Probing beyond-$\Lambda$CDM cosmology with Gravitational Waves

The propagation of Gravitational Waves has been reliably recognised as a test-bed for beyond standard models of gravity and cosmology. We utilise this property to examine the effects of a class of parametrised beyond-$\Lambda$CDM cosmology on inferece of GW parameters. We find that the combined beyond-$\Lambda$CDM likelihood function exhibits correlations between the parameters which are especially dependent upon binary eccentricity. Expanding on previous results, we demonstrate through Fisher forecasts that we would need nearly 1 year of 3G GW data to be able to infer the beyond-$\Lambda$CDM model to $2\sigma$ significance. We also find counter-intuitively that errors of source-modelling leave large biases upon the inference of the beyond-$\Lambda$CDM parameters which come into play only during GW propagation.