Weak lensing effects in the measurement of the dark energy equation of state with LISA

TL;DR

This paper assesses how weak lensing impacts the precision of measuring the dark energy equation of state using LISA's observations of supermassive binary black holes, highlighting the need for lensing mitigation.

Contribution

It provides an in-depth analysis of the effects of weak lensing on parameter estimation for dark energy measurements with LISA, including sky localization and redshift determination.

Findings

Weak lensing significantly degrades the accuracy of $w$ measurement.

Most SMBBH mergers allow for sky localization and redshift measurement.

Lensing mitigation methods are necessary to fully utilize LISA's potential.

Abstract

The Laser Interferometer Space Antenna's (LISA's) observation of supermassive binary black holes (SMBBH) could provide a new tool for precision cosmography. Inclusion of sub-dominant signal harmonics in the inspiral signal allows for high-accuracy sky localization, dramatically improving the chances of finding the host galaxy and obtaining its redshift. A SMBBH merger can potentially have component masses from a wide range ($10^5 - 10^8\,\Ms$) over which parameter accuracies vary considerably. We perform an in-depth study in order to understand (i) what fraction of possible SMBBH mergers allow for sky localization, depending on the parameters of the source, and (ii) how accurately $w$ can be measured when the host galaxy can be identified. We also investigate how accuracies on all parameters improve when a knowledge of the sky position can be folded into the estimation of errors. We find that $w$ can be measured to within a few percent in most cases, if the only error in measuring the luminosity distance is due to LISA's instrumental noise and the confusion background from Galactic binaries. However, weak lensing-induced errors will severely degrade the accuracy with which $w$ can be obtained, emphasizing that methods to mitigate weak lensing effects would be required to take advantage of LISA's full potential.