Cosmological inference with MBHB as standard sirens [4.5 yr]
FoM
- OK 0.03322547094028156 [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 0.04851927842913126 [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 \(\Delta H_0\). | 0.605951 | 0.130067 | 0.437177 | 0.254338 | 7 |
| Pop3 median \(\Delta H_0\). | 0.580869 | 0.228175 | 0.491119 | 0.286130 | 9 |
| Pop3 highest\(\Delta H_0\). | 0.604979 | 0.231057 | 0.481193 | 0.288493 | 3 |
| Q3d lowest \(\Delta H_0\). | 0.729886 | 0.008265 | 0.249207 | 0.017546 | 3 |
| Q3d median \(\Delta H_0\). | 0.745043 | 0.033225 | 0.236578 | 0.048519 | 1 |
| Q3d highest\(\Delta H_0\). | 0.628581 | 0.079160 | 0.422102 | 0.196871 | 6 |
| Q3nd lowest \(\Delta H_0\). | 0.558492 | 0.006192 | 0.989685 | 0.014729 | 9 |
| Q3nd median \(\Delta H_0\). | 0.608275 | 0.146747 | 0.448364 | 0.283446 | 0 |
| Q3nd highest\(\Delta H_0\). | 0.615710 | 0.227154 | 0.517033 | 0.282028 | 1 |
We selected the population with the worst median \(H_0\) error and the corresponding realisation (realisation 9 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.
