  We search for evidence of dark matter (DM) annihilation in the isotropic
gamma-ray background (IGRB) measured with 50 months of Fermi Large Area
Telescope (LAT) observations. An improved theoretical description of the
cosmological DM annihilation signal, based on two complementary techniques and
assuming generic weakly interacting massive particle (WIMP) properties, renders
more precise predictions compared to previous work. More specifically, we
estimate the cosmologically-induced gamma-ray intensity to have an uncertainty
of a factor ~20 in canonical setups. We consistently include both the Galactic
and extragalactic signals under the same theoretical framework, and study the
impact of the former on the IGRB spectrum derivation. We find no evidence for a
DM signal and we set limits on the DM-induced isotropic gamma-ray signal. Our
limits are competitive for DM particle masses up to tens of TeV and, indeed,
are the strongest limits derived from Fermi LAT data at TeV energies. This is
possible thanks to the new Fermi LAT IGRB measurement, which now extends up to
an energy of 820 GeV. We quantify uncertainties in detail and show the
potential this type of search offers for testing the WIMP paradigm with a
complementary and truly cosmological probe of DM particle signals.
