Baryonic Acoustic Oscillations & Redshift Distortions

Synopsis:: BAO, f_sigma8 and other measurements at single redshifts, with correlations
Author:: Antony Lewis, Pablo Lemos (adapted to Cobaya by Jesus Torrado, with little modification)

This code provides a template for BAO, \(f\sigma_8\), \(H\) and other redshift-dependent functions.

Usage

To use any of these likelihoods, simply mention them in the likelihoods block, or add them using the input generator. For example:

likelihood:
  bao.desi_dr2

Please cite the relevant papers, for bibtex run e.g. cobaya-bib bao.desi_dr2.

These likelihoods have no nuisance parameters or particular settings that you may want to change.

Note that although called “bao”, some of these data combinations also include redshift distortion data (RSD), encapsulated via a single “f sigma8” parameter (which is not accurate for some non-LCDM models). The DESI likelihoods are all BAO-only.

Defining your own BAO likelihood

You can use the likelihood bao.generic as a template for any BAO data.

To do that, create a file containing the data points, e.g. myBAO.dat, as

[z] [value at z] [quantity]
...

where you can use as many different quantities and redshifts as you like.

The available quantities are

DV_over_rs: Spherically-averaged distance, over sound horizon radius
rs_over_DV: Idem, inverse
DM_over_rs: Comoving angular diameter distance, over sound horizon radius
DA_over_rs: Physical angular diameter distance, over sound horizon radius
Hz_rs: Hubble parameter, times sound horizon radius
f_sigma8: Differential matter linear growth rate, times amplitude of present-day fluctuations
F_AP: Anisotropy (Alcock-Paczynski) parameter

In addition create a file, e.g. myBAO.cov, containing the covariance matrix for those data, with the same row order as the data file.

Now, add to your likelihood block:

measurements_file: /full/path/to/myBAO.dat
cov_file: /full/path/to/myBAO.cov         # either this one,
invcov_file: /full/path/to/myBAO_inv.cov  # or this one!
# Fiducial sound horizon with which data have been stored
rs_fid:  #  in Mpc
# [Optional] Speed in evaluations/second
# (will be measured automatically if not specified)
speed: 2500

You can rename your BAO likelihood and use multiple ones with different data (see Custom names and multiple instances of the same internal class).

Installation

This likelihood can be installed automatically as explained in Installing cosmological codes and data.

Available internal likelihoods

bao.desi_2024_bao_all:
  DESI BAO likelihood for all tracers.

bao.desi_2024_bao_bgs_z1:
  DESI BAO likelihood for BGS_BRIGHT-21.5 in 0.1 < z < 0.4.

bao.desi_2024_bao_elg_z2:
  DESI BAO likelihood for ELG_LOPnotqso in 1.1 < z < 1.6.

bao.desi_2024_bao_lrg_z1:
  DESI BAO likelihood for LRG in 0.4 < z < 0.6.

bao.desi_2024_bao_lrg_z2:
  DESI BAO likelihood for LRG in 0.6 < z < 0.8.

bao.desi_2024_bao_lrgpluselg_z1:
  DESI BAO likelihood for LRG+ELG_LOPnotqso in 0.8 < z < 1.1.

bao.desi_2024_bao_lya:
  DESI BAO likelihood for Lya.

bao.desi_2024_bao_qso_z1:
  DESI BAO likelihood for QSO in 0.8 < z < 2.1.

bao.desi_2024_eboss_bao_lya:
  DESI BAO likelihood for Lya, in combination with eBOSS.

bao.desi_dr2.desi_bao_all:
  DESI BAO likelihood for all tracers \cite{DESI:2025zpo,DESI:2025zgx}. (bao.desi_dr2 is same as desi_bao_all)

bao.desi_dr2.desi_bao_bgs:
  DESI BAO likelihood for BGS_BRIGHT-21.35 \cite{DESI:2025zgx}.

bao.desi_dr2.desi_bao_elg2:
  DESI BAO likelihood for ELG_LOPnotqso in 1.1 < z < 1.6 \cite{DESI:2025zgx}.

bao.desi_dr2.desi_bao_lrg1:
  DESI BAO likelihood for LRG in 0.4 < z < 0.6 \cite{DESI:2025zgx}.

bao.desi_dr2.desi_bao_lrg2:
  DESI BAO likelihood for LRG in 0.6 < z < 0.8 \cite{DESI:2025zgx}.

bao.desi_dr2.desi_bao_lrg3pluselg1:
  DESI BAO likelihood for LRG+ELG_LOPnotqso \cite{DESI:2025zgx}.

bao.desi_dr2.desi_bao_lya:
  DESI BAO likelihood for Lya \cite{DESI:2025zpo}.

bao.desi_dr2.desi_bao_qso:
  DESI BAO likelihood for QSO \cite{DESI:2025zgx}.

bao.generic:
  Generic BAO likelihood, where you set the data and covariance matrix via the input
  yaml file.

bao.sdss_dr12_consensus_bao:
  Likelihood of the power spectrum BAO of SDSS DR12 \cite{Alam:2016hwk}.

bao.sdss_dr12_consensus_final:
  Likelihood of the combined power spectrum BAO and full-shape measurements of
  SDSS DR12 \cite{Alam:2016hwk}.

bao.sdss_dr12_consensus_full_shape:
  Likelihood of the full-shape measurements of SDSS DR12 \cite{Alam:2016hwk}.

bao.sdss_dr12_lrg_bao_dmdh:
  Likelihood of the power spectrum LRG BAO of SDSS DR12 \cite{Alam:2016hwk}.

bao.sdss_dr16_bao_elg:
  Likelihood of the ELG BAO from SDSS DR16 \cite{Alam:2020sor}.

bao.sdss_dr16_baoplus_elg:
  Likelihood of the power spectrum ELG BAO of SDSS DR16 \cite{Alam:2020sor}.

bao.sdss_dr16_baoplus_lrg:
  Likelihood of the power spectrum LRG BAO of SDSS DR16 \cite{Alam:2020sor}.
  As recommended in the official data release, it combines measurements
  of LRGs from eBOSS DR16 and BOSS DR12.

bao.sdss_dr16_baoplus_lyauto:
  Likelihood of the power spectrum Lyman alpha BAO of SDSS DR16 \cite{Alam:2020sor}.

bao.sdss_dr16_baoplus_lyxqso:
  Likelihood of the power spectrum Lya x QSO BAO of SDSS DR16 \cite{Alam:2020sor}.

bao.sdss_dr16_baoplus_qso:
  Likelihood of the power spectrum QSO BAO of SDSS DR16 \cite{Alam:2020sor}.

bao.sdss_dr16_lrg_bao_dmdh:
  Likelihood of the power spectrum LRG BAO of SDSS DR16 \cite{Alam:2020sor}.
  It does not include the DR12 measurements.

bao.sdss_dr16_qso_bao_dmdh:
  Likelihood of the QSO BAO from SDSS DR16 \cite{Alam:2020sor}.

bao.sdss_dr7_mgs:
  Likelihood of the BAO scale measurement of SDSS DR7 Main Galaxy Sample
  \cite{Ross:2014qpa}.

bao.sixdf_2011_bao:
  Likelihood of the BAO detection of the 6dF Galaxy Survey \cite{Beutler:2012px}.

Use cobaya-doc and cobaya-bib to see details for a given likelihood.