Cosmological
N
-body simulations are the standard tools 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 (
≡
photons and neutrinos). In this
Letter, we investigate novel hybrid simulations that 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
this work, we focus on simulations initialized at
z
=
99 and show that the extracted matter
power spectrum receives up to 3 per cent corrections on very large scales through radiation.
Our numerical findings compare favourably with linear analytical results from Fidler et al.,
from which we deduce that there cannot be any significant non-linear mode-coupling induced
through linear radiation corrections.