  In recent years, the Lambda Cold Dark Matter (LCDM) model, which has been
pivotal in cosmological studies, has faced significant challenges due to
emerging observational and theoretical inconsistencies. This paper explores
alternative cosmological models to address these discrepancies, using simulated
three years photometric Supernovae Ia data from the Legacy Survey of Space and
Time (LSST), supplemented with additional Pantheon+, Union, and the recently
released Dark Energy Survey 5 Years (DESY5) supernova compilations and Baryon
Acoustic Oscillation (BAO) measurements. We assess the constraining power of
these datasets on various dynamic dark energy models, including CPL, BA, JBP,
SCPL, and GCG. Our analysis demonstrates that the LSST with its high precision
data, can provide tighter constraints on dark energy parameters compared to
other datasets. Additionally, the inclusion of BAO measurements significantly
improves parameter constraints across all models.
  Except for Pantheon+, we find that across all the cosmological datasets, and
the dark energy models considered in this work, there is a consistent deviation
from the LCDM model that exceeds a 2-sigma significance level. Our findings
underscore the necessity of exploring dynamic dark energy models, which offer
more consistent frameworks with fundamental physics and observational data,
potentially resolving tensions within the LCDM paradigm. Furthermore, the use
of simulated LSST data highlights the survey's potential in offering
significant advantages for exploring alternative cosmologies, suggesting that
future LSST observations would play a crucial role.
