Combining strongly lensed and unlensed fast radio bursts: To be a more precise late-universe probe

The Macquart relation and time-delay cosmography are now two promising ways to fast radio burst (FRB) cosmology. In this work, we propose a joint method that combines strongly lensed and unlensed FRBs for improving cosmological parameter estimation using simulated FRB data from the future sensitive coherent all-sky monitor survey, which is expected to detect a large number of FRBs including galaxy-galaxy strongly lensed events. We find that using a detectable sample of 100000 localized FRBs including 40 lensed events can simultaneously constrain the Hubble constant and the equation of state of dark energy, with high precision of ε(H₀) = 0.4% and ε(w) = 4.5% in the simplest dynamical dark energy model. The joint analysis of unlensed and lensed FRBs significantly improves the constraint on H₀, which could be more effective than combining either the unlensed FRBs with future gravitational wave (GW) standard sirens or the lensed FRBs with CMB. Furthermore, combining the full FRB sample with the CMB+BAO+SNe data yields σ(H₀) = 0.29 km s⁻¹ Mpc⁻¹, σ(w₀) = 0.046, and σ(w_a) = 0.15 in the two-parameter dynamical dark energy model, which outperforms the results from the CMB+BAO+SNe+GW data. This reinforces the cosmological implications of a multi-wavelength observational strategy in optical and radio bands. We conclude that the future FRB observations will shed light on the nature of dark energy and also the Hubble tension if enough events with long-duration lensing are incorporated.