Strongly lensed repeating fast radio bursts as precision probes of the universe

Abstract

Fast radio bursts (FRBs), bright transients with millisecond durations at ∼GHz and typical redshifts probably >0.8, are likely to be gravitationally lensed by intervening galaxies. Since the time delay between images of strongly lensed FRB can be measured to extremely high precision because of the large ratio ∼10⁹ between the typical galaxy-lensing delay time [Formula: see text] (10 days) and the width of bursts [Formula: see text] (ms), we propose strongly lensed FRBs as precision probes of the universe. We show that, within the flat ΛCDM model, the Hubble constant H₀ can be constrained with a ~0.91% uncertainty from 10 such systems probably observed with the square kilometer array (SKA) in <30 years. More importantly, the cosmic curvature can be model independently constrained to a precision of ∼0.076. This constraint can directly test the validity of the cosmological principle and break the intractable degeneracy between the cosmic curvature and dark energy.

Fig. 1

Probability distribution functions (PDFs) of the Hubble constant constrained from 10 lensed FRBs and some other currently available observations. Besides the result obtained from 10 lensed FRB systems in this work (the black solid line), from top to bottom the lines represent H₀ inferred from the Planck satellite CMB measurements (67.27 ± 0.66 km s⁻¹ Mpc⁻¹) , local distance measurements (73.24 ± 1.74 km s⁻¹ Mpc⁻¹), time-delay cosmography of strongly lensed quasars $\left(71.9_{-3.0}^{+2.4}\mathrm{km}{\mathrm{s}}^{-\mathrm{1}}{\mathrm{Mpc}}^{-\mathrm{1}}\right)$, distance measurements from the Hubble Space Telescope (HST) key project (74.3 ± 2.6 km s⁻¹ Mpc⁻¹), and VLBI observations of water masers orbiting within the accretion disc of UCG 3789 (71.6 ± 5.7 km s⁻¹ Mpc⁻¹), respectively

Fig. 2

Model-independent probability distribution functions (PDFs) of the cosmic curvature estimated from 10 lensed FRBs and some other currently available observations. Besides the result obtained from 10 lensed FRB systems in this work (the black solid line), from top to bottom the lines are Ω_k inferred from the integral method with expansion rate (i.e., the Hubble parameter H(z)) and SNe Ia observations (−0.140 ± 0.161), the integral method with expansion rate and BAO observations (−0.09 ± 0.19), distance sum rule with the prior ${\Omega }_k>-0.1\left(0.25_{-0.33}^{+0.72}\right)$, distance sum rule without the prior ${\Omega }_k>-0.1\left(-0.38_{-0.84}^{+1.01}\right)$, and the differential approach with the expansion rate and SNe Ia observations $\left(-0.50_{-0.36}^{+0.54}\right)$, respectively

Fig. 3

Left: Simulation results based on HST, WFC3/F160w with image drizzled to 0.08′′. Middle: Best-fit image. Right: Residual map

Fig. 4

The contours of parameters inferred from the MCMC technique. The demonstrated parameters are the Einstein radius R_ein (in units of arcsecond), power-law mass profile slope γ, and differences of Fermat potentials between each pair of images. Note that Fermat potentials have no units, and we have re-scaled their values to better present the uncertainty level

Fig. 5

Results of the simulation tests by generating the lensed arc with a power-law mass distribution model but fitting with the Jaffe model

Fig. 6

The reduced χ² values by fitting the mock data with true model (i.e., power-law) and the wrong model (i.e., Jaffe) when varying the exposure time from 1000 to 10,000 s