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We investigate the gravitational effect of large-scale radiationperturbations on small-scale structure formation. In addition to making thegrowth of matter perturbations scale dependent, the free-streaming of radiationalso affects the coupling between structure formation at small and largescales. We study this using Separate Universe N-body simulations to compute the(isotropized) squeezed-limit matter bispectrum and the linear halo bias. Ourresults show that the scale dependence in the growth of long-wavelength matterperturbations, caused by radiation, translates into these quantities acquiringa non-trivial scale-dependence at $k\lesssim 0.05$ Mpc$^{-1}$. In a universewith radiation composed of cosmic microwave background photons and threespecies of massless neutrinos, the bias of halos with $b = 2$ at high $k$ willdecrease 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 objectswith $b\gg1$, these differences approach $0.43\%,\ 0.68\%$ and $1.2\%$respectively.

Scale-dependent halo bias and the squeezed limit bispectrum in the presence of radiation