Cosmological inference with MBHB as standard sirens [4.5 yr]
FoM
- OK 0.030643027679789877 [0.25 0.05 0.01] : SO6 cosmography (best population) \(H_0\) error
\(\Delta H_0\) for realisation 1 of population Q3d (see below for details).
- OK 0.036546541465806895 [0.3 0.1 0.01] : SO6 cosmography (best population) \(\Omega_m\) error
\(\Delta \Omega_m\) for realisation 1 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 4.5 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 \(\Delta H_0\). | 0.682610 | 0.130983 | 0.472121 | 0.262726 | 4 |
| Pop3 median \(\Delta H_0\). | 0.591234 | 0.228655 | 0.477129 | 0.286121 | 6 |
| Pop3 highest\(\Delta H_0\). | 0.610743 | 0.230022 | 0.506571 | 0.291853 | 5 |
| Q3d lowest \(\Delta H_0\). | 0.734909 | 0.008429 | 0.236392 | 0.016935 | 3 |
| Q3d median \(\Delta H_0\). | 0.777334 | 0.030643 | 0.185314 | 0.036547 | 1 |
| Q3d highest\(\Delta H_0\). | 0.685932 | 0.076711 | 0.317356 | 0.156401 | 6 |
| Q3nd lowest \(\Delta H_0\). | 0.545287 | 0.047736 | 0.988413 | 0.206814 | 9 |
| Q3nd median \(\Delta H_0\). | 0.635878 | 0.142594 | 0.457113 | 0.283351 | 5 |
| Q3nd highest\(\Delta H_0\). | 0.612908 | 0.226945 | 0.488084 | 0.286597 | 1 |
We selected the population with the worst median \(H_0\) error and the corresponding realisation (realisation 6 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 1 for population Q3d) and use this realisation to compute the FOMs above and to produce the corner plot below.
