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Gamma-ray observations of blazars and the intergalactic magnetic field spectrum

Very-high energy observations of blazars can be used to constrain the strength of the intergalactic magnetic field. A simplifying assumption which is often made is that of a magnetic field of constant strength composed by randomly oriented and identical cells. In this paper, we demonstrate that a more realistic description of the structure of the intergalactic magnetic field is indeed needed. If such a description is adopted, the observational bounds on the field strength are significantly affected in the limit of short field correlation lengths: in particular, they acquire a dependence on the magnetic field power spectrum. In the case of intergalactic magnetic fields which are generated causally, for which the magnetic field large scale spectral index is $n_B\geq 2$ and even, the observational lower bound becomes more constraining by about a factor 3. If instead $-3<n_B<-2$, the lower bound is significantly relaxed. Such magnetic fields with very red spectra can in principle be produced during inflation, but remain up to now speculative.