  Massive particles produced during inflation impact soft limits of primordial
correlators. Searching for these signatures presents an exciting opportunity to
uncover the particle spectrum in the inflationary epoch. We present
non-perturbative methods to constrain intermediate-mass scalars ($0\leq
m/H<3/2$, where $H$ is the inflationary Hubble scale) produced during
inflation, which give rise to a power-law scaling in the squeezed primordial
bispectrum. Exploiting the large-scale structure consistency relations and the
separate universe approach, we derive models for the late-time squeezed matter
bispectrum and collapsed matter trispectrum sourced by these fields. To
validate our models, we run $N$-body simulations with the "Cosmological
Collider" squeezed bispectrum for two different particle masses. Our models
yield unbiased constraints on the amplitude of non-Gaussianity, $f_{\rm
NL}^{\Delta}$, from the squeezed bispectrum and collapsed trispectrum deep into
the non-linear regime ($k_{\rm max}\approx 2~h/{\rm Mpc}$ at $z=0$). We assess
the information content of these summary statistics, emphasizing the importance
of sample variance cancellation in the matter sector. We also study the
scale-dependent halo bias in our simulations. For mass-selected halos, the
non-Gaussian bias estimated from our simulations agrees with predictions based
on (i) separate universe simulations and (ii) universal mass functions. With
further work, these results can be used to search for inflationary massive
particle production with upcoming galaxy surveys.
