Multimessenger time delays from lensed gravitational waves

Abstract

We investigate the potential of high-energy astrophysical events, from which both massless and massive signals are detected, to probe fundamental physics. In particular, we consider how strong gravitational lensing can induce time delays in multi-messenger signals from the same source. Obvious messenger examples are massless photons and gravitational waves, and massive neutrinos, although more exotic applications can also be imagined, such as to massive gravitons or axions. The different propagation times of the massive and massless particles can, in principle, place bounds on the total neutrino mass and probe cosmological parameters. Whilst measuring such an effect may pose a significant experimental challenge, we believe that the 'massive time delay' represents an unexplored fundamental physics phenomenon.

Time delay of timelike particles in gravitational lensing of the Schwarzschild spacetime

“…The r 0 in Eq. (43), which was given by Eq. (40), can also be further simplified in the weak field limit.…”

“…Note that if the relativistic limit is taken, then the first term agrees with Eq. (19) of Ref [43]. at the O(1 − v) 1 order.…”

“…Ref. [43] studied the difference between time delay of massive neutrino and that of massless GW to place bounds on total neutrino mass and some cosmological parameters. We emphasize that our work is different from theirs in a few ways.…”

“…Ref. [42,43] which works only in the relativistic limit of the signal and weak field limit of the lens, we computed the exact total travel time that works for arbitrary velocity, i.e., velocities not very close to c. Secondly, even in the relativistic limit, the total time and time delay in these works are only to the order O(c − v) 1 while our approximation formulas can works to higher orders. Thirdly, we have computed two time delays, ∆t v due to velocity difference and ∆t p due to path difference, instead of only ∆t p .…”

The Legacy of Einstein’s Eclipse, Gravitational Lensing

“…The masses of left-handed neutrinos are so low (mν < 0.1 eV) that even over cosmological distances (z~5), the time delay is less than a second. If the signal were strong and clear, it might be possible to see the neutrinos arrive in narrowly spaced delays corresponding to mass [189].…”