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

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 $klesssim 0.05$ 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 $bgg1$, these differences approach $0.43%, 0.68%$ and $1.2%$ respectively.