Cosmological inference with MBHB as standard sirens [4.5 yr]
FoM
- OK 0.03381509218036794 [0.25 0.05 0.01] : SO6 cosmography (best population) \(H_0\) error
\(\Delta H_0\) for realisation 0 of population Q3d (see below for details).
- OK 0.05888585412377217 [0.3 0.1 0.01] : SO6 cosmography (best population) \(\Omega_m\) error
\(\Delta \Omega_m\) for realisation 0 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 \(\Delta H_0\). | 0.603945 | 0.136085 | 0.484245 | 0.279034 | 4 |
| Pop3 median \(\Delta H_0\). | 0.591801 | 0.230237 | 0.508130 | 0.293545 | 3 |
| Pop3 highest\(\Delta H_0\). | 0.598886 | 0.233970 | 0.485422 | 0.283812 | 5 |
| Q3d lowest \(\Delta H_0\). | 0.745821 | 0.007906 | 0.211869 | 0.014871 | 3 |
| Q3d median \(\Delta H_0\). | 0.691434 | 0.033815 | 0.292481 | 0.058886 | 0 |
| Q3d highest\(\Delta H_0\). | 0.783902 | 0.072535 | 0.186327 | 0.093218 | 6 |
| Q3nd lowest \(\Delta H_0\). | 0.735367 | 0.039618 | 0.214748 | 0.081057 | 7 |
| Q3nd median \(\Delta H_0\). | 0.625987 | 0.141008 | 0.466625 | 0.278137 | 5 |
| Q3nd highest\(\Delta H_0\). | 0.564532 | 0.224900 | 0.478493 | 0.277583 | 1 |
We selected the population with the worst median \(H_0\) error and the corresponding realisation (realisation 3 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 0 for population Q3d) and use this realisation to compute the FOMs above and to produce the corner plot below.
