  The reduced speed of light approximation is used in a variety of simulations
of the epoch of reionization and galaxy formation. Its popularity stems from
its ability to drastically reduce the computing cost of a simulation, by
allowing the use of larger, and therefore fewer timesteps to reach a solution.
It is physically motivated by the fact that ionization fronts rarely propagate
faster than some fraction of the speed of light. However, no global proof of
the physical validity of this approach is available, and possible artefacts
resulting from this approximation therefore need to be identifited and
characterized to allow its proper use. In this paper we investigate the impact
of the reduced speed of light approximation on the predicted properties of the
intergalactic medium. To this end we use fully coupled radiation-hydrodynamics
RAMSES-CUDATON simulations of the epoch of reionization. We find that reducing
the speed of light by a factor 5 (20, 100) leads to overestimating the
post-reionization volume-weighted $x_{HI}$ by a similar factor ~5 (20, 100)
with respect to full speed of light simulations. We show that the error is
driven by the hydrogen - photon chemistry. In photo-ionization equilibrium,
reducing the speed of light has the same effect as artificially reducing the
photon density or the reaction cross-section and leads to an underestimated
ionizing flux. We confirm this interpretation by running additional simulations
using a reduced speed of light in the photon propagation module, but keeping
this time the full speed of light in the chemistry module. With this setup, the
post-reionization neutral hydrogen fractions converge to the full speed of
light value, which validates our explanation. Increasing spatial resolution
beyond a cell size of 1 kpc physical, so as to better resolve Lyman-limit
systems, does not significantly affect our conclusions.
