  We investigate the gravitational effect of large-scale radiation
perturbations on small-scale structure formation. In addition to making the
growth of matter perturbations scale dependent, the free-streaming of radiation
also affects the coupling between structure formation at small and large
scales. We study this using Separate Universe N-body simulations to compute the
(isotropized) squeezed-limit matter bispectrum and the linear halo bias. Our
results show that the scale dependence in the growth of long-wavelength matter
perturbations, caused by radiation, translates into these quantities acquiring
a non-trivial scale-dependence at $k\lesssim 0.05$ Mpc$^{-1}$. In a universe
with radiation composed of cosmic microwave background photons and three
species of massless neutrinos, the bias of halos with $b = 2$ at high $k$ will
decrease by $0.29\%,\ 0.45\%$ and $0.8\%$ between $k = 0.05$ Mpc$^{-1}$ and $k
= 0.0005$ Mpc$^{-1}$ at redshifts $z=0,\ 1$, and $3$ respectively. For objects
with $b\gg1$, these differences approach $0.43\%,\ 0.68\%$ and $1.2\%$
respectively.
