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Active galactic nuclei (AGN) produce a dominant fraction  ( F  AGN ∼ 80 per cent)  of the soft X‐ray background (SXB) at photon energies  0.5 &lt;  E  &lt; 2 keV . If dust pervaded throughout the intergalactic medium, its scattering opacity would have produced diffuse X‐ray haloes around AGN. Taking account of known galaxies and galaxy clusters, only a fraction   F  halo ≲ 10 per cent  of the SXB can be in the form of diffuse X‐ray haloes around AGN. We therefore limit the intergalactic opacity to optical/infrared photons from large dust grains, with radii in the range   a = 0.2–2.0 μm , to a level  τ GD ≲ 0.15( F  halo /10 per cent)(F AGN /80 per cent) −1   to a redshift   z ∼ 1 . Our results are only weakly dependent on the grain size distribution in this size range or the redshift evolution of the intergalactic dust. Stacking X‐ray images of AGN can be used to improve our constraints and diminish the importance of dust as a source of systematic uncertainty for future supernova surveys which aim to improve the precision on measuring the redshift evolution of the dark energy equation‐of‐state.

Upper limit on dimming of cosmological sources by intergalactic grey dust from the soft X‐ray background