  Einstein-dilaton-Gauss-Bonnet gravity is a theoretically well-motivated
alternative theory of gravity emerging as a low-energy 4-dimensional model from
heterotic string theory. Its rotating black hole solutions are known
numerically and can have macroscopic deviations from the Kerr black holes of
Einstein's gravity. Einstein-dilaton-Gauss-Bonnet gravity can thus be tested
with observations of astrophysical black holes. In the present paper, we
simulate observations of the reflection spectrum of thin accretion disks with
present and future X-ray facilities to understand whether X-ray reflection
spectroscopy can distinguish the black holes in Einstein-dilaton-Gauss-Bonnet
gravity from those in Einstein's gravity. We find that this is definitively out
of reach for present X-ray missions, but it may be achieved with the next
generation of facilities.
