Probing the peak of the star formation rate density with the
  extragalactic background light
  The extragalactic background light (EBL), i.e., the diffuse meta-galactic
photon field in the ultraviolet to infrared, is dominated by the emission from
stars in galaxies. It is, therefore, intimately connected with the integrated
star formation rate density (SFRD). In this paper, the SFRD is constrained
using recent limits on the EBL density derived from observations of distant
sources of high and very-high energy gamma-rays. The stellar EBL contribution
is modeled utilizing simple stellar population spectra including dust
attenuation and emission. For modeling the SFRD up to z=4 a broken power law
function in z+1 is assumed. A wide range of values for the different model
parameters (SFRD(z), metallicity, dust absorption) is investigated and their
impact on the resulting EBL is studied. The calculated EBL densities are
compared with the specific EBL density limits and constraints on the SFRD are
derived. For the fiducial model, adopting a Chabrier initial mass function
(IMF) and a second power law index for the SFRD of beta=0.3, the SFRD is
constrained to <~ 0.1 M_solar yr^-1 Mpc^-3 and < 0.2 M_solar yr^-1 Mpc^-3 for a
redshift of z~1 and z~2, respectively. The limits for a redshift of z~1 are in
tension with SFRD measurements derived from instantaneous star formation
tracers. While the tension for the conservative fiducial model in this study is
not yet overly strong, the tension increases when applying plausible changes to
the model parameters, e.g., using a Salpeter instead of a Chabrier IMF or a
adopting a sub-solar metallicity.
