  In this work, FRW universe filled with dark matter (perfect fluid with
negligible pressure) along with dark energy in the background of Galileon
gravity is considered. Four dark energy models with different EoS
parametrizations have been employed namely, Linear, CPL, JBP and Logarithmic
parametrizations. From Stern, Stern+BAO and Stern+BAO+CMB joint data analysis,
we have obtained the bounds of the arbitrary parameters $\omega_{0}$ and
$\omega_{1}$ by minimizing the $\chi^{2}$ test. The best-fit values and bounds
of the parameters are obtained at 66\%, 90\% and 99\% confidence levels which
are shown by closed confidence contours in the figures. For the logarithmic
model unbounded confidence contours are obtained and hence the model parameters
could not be finitely constrained. The distance modulus $\mu$(z) against
redshift $z$ has also been plotted for our predicted theoretical models for the
best fit values of the parameters and compared with the observed Union2 data
sample and SNe Type Ia 292 data and we have shown that our predicted
theoretical models permits the observational data sets. From the data fitting
it is seen that at lower redshifts $(z<0.3)$ the SNe Type Ia 292 data gives a
better fit with our theoretical models compared to the Union2 data sample. So,
from the data analysis, SNe Type Ia 292 data is the more favoured data sample
over its counterpart given the present choice of free parameters. From the
study, it is also seen that the logarithmic parametrization model is less
supported by the observational data. Finally we have generated the plot for the
deceleration parameter against the redshift parameter for all the theoretical
models and compared the results with the work of Farooq et al, 2013.
