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Abstract We present a detailed exposition of a statistical method for estimating cosmological parameters from the observation of a large number of strongly lensed binary-black-hole (BBH) mergers observable by next (third) generation (XG) gravitational-wave (GW) detectors. This method, first presented in Jana (2023Phys. Rev. Lett.130261401), compares the observed number of strongly lensed GW events and their time delay distribution (between lensed images) with observed events to infer cosmological parameters. We show that the precision of the estimation of the cosmological parameters does not have a strong dependance on the assumed BBH redshift distribution model. Using the large number of unlensed mergers, XG detectors are expected to measure the BBH redshift distribution with sufficient precision for the cosmological inference. However, a biased inference of the BBH redshift distribution will bias the estimation of cosmological parameters. An incorrect model for the distribution of lens properties can also lead to a biased cosmological inference. However, Bayesian model selection can assist in selecting the right model from a set of available parametric models for the lens distribution. We also present a way to incorporate the effect of contamination in the data due to the limited efficiency of lensing identification methods, so that it will not bias the cosmological inference. 

ABSTRACT Tidal interactions in coalescing binary neutron stars modify the dynamics of the inspiral and hence imprint a signature on their gravitational wave (GW) signals in the form of an extra phase shift. We need accurate models for the tidal phase shift in order to constrain the supranuclear equation of state from observations. In previous studies, GW waveform models were typically constructed by treating the tide as a linear response to a perturbing tidal field. In this work, we incorporate non-linear corrections due to hydrodynamic three- and four-mode interactions and show how they can improve the accuracy and explanatory power of waveform models. We set up and numerically solve the coupled differential equations for the orbit and the modes and analytically derive solutions of the system’s equilibrium configuration. Our analytical solutions agree well with the numerical ones up to the merger and involve only algebraic relations, allowing for fast phase shift and waveform evaluations for different equations of state over a large parameter space. We find that, at Newtonian order, non-linear fluid effects can enhance the tidal phase shift by $$\gtrsim 1\, {\rm radian}$$ at a GW frequency of 1000 Hz, corresponding to a $$10{{\%}}-20{{\%}}$$ correction to the linear theory. The scale of the additional phase shift near the merger is consistent with the difference between numerical relativity and theoretical predictions that account only for the linear tide. Non-linear fluid effects are thus important when interpreting the results of numerical relativity and in the construction of waveform models for current and future GW detectors. 

This review provides a conceptual and technical survey of methods for parameter estimation of gravitational-wave signals in ground-based interferometers such as Laser Interferometer Gravitational-Wave Observatory (LIGO) and Virgo. We introduce the framework of Bayesian inference and provide an overview of models for the generation and detection of gravitational waves from compact binary mergers, focusing on the essential features that are observable in the signals. Within the traditional likelihood-based paradigm, we describe various approaches for enhancing the efficiency and robustness of parameter inference. This includes techniques for accelerating likelihood evaluations, such as heterodyne/relative binning, reduced-order quadrature, multibanding, and interpolation. We also cover methods to simplify the analysis to improve convergence, via reparameterization, importance sampling, and marginalization. We end with a discussion of recent developments in the application of likelihood-free (simulation-based) inference methods to gravitational-wave data analysis.