Cosmological inference with MBHB as standard sirens [7.5 yr]
FoM
- OK 0.016320381194493735 [0.25 0.05 0.01] : SO6 cosmography (best population) \(H_0\) error
\(\Delta H_0\) for realisation 3 of population Q3d (see below for details).
- OK 0.02595201276257492 [0.3 0.1 0.01] : SO6 cosmography (best population) \(\Omega_m\) error
\(\Delta \Omega_m\) for realisation 3 of population Q3d (see below for details).
Summary
We took a catalog of MBHB events (for the populations Pop3, Q3d, Q3nd) and, for each population, build 10 realisation of standard sirens (events with EM conterpart) for a mission duration of 7.5 years. We then computed the errors in parameter estimation for each realisation source, and, for sources with \(\Delta \Omega < 10\), we generated 32000 MCMC samples for the \(H_0\) and \(\Omega_m\) cosmological parameters. For each population we selected the realisation with the best, the worst and the median error on the \(H_0\) parameter. The table is reported below.
| Realisation | \(H_0\) median | \(H_0\) error | \(\Omega_m\) median | \(\Omega_m\) err | Realisation id |
|---|---|---|---|---|---|
| Pop3 lowest \(\Delta H_0\). | 0.730029 | 0.128924 | 0.562261 | 0.237805 | 0 |
| Pop3 median \(\Delta H_0\). | 0.583235 | 0.224178 | 0.470087 | 0.282816 | 5 |
| Pop3 highest\(\Delta H_0\). | 0.482467 | 0.248464 | 0.453331 | 0.304275 | 9 |
| Q3d lowest \(\Delta H_0\). | 0.732217 | 0.007769 | 0.251282 | 0.014865 | 7 |
| Q3d median \(\Delta H_0\). | 0.726672 | 0.016320 | 0.263026 | 0.025952 | 3 |
| Q3d highest\(\Delta H_0\). | 0.538528 | 0.097579 | 0.990048 | 0.319700 | 6 |
| Q3nd lowest \(\Delta H_0\). | 0.746312 | 0.029089 | 0.229889 | 0.055876 | 3 |
| Q3nd median \(\Delta H_0\). | 0.596456 | 0.129527 | 0.462082 | 0.279821 | 9 |
| Q3nd highest\(\Delta H_0\). | 0.413650 | 0.199014 | 0.285729 | 0.275513 | 6 |
We selected the population with the worst median \(H_0\) error and the corresponding realisation (realisation 5 for population Pop3) and use this realisation to produce the corner plot below.
We then selected the population with the best median \(H_0\) error and the corresponding realisation (realisation 3 for population Q3d) and use this realisation to compute the FOMs above and to produce the corner plot below.
