# Joint cosmological inference of standard sirens and gravitational wave weak lensing

## TL;DR

This paper demonstrates a novel joint inference method combining standard sirens and gravitational wave weak lensing to improve cosmological parameter constraints without external priors, especially in a future post-LISA scenario.

## Contribution

It introduces the first combined analysis of standard sirens and gravitational wave weak lensing from the same dataset, enhancing constraints on cosmological parameters.

## Key findings

- Achieves 2-3% precision on dark matter and clustering parameters
- Constrains Hubble constant to better than 1%
- Provides independent cosmological constraints that could resolve existing tensions

## Abstract

We present the first joint inference of standard sirens and gravitational wave weak lensing by filtering of the same dataset. We imagine a post-LISA scenario emerging around the late 2030s when LISA will have accumulated a number of detections at high redshift; LIGO-VIRGO will have finished observing at low redshift, and Einstein Telescope will have started making new observations out to redshifts possibly overlapping with LISA. Euclid and other cosmological probes will have provided constraints at percent level by then, but mostly exhausted their ability to improve any further. We derive forecasts assuming $\sim1\,\text{deg}^{-2}$ detected sources, in conjunction with a spectroscopic follow-up (e.g. by Euclid, DESI, or ATHENA). Thanks to the statistical power of standard sirens as a geometry probe -- lifting key degeneracies in the gravitational wave weak lensing -- and no external priors assumed, the constraints on dark matter and its clustering, namely $\Omega_m$ and $\sigma_8$, could be achieved to $2\%$ and $3\%$. The Hubble constant could be constrained to better than $1\%$ in all cases; the dark energy density, $\Omega_\Lambda$, to $2\%$, and curvature, $\Omega_K$, to $0.02$; the amplitude and spectral tilt of the scalar fluctuations, $\ln(10^{10}A_s)$ and $n_s$, to $2\%$ and $7\%$. As a completely independent cosmological probe, with less calibration requirements, the joint inference of standard sirens and gravitational wave weak lensing might help solve the tensions currently observed between other cosmological probes, such as CMB, galaxy lensing, and Type Ia SNs, and distinguish between residual systematics and new physics.