Combinations of Standard Pings and Standard Candles: An Effective and Hubble Constant-free Probe of Dark Energy Evolution

On the basis of the theoretical predication that a small fraction of fast radio bursts (FRBs) might be associated with gravitational waves (GWs), Wei et al. proposed FRB/GW association systems, i.e., the joint measurement of dispersion measures (DM) of FRBs and luminosity distances D _L of GWs (the combination DM · D _L), as an effective complementary cosmic probe, which has the advantage of being independent of the Hubble constant H ₀. However, it is still unclear what the progenitor of FRBs is and whether a GW signal should be associated with them. In this paper, we propose that, with the fundamental assumption that luminosity distance is a monotonously increasing function of redshift, this DM · D _L method could be further extended to the combination of DM measurements of localized FRBs and independent D _L measurements of type Ia supernovae (SNe Ia) at similar redshifts. In practice, this extended combination, i.e., DM · D _L as a function of redshift from independent DM and D _L measurements, may be more applicable. In addition, we investigated the constraining power of this extended combination on dark energy evolution. It was obtained that, in the frame of the Chevalier–Polarski–Linder parameterization, the power of constraints on the dark energy equation of state from only ∼500 DM · D _L combinations is even stronger than the one from the currently available 1048 Pantheon SNe Ia. More interestingly, we also found that, compared with the popular luminosity distance–redshift relation alone, the combination DM · D _L, as a function of redshift, is more effective in constraining the parameter characterizing the evolution of dark energy. This benefit, along with rapid progress in the upcoming FRB observations, can be of great importance for studying the nature of dark energy.