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

$\mathrm{\Delta }{H}_0$ for realisation 3 of population Q3d (see below for details).

- OK 0.02595201276257492 [0.3 0.1 0.01] : SO6 cosmography (best population) ${\mathrm{\Omega }}_m$ error

$\mathrm{\Delta }{\mathrm{\Omega }}_m$ 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 $\mathrm{\Delta }\mathrm{\Omega }<10$, we generated 32000 MCMC samples for the $H_0$ and ${\mathrm{\Omega }}_m$ 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	${\mathrm{\Omega }}_m$ median	${\mathrm{\Omega }}_m$ err	Realisation id
Pop3 lowest $\mathrm{\Delta }{H}_0$.	0.730029	0.128924	0.562261	0.237805	0
Pop3 median $\mathrm{\Delta }{H}_0$.	0.583235	0.224178	0.470087	0.282816	5
Pop3 highest$\mathrm{\Delta }{H}_0$.	0.482467	0.248464	0.453331	0.304275	9
Q3d lowest $\mathrm{\Delta }{H}_0$.	0.732217	0.007769	0.251282	0.014865	7
Q3d median $\mathrm{\Delta }{H}_0$.	0.726672	0.016320	0.263026	0.025952	3
Q3d highest$\mathrm{\Delta }{H}_0$.	0.538528	0.097579	0.990048	0.319700	6
Q3nd lowest $\mathrm{\Delta }{H}_0$.	0.746312	0.029089	0.229889	0.055876	3
Q3nd median $\mathrm{\Delta }{H}_0$.	0.596456	0.129527	0.462082	0.279821	9
Q3nd highest$\mathrm{\Delta }{H}_0$.	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.

Detailed results

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