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 \lesssim 0.1 \text { M } _ { \odot } \text { yr } ^ { -1 } \text { Mpc } ^ { -3 } and < 0.2 \text { M } _ { \odot } \text { yr } ^ { -1 } \text { Mpc } ^ { -3 } for a redshift of z \sim 1 and z \sim 2 , respectively .
The limits for a redshift of z \sim 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 .