Abstract
The Lambda cold dark matter ($\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$) model, while pivotal in cosmological studies, has faced significant challenges due to emerging observational and theoretical inconsistencies. In this work, we analyze constraints on dynamic dark energy models---Chevallier-Polarski-Linder (CPL), Barboza-Alcaniz (BA), Jassal-Bagla-Padmanabhan (JBP), Scaled CPL (SCPL), and Generalized Chaplygin Gas (GCG)---using current datasets, including PantheonPlus, Union, the Dark Energy Survey 5-Year (DESY5) supernova compilations, and baryon acoustic oscillation (BAO) measurements. Our findings reveal that, except for PantheonPlus, these datasets exhibit consistent deviations from the $\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$ model, with significance exceeding $2\ensuremath{\sigma}$ across all considered dynamic dark energy models. We further forecast the constraining power of three years of simulated photometric Supernova Ia data from the Legacy Survey of Space and Time (LSST). Our analysis shows that LSST's high-precision data can significantly tighten constraints on dark energy parameters, surpassing the precision of current datasets. Additionally, the inclusion of BAO measurements alongside LSST data further improves parameter constraints for all models. These results underscore the necessity of exploring dynamic dark energy frameworks as a potential resolution to the tensions within the $\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$ paradigm and highlight LSST's crucial role in advancing our understanding of alternative cosmologies.