Constraining Quintessence Models with ISW-tSZ Cross-Correlations: A Comparative Analysis of Thawing, Tracker, and Scaling-Freezing Dynamics

We present constraints on quintessence dark energy models using the observational detection of the Integrated Sachs-Wolfe (ISW)--thermal Sunyaev-Zeldovich (tSZ) cross-correlation dataset. Our analysis compares three classes of quintessence dynamics: thawing, tracker, and scaling-freezing with the standard $\Lambda$CDM cosmology. Through a comprehensive likelihood analysis, we derive best-fit values and 68\% confidence intervals for key cosmological parameters, finding $\Omega_{\rm m} = 0.322^{+0.027}_{-0.030}$ and $\sigma_8 = 0.735^{+0.045}_{-0.035}$ for $\Lambda$CDM, with deviations in alternative models consistent within $1\sigma$. For the thawing model, we consider an exponential potential with slope $\lambda = 0.736^{+0.270}_{-0.227}$, while for the tracker and scaling-freezing models, we use inverse axion-like and double exponential potentials, respectively. Observationally, the tracker model yields $n = 5.651^{+1.625}_{-1.604}$ and $f = 0.258^{+0.149}_{-0.096}$, and the scaling-freezing model gives $\lambda_1 = 0.405^{+0.293}_{-0.322}$ and $\lambda_2 = 23.226^{+7.975}_{-7.258}$. The dimensionless tSZ amplitude ($\widetilde{W}^{\rm SZ}$) and cosmic infrared background (CIB) parameters are tightly constrained across all models, providing additional insights into astrophysical foregrounds. Our results demonstrate the effectiveness of ISW--tSZ cross-correlations as a probe of dark energy dynamics, with the Thawing quintessence model yielding the lowest $\chi^2_{\rm min}$ among the tested scenarios, and highlight the need for future high-precision measurements to distinguish between quintessence models and $\Lambda$CDM.