The Effect of Gravitational Lensing on Fast Transient Event Rates

Abstract: Fast cosmological transients such as fast radio bursts (FRBs) and gamma-ray bursts (GRBs) represent a class of sources more compact than any other cosmological object. As such they are sensitive to significant magnification via gravitational lensing from a class of lenses which are not well-constrained by observations today. Low-mass primordial black holes are one such candidate which may constitute a significant fraction of the Universe's dark matter. Current observations only constrain their density in the nearby Universe, giving fast transients from cosmological distances the potential to form complementary constraints. Motivated by this, we calculate the effect that gravitational lensing from a cosmological distribution of compact objects would have on the observed rates of FRBs and GRBs. For static lensing geometries, we rule out the prospect that all FRBs are gravitationally lensed for a range of lens masses and show that lens masses greater than $10<sup>{-5}M_\odot$ can be constrained with 8000 un-localised high fluence FRBs at 1.4GHz, as might be detected by the next generation of FRB-finding telescopes.