Multi-messenger standard-siren cosmology for third-generation gravitational-wave detectors: forecasts considering observations of gamma-ray bursts and kilonovae

Abstract In the third-generation (3G) gravitational-wave (GW) detector era, GW multi-messenger observations for binary neutron star merger events can exert significant effects on exploring the cosmic expansion history. Extending a previous work, we explore the potential of 3G GW standard siren observations in cosmological parameter estimation by considering their associated electromagnetic (EM) counterparts, including $$\gamma $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>γ</mml:mi> </mml:math> -ray burst (GRB) coincidence observations by the Gravitational Wave High-energy Electromagnetic Counterpart All-sky Monitor and GW-triggered target-of-opportunity observations of kilonovae by different optical survey projects. During an assumed 10-year observation, we predict that the number of detectable GW-kilonova events is $$\sim 4900$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mo>∼</mml:mo> <mml:mn>4900</mml:mn> </mml:mrow> </mml:math> with redshifts below $$\sim 0.4$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mo>∼</mml:mo> <mml:mn>0.4</mml:mn> </mml:mrow> </mml:math> under the GW detector network and Large Synoptic Survey Telescope in the i band, which is more than three times that of GW-GRB detections. For the cosmological analysis, we find that with the inclusion of GW-kilonova detections, the constraints on cosmological parameters from GW-EM detections are significantly improved compared to those from GW-GRB detections. In particular, GW-EM detections can tightly constrain the Hubble constant with precision ranging from $$0.076\%$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mn>0.076</mml:mn> <mml:mo>%</mml:mo> </mml:mrow> </mml:math> to $$0.034\%$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mn>0.034</mml:mn> <mml:mo>%</mml:mo> </mml:mrow> </mml:math> . Moreover, GW multi-messenger observations can effectively break the cosmological parameter degeneracies generated by the typical EM observations, CMB+BAO+SN (CBS). The combination of CBS and GW-EM can tightly constrain the equation-of-state parameters of dark energy w in the w CDM model and $$w_0$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>w</mml:mi> <mml:mn>0</mml:mn> </mml:msub> </mml:math> in the $$w_0w_a$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>w</mml:mi> <mml:mn>0</mml:mn> </mml:msub> <mml:msub> <mml:mi>w</mml:mi> <mml:mi>a</mml:mi> </mml:msub> </mml:mrow> </mml:math> CDM model with precision of $$0.72\%$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mn>0.72</mml:mn> <mml:mo>%</mml:mo> </mml:mrow> </mml:math> and $$0.99\%$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mn>0.99</mml:mn> <mml:mo>%</mml:mo> </mml:mrow> </mml:math> , respectively, meeting the standard of precision cosmology. In conclusion, GW multi-messenger observations could play a crucial role in helping solve the Hubble tension and probing the fundamental nature of dark energy.