Weak lensing of bright standard sirens: prospects for $σ_8$

Abstract

Gravitational wave events with electromagnetic counterparts provide direct measurements of the Hubble diagram. We demonstrate that incorporating weak lensing into bright standard siren analyses allows measurements of cosmological parameters that do not influence the mean luminosity distance-redshift relation but do impact the cosmic structures. In particular, we examine the prospects for measuring the standard deviation of matter perturbations $σ_8$, in addition to the Hubble constant and the matter abundance. We find that a $10\%$ measurement of $σ_8$ would be feasible with ET, provided a population of $300$ neutron star binaries with electromagnetic counterparts is observed. With LISA, the measurement of $σ_8$ would have $30\%$ accuracy, assuming a population of $12$ massive black hole binaries with electromagnetic counterparts is observed.

Figures (5)

• Figure 1: The PDF of lenses for sources at $z_s = 5$, integrated over the transverse distance $r$. In the purple region $r_{\rm max} = 0$.
• Figure 2: The PDF of lensing magnifications for different source redshifts for the Planck 2018 values of the cosmological parameters.
• Figure 3: The variance of luminosity distances induced by weak lensing in various approximations of the lens population. For comparison, the dashed curve shows the result of Takahashi:2011qd. The open symbols depict the numerical results, while the curves illustrate the fit using the ansatz \ref{['eq:sigmaDfit']}.
• Figure 4: The solid curve shows the true luminosity distance-redshift relation $\tilde{D}_L(z)$, while the surrounding gray band indicates 99% range of the apparent luminosity distances. The points represent a benchmark catalogue of 500 NS binaries and 10 MBH binaries.
• Figure 5: Posteriors of the Hubble diagram reconstruction from the catalogues shown in Fig. \ref{['fig:catalogue']}. The contours indicate the 68% and 95% credible regions. The dashed lines indicate the benchmark parameter values used to generate the catalogues.