Cosmology and modified GW propagation from the BNS mass function at third-generation detector networks

Abstract

We perform forecasts for the Hubble parameter H_0 and for the parameter Xi_0 that describes modified gravitational-wave propagation, using information from the binary neutron star (BNS) mass function, for Einstein Telescope (ET), taken either in the triangle or in the ``2L'' configuration, as well as for detector network made by ET together with a 40-km Cosmic Explorer (CE). We restrict ourselves to BNSs with a large signal-to-noise ratio, SNR>50, which still give O(10^3) events yr-1, and we perform a full joint cosmology-population Bayesian inference. We find that, for ET in isolation, the two ET configurations perform comparably, yielding uncertainties of 12% and 11% on H_0 for the triangular and 2L designs, respectively, and 18% uncertainty on Xi_0 in both cases. For networks including ET and CE, we can constrain H_0 and Xi_0 to precisions of 9% and 6%, respectively. These results should be taken as a very conservative estimate of third-generation detectors' capabilities as a consequence of the high SNR cut. We project the constraints on the Lambda CDM expansion history and find that ET alone (triangular and 2L configurations) achieves its best precision on H(z) at z=0.23 and z=0.28, yielding a 10% and 6% precision, respectively. When CE is added to the network, the precision improves to 4% and 3% at z=0.37 and z=0.38, respectively.

Figures (6)

• Figure 1: The distribution in redshift of the observed BNSs, for different cuts on the network SNR, for a network ET-2L+CE-40km. The black curve is the full injected BNS population, while the colored curves show the distribution of the events recovered with a given SNR threshold. In particular, the green-filled histogram represents the employed dataset.
• Figure 2: Posterior distributions for $H_0$ (left) and $\Xi_0$ (right) marginalized over the other hyper-parameters for the four networks considered. The black dotted line shows the fiducial values as referenced in table \ref{['Table:priors']}. The posteriors are smoothed using a kernel distribution estimate.
• Figure 3: Posterior distributions of the parameters shown at the bottom for the ET-$\Delta$ and ET-2L network configurations. Contour shades represent, from dark to light, $1\sigma$ and $2\sigma$ credible regions. The black lines refer to the fiducial values. $\Xi_0$, $n$ (left) and $H_0$, $\Omega_{\rm M}$ (right) are fixed to their fiducial values.
• Figure 4: Posterior distribution of the parameters shown at the bottom for the ET-$\Delta$+CE and ET-2L+CE network configurations. Contour shades represent, from dark to light, $1\sigma$ and $2\sigma$ credible regions. The black lines refer to the fiducial values. $\Xi_0$, $n$ (left) and $H_0$, $\Omega_{\rm M}$ (right) are fixed to their fiducial values.
• Figure 5: Constraints on the Hubble parameter $H(z)$ (top row) and its relative precision as defined in footnote \ref{['foot:accuracy']} as a function of redshift (bottom row), for the configurations labeled at the top of each column. In the top row panels the shaded regions refer to the 68% c.l., while the solid-orange (dotted-black) line labels the median (fiducial) curve.