Lower Bound on the Cosmic TeV Gamma-ray Background Radiation
  The Fermi gamma-ray space telescope has revolutionized our understanding of
the cosmic gamma-ray background radiation in the GeV band. However,
investigation on the cosmic TeV gamma-ray background radiation still remains
sparse. Here, we report the lower bound on the cosmic TeV gamma-ray background
spectrum placed by the cumulative flux of individual detected extragalactic TeV
sources including blazars, radio galaxies, and starburst galaxies. The current
limit on the cosmic TeV gamma-ray background above 0.1 TeV is obtained as
$2.8\times10^{-8} (E/100~{\rm GeV})^{-0.55} \exp(-E/2100~{\rm GeV})~{\rm
[GeV/cm^2/s/sr]} < E^2dN/dE < 1.1\times10^{-7} (E/100~{\rm GeV})^{-0.49}~{\rm
[GeV/cm^2/s/sr]}$, where the upper bound is set by requirement that the cascade
flux from the cosmic TeV gamma-ray background radiation can not exceed the
measured cosmic GeV gamma-ray background spectrum (Inoue & Ioka, 2012). Two
nearby blazars, Mrk 421 and Mrk 501, explain ~70% of the cumulative background
flux at 0.8-4 TeV, while extreme blazars start to dominate at higher energies.
We also provide the cumulative background flux from each population, i.e.
blazars, radio galaxies, and starburst galaxies which will be the minimum
requirement for their contribution to the cosmic TeV gamma-ray background
radiation.
