced BAO analysis (ShapeFit).
• 3. The classic BAO and RSD analyses compress the power spectrum data into similar observables, such as $\alpha$, ${\alpha }_{\mathrm{\perp }}$, and $f{\sigma }_8$ (ShapeFit).
• 4. The classic approach treats $f{\sigma }_8$ as an independent quantity to be measured directly (ShapeFit).

Why the RSD analysis can be thought of as an enhanced BAO analysis.

• 1. The RSD signal is degenerated with the anisotropy generated by the Alcock-Paczynski effect, which is mainly driven by the detection of BAO. Therefore, the better the BAO is resolved, the better $f{\sigma }_8$ is measured Gil-Marín 2022.
• 2. RSD gives constraints on ${\mathrm{\Omega }}_m$ (through $f(z)$) which are superseded by the excellent precision of the ${\mathrm{\Omega }}_m$ determination from the Alcock-Paczyński effect of the BAO. This holds for any model leaving the late-time expansion history unchanged Schöneberg 2022

Some explanations

• 1. Alcock-Paczynski effect:

  When determining the redshift, a cosmology model should be assumed. Since you cannot assume a exactly correct cosmology model, the redshift you get is not exactly correct. The difference between the redshift you get and the real redshift is called Alcock-Paczynski effect.

• 2. BAO helps to resolve the Alcock-Paczynski effect:

  The BAO signal is degenerated with the Alcock-Paczynski effect. The scale of BAO is 150 Mpc, which can be used to reduce the Alcock-Paczynski effect.

• 3. RSD and Alcock-Paczynski effect are degenerated:

  The RSD signal originates from the peculiar velocity of galaxies. The peculiar velocity results in some distortion in the redshift space.