Complementary constraints on dark energy equation of state from strongly lensed gravitational wave

Abstract

It has been shown that time delay of strong gravitational lensing is not only an effective cosmological probe to constrain the Hubble constant, the matter density and the curvature of the universe but also useful for breaking the degeneracy of the dark energy equation of state and thus provide complementarity with other popular probes, such as type Ia supernovae, baryon acoustic oscillations, and cosmic microwave background radiation. Interestingly, compared to traditional strong lensing systems where quasars act as sources, strongly lensed gravitational waves (GWs) from compact binary coalescence and their electromagnetic (EM) counterparts systems have been recently proposed to be more powerful for studying cosmology since GWs and their EM counterparts are transients. Short durations of GWs and their EM counterparts are very advantageous to time delay measurement and lens profile modeling. Here, in the framework of Chevalier-Polarski-Linder (CPL) parametrization, we investigate improvement of constraining power on dark energy equation of state due to including time delay measurements of strong lensed GW systems. It is suggested that, on the basis of the third generation ground-based detector, e.g. Einstein Telescope, adding time delay of only 30 strong lensed GW systems to type Ia supernovae and cosmic microwave background radiation can improve the dark energy figure of merit by a factor 2. For the traditional standard siren method where the uncertainties of luminosity distances of GWs are ∼ 10%, a few × 10 4 events are expected to present similar constraints. In the precision cosmology era, this progress is of great significance for studying the nature of dark energy.

Gravitational wave interference via gravitational lensing: Measurements of luminosity distance, lens mass, and cosmological parameters

“…where H 0 is the present-day Hubble constant, and Ω l are the density parameters for the radiation (l = r), the matter (l = m), the spatial curvature l = k and the dark energy l = Λ, respectively. Therefore, D ∆t could be used to constrain the cosmological parameters, especially the Hubble constant H 0 [29,51]. For this purpose, one has to use the electromagnetic follow-up observations to determine the host galaxy of the GW source and thus z S [18].…”

Investigating the dynamical models of cosmology with recent observations and upcoming gravitational-wave data

“…In this section, we briefly introduce the two typical dynamical models investigated in this work, including the ω 0 ω a CDM model which has been widely studies in previous works [28,29,26,30,31] and the ξ-index model which also has been studied with several different cosmological probes [32,33,34,35,36].…”

Probing modified gravitational wave propagation with strongly lensed coalescing binaries

“…The possibility of using strongly lensed GW events with an electromagnetic counterpart to perform cosmography has been discussed in [19,20], but BBH coalescences are not expected, in general, to have electromagnetic counterparts. However, as shown in [22], quadruply lensed events (which are estimated to be about 30% of the total lensed events at LIGO/Virgo, and 6% for ET [10]) are especially interesting, because they can be used as standard sirens even in the absence of an associated electromagnetic flare, by comparing the lensing pattern obtained from GW observations with that observed electromagnetically.…”

“…Just as for lensing of electromagnetic signals, which is now a standard tool in astrophysics [16,17], lensing of GWs could be used as a probe of several effects. In particular, the detection of multiply lensed GW events would provide a new tool for cosmography, allowing a measurement of the Hubble parameter H 0 and of the dark energy equation of state [18][19][20][21]. In this paper we explore another potentially very interesting application of strong lensing of GW events, to the study of modified GW propagation.…”