  In this work we perform an observational data analysis on the energy momentum
squared gravity model. Possible solutions for matter density are obtained from
the model and their cosmological implications are studied. Some recent
observational data is used to constrain model parameters using statistical
techniques. We have used the cosmic chronometer and SNe Type-Ia Riess (292)
$H(z)-z$ data-sets in our study. Along with the data-sets we have also used
baryon acoustic oscillation (BAO) peak parameter and cosmic microwave
background (CMB) peak parameter to obtain bounds on the model parameters. Joint
analysis of the data with the above mentioned parameters have been performed to
obtain better results. For the statistical analysis we have used the
minimization technique of the $\chi^{2}$ statistic. Using this tool we have
constrained the free parameters of the model. Confidence contours have been
generated for the predicted values of the free parameters at the $66\%$, $90\%$
and $99\%$ confidence levels. Finally we have compared our analysis with the
union2 data sample presented by Amanullah et al.,2010 and the recently
published Pantheon data sample. Finally a multi-component model is investigated
by adding dust to a general cosmological fluid with equation of state $w=-1/3$.
The density parameters were studied and their values were found to comply with
the observational results.
