# Precision cosmology from future lensed gravitational wave and electromagnetic signals

## TL;DR

This paper proposes a new method for precise cosmological measurements using strongly lensed gravitational wave and electromagnetic signals, reducing reliance on waveform details and calibration uncertainties, and demonstrating high accuracy with only ten systems.

## Contribution

It introduces a waveform-independent approach combining time delays and electromagnetic observations for cosmography, enhancing precision in measuring the Hubble constant.

## Key findings

- Ten lensed systems can determine the Hubble constant with 0.68% uncertainty.
- The method does not depend on waveform calibration, reducing systematic errors.
- Future detectors will detect thousands of such systems, enabling precise cosmology.

## Abstract

The standard siren approach of gravitational wave cosmology appeals to the direct luminosity distance estimation through the waveform signals from inspiralling double compact binaries, especially those with electromagnetic counterparts providing redshifts. It is limited by the calibration uncertainties in strain amplitude and relies on the fine details of the waveform. The Einstein Telescope is expected to produce $10^4-10^5$ gravitational wave detections per year, $50-100$ of which will be lensed. Here we report a waveform-independent strategy to achieve precise cosmography by combining the accurately measured time delays from strongly lensed gravitational wave signals with the images and redshifts observed in the electromagnetic domain. We demonstrate that just 10 such systems can provide a Hubble constant uncertainty of $0.68\%$ for a flat Lambda Cold Dark Matter universe in the era of third generation ground-based detectors.