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.
