  We argue that massive quantum fields source low-frequency long-wavelength
metric fluctuations through the quantum fluctuations of their stress-energy,
given reasonable assumptions about the analytic structure of its correlators.
This can be traced back to the non-local nature of the gauge symmetry in
General Relativity, which prevents an efficient screening of UV scales (what we
call the cosmological non-constant problem). We define a covariant and
gauge-invariant observable which probes line-of-sight spacetime curvature
fluctuations on an observer's past lightcone, and show that current pulsar
timing data constrains any massive particle to $m\lesssim 600$ GeV. This
astrophysical bound severely limits the possibilities for physics beyond the
standard model below the scale of quantum gravity.
