  Large-scale extragalactic magnetic fields may induce conversions between
very-high-energy photons and axionlike particles (ALPs), thereby shielding the
photons from absorption on the extragalactic background light. However, in
simplified "cell" models, used so far to represent extragalactic magnetic
fields, this mechanism would be strongly suppressed by current astrophysical
bounds. Here we consider a recent model of extragalactic magnetic fields
obtained from large-scale cosmological simulations. Such simulated magnetic
fields would have large enhancement in the filaments of matter. As a result,
photon-ALP conversions would produce a significant spectral hardening for
cosmic TeV photons. This effect would be probed with the upcoming Cherenkov
Telescope Array detector. This possible detection would give a unique chance to
perform a tomography of the magnetized cosmic web with ALPs.
