  Despite the significant accomplishments of general relativity, numerous
unresolved issues persist in our understanding of the cosmos. One of the most
perplexing challenges is the ongoing accelerated expansion of the Universe,
which continues to elude a complete explanation. Consequently, scientists have
proposed various alternative theories to GR in pursuit of a deeper
understanding. In our analysis, we delve into the recently proposed modified
$f(Q)$ gravity, where $Q$ represents the non-metricity scalar responsible for
gravitational effects. Specifically, we investigate a cosmological model
characterized by the functional form $f(Q) = Q+\alpha Q^n$, where $\alpha$
(with $\alpha \neq 0$) and $n$ serve as free parameters. Utilizing this
functional form, we construct our Hubble rate, incorporating a specific
equation of state to describe the cosmic fluid. Furthermore, we leverage a
dataset consisting of 31 data points from Hubble measurements and an additional
1048 data points from the Pantheon dataset. These data serve as crucial
constraints for our model parameters, and we employ the Markov Chain Monte
Carlo (MCMC) method to explore the parameter space and derive meaningful
results. With our parameter values constrained, our analysis yields several
noteworthy findings. The deceleration parameter suggests a recent accelerated
phase in the cosmic expansion. In addition, the EoS parameter paints a portrait
of dark energy exhibiting phantom-like characteristics. Furthermore, we delve
into the application of cosmological diagnostic tools, specifically the
statefinder and the $Om(z)$ diagnostics. Both of these tools align with our
previous conclusions, confirming the phantom-like behavior exhibited by our
cosmological model. These results collectively contribute to our understanding
of the dynamic interplay between gravity, dark energy, and the expanding
cosmos.
