  Taking into consideration of a fractal structure for the black hole horizon,
Barrow argued that the area law of entropy get modified due to
quantum-gravitational effects. Accordingly, the corrected entropy takes the
form $S\sim A^{1+\frac{\Delta}{2}}$, where $0\leq\Delta\leq1,$ indicates the
amount of the quantum-gravitational deformation effects. By considering the
modified Barrow entropy associated with the apparent horizon, the Friedmann
equations get modified as well. We show that considering a universe filled with
the matter and cosmological constant $\Lambda$, it is possible to determine the
amount of deviation from standard cosmology by reconstructing the parameter
$\delta$ in terms of curvature parameters $\{q,Q,\Omega_{k}\}$ as
$\Delta=\frac{(Q-1-\Omega_k)(1+\Omega_k)}{(1+\Omega_k+q)^{2}}$. Here, $q$ is
the deceleration parameter and $Q$ is the third derivative of scale factor .
This relation provides some advantages. The first is that it indicates that
there is profound connection between quantum-gravitational deformation effects
and curvature effects, for $\Omega_k\simeq0$ the pair $\{q,Q\}$ can be regarded
as deviation curvature factors which reflect the amount of deviation of the
model from the standard model. The second interesting feature is that, since
this pair are observational parameters which can be directly measured in a
model independent approach, they can be regarded as powerful tools to enable us
to put constraint on parameter $\Delta$ and test the Barrow entropy model. Our
analysis predicts the value for $Q_{0}$ which is slightly deviates from 1 as
$(Q_{0}-1)<0.001$. This can be a relativity well target and criterion for
theoretical and observational measurements of parameter $Q_{0}$. Hence we can
hope and wait the improvement of the high redshift data in the future to
support it.
