Short GRB and binary black hole standard sirens as a probe of dark energy

TL;DR

This work analyzes gravitational-wave standard sirens from inspiraling binaries as a cosmological probe, emphasizing the need for electromagnetic redshift information to translate GW distance measurements into expansion history constraints. It considers short GRBs as low-to-intermediate redshift standard sirens detectable by a global ground-based GW network and LISA-detectable supermassive black-hole binaries, forecasting constraints on the Hubble constant and the dark-energy equation of state parameter w. Using Fisher-matrix techniques and realistic detector networks, the authors quantify distance errors and show how beaming and multi-detector geometry improve cosmological inferences; they find that ~600 Mpc GRB sirens can constrain h effectively, while ~100 SMBBHs with LISA could reach σ_w around a few percent, contingent on lensing and priors. The study highlights the synergy between GW measurements, EM counterparts, SN surveys, and CMB data, and discusses practical requirements such as detector overlap, GRB localization, and lensing mitigation for maximizing the cosmological impact of standard sirens.

Abstract

Observations of the gravitational radiation from well-localized, inspiraling compact object binaries can measure absolute source distances with high accuracy. When coupled with an independent determination of redshift through an electromagnetic counterpart, these standard sirens can provide an excellent probe of the expansion history of the Universe and the dark energy. Short gamma-ray bursts, if produced by merging neutron star binaries, would be standard sirens with known redshifts detectable by ground-based GW networks such as LIGO-II, Virgo, and AIGO. Depending upon the collimation of these GRBs, a single year of observation of their gravitational waves can measure the Hubble constant to about 2%. When combined with measurement of the absolute distance to the last scattering surface of the cosmic microwave background, this determines the dark energy equation of state parameter w to 9%. Similarly, supermassive binary black hole inspirals will be standard sirens detectable by LISA. Depending upon the precise redshift distribution, 100 sources could measure w at the 4% level.

Figures (5)

• Figure 1: Noise curve for the LIGO detectors, for initial (dotted) and advanced (solid) sensitivity.
• Figure 2: Distribution of measured distances for a source at $D=250$ Mpc, averaged over 100 source directions $\hat{\bm{n}}$ and orientations $\hat{\bm{L}}$. The solid curve shows constraints for randomly oriented sources, while the dashed curve shows constraints for collimated sources with $\sigma_v=0.05$.
• Figure 3: Fractional distance errors as a function of source distance $D$. The + symbols are for unbeamed GRBs, while circles are for $\sigma_v=0.05$. The two lines show the best-fit linear relations; note that there may be departures from linear scaling at the highest distances.
• Figure 4: Errors on $h$ and $w$ as a function of GRB exposure, assuming Planck-quality errors from CMB. Solid curves are for $\sigma_h$, the error on the Hubble constant, while dashed curves correspond to $\sigma_w$, for the dark energy equation of state parameter. The lower curves are for beamed GRBs with $\sigma_v=0.05$ while the upper curves are for unbeamed GRBs.
• Figure 5: LISA constraints on dark energy. The solid contours show the 68% and 95% confidence regions expected for a sample of 100 SMBBH sources observed by LISA, distributed with constant comoving density between $0<z<2$. A Planck prior also has been used on $\Omega_m h^2$ and $l_A$, as discussed in the text. The dotted contours correspond to a sample of 3000 SNe with intrinsic luminosity scatter of 10%, with redshift distribution $\propto \exp(-(z-0.5)^2)$ over $0.02<z<2$. The dashed (dark shaded) contour shows the 68% confidence region for the combined constraints GW+SNe+CMB.