  Axion quark nuggets (AQNs) are hypothetical objects with a mass greater than
a few grams and sub-micrometer size, formed during the quark-hadron transition.
Originating from the axion field, they offer a possible resolution of the
similarity between visible and dark components of the Universe. These composite
objects behave as cold dark matter, interacting with ordinary matter and
resulting in pervasive electromagnetic radiation throughout the Universe. This
work aims to predict the electromagnetic signature in large-scale structures
from the AQN-baryon interaction, accounting for thermal and non-thermal
radiations. We use Magneticum hydrodynamical simulations to describe the
distribution and dynamics of gas and dark matter at cosmological scales. We
calculate the electromagnetic signature from radio, starting at $\nu \sim$ 1
GHz, up to a few keV X-ray energies. We find that the AQNs signature is
characterized by monopole and fluctuation signals. The amplitude of both
signals strongly depends on the average AQN mass and the ionization level of
the baryonic environment. We identify a most optimistic scenario with a signal
often near the sensitivity limit of existing instruments, such as FIRAS and the
South Pole Telescope for high-resolution. Fluctuations in the Extra-galactic
Background Light caused by the AQN can be tested with space-based imagers
Euclid and James Webb Space Telescope. We also identify a minimal
configuration, still out of reach of existing instruments, but future
experiments might be able to pose constraints on the AQN model. We conclude
that this is a viable dark matter model, which does not violate the canons of
cosmology, nor existing observations. The best chances for testing this model
reside in 1) ultra-deep IR and optical surveys, 2) spectral distorsions of the
CMB and 3) low-frequency (1 GHz < $\nu $ < 100 GHz) and high-resolution ($\ell
> 10^4$) observations.
