Cosmological $N$-body simulations including radiation perturbations
  Cosmological $N$-body simulations are the standard tool to study the
emergence of the observed large-scale structure of the Universe. Such
simulations usually solve for the gravitational dynamics of matter within the
Newtonian approximation, thus discarding general relativistic effects such as
the coupling between matter and radiation ($\equiv$ photons and neutrinos). In
this paper we investigate novel hybrid simulations which incorporate
interactions between radiation and matter to the leading order in General
Relativity, whilst evolving the matter dynamics in full non-linearity according
to Newtonian theory. Our hybrid simulations come with a relativistic space-time
and make it possible to investigate structure formation in a unified framework.
In the present work we focus on simulations initialized at $z=99$, and show
that the extracted matter power spectrum receives up to $3\%$ corrections on
very large scales through radiation. Our numerical findings compare favourably
with linear analytical results from Fidler et al. (2016), from which we deduce
that there cannot be any significant non-linear mode-coupling induced through
linear radiation corrections.
