  The redshift ($z$) evolution of the Extragalactic Background Light (EBL)
photon density is very important to understand the history of cosmological
structure formation of galaxies and stars since the epoch of recombination. The
EBL photons with the characteristic spectral energy distribution ranging from
ultraviolet/optical to far-infrared provide a major source of opacity of the
Universe to the GeV-TeV $\gamma$-rays travelling over cosmological distances.
The effect of the EBL is very significant through $\gamma \gamma \rightarrow
e^- e^+$ absorption process on the propagation of the $\gamma$-ray photons with
energy $E >$ 50 GeV emitted from the sources at $z \sim 1$. This effect is
characterized by the optical depth ($\tau$) which strongly depends on $E$, $z$
and density of the EBL photons. The proper density of the EBL photons increases
with $z$ due to expansion of the Universe whereas evolution of radiation
sources contributing to the EBL leads to a decrease in the density with
increasing $z$. Therefore, the resultant volumetric evolution of the EBL photon
density is approximated by a modified redshift dependence. In this work, we
probe evolution of the EBL photon density predicted by two prominent models
using cosmic gamma-ray horizon ($\tau (E,z)=$ 1) determined by the measurements
from the \emph{Fermi}-Large Area Telescope (LAT) observations. The modified
redshift dependence of the EBL photon density is optimized for a given EBL
model by estimating the same gamma-ray horizon as predicted by the
\emph{Fermi}-LAT observations. We further compare the optical depth estimates
in the energy range $E =$ 4 GeV-1 TeV and redshift range $z =0.01-1$ from the
\emph{Fermi}-LAT observations with the values derived from the two EBL models
to further constrain the evolution of the EBL photon density in the $z~\sim 1$
Universe.

Cosmology and Nongalactic Astrophysics;High Energy Astrophysical Phenomena