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

TL;DR

This work constrains dynamical dark energy by exploiting the ISW–tSZ cross-correlation to test three quintessence classes—thawing, tracker, and scaling-freezing—against $\Lambda$CDM in a flat universe with $w\ge -1$. It models the scalar field with EXP, IAX, and DEXP potentials, computes the matter power spectrum, and predicts the ISW–tSZ signal using Limber-based angular spectra within a Bayesian framework using nested sampling. The results indicate the thawing model provides the best statistical fit, with non-phantom dynamics; however, a persistent $\sigma_8$ tension remains between ISW–tSZ inferences ($\sim 0.74$) and Planck priors ($0.811\pm0.012$). Overall, ISW–tSZ cross-correlations demonstrate their value as a complementary late-time probe of dark energy, while the authors emphasize the need for higher-precision data to decisively distinguish quintessence dynamics from $\Lambda$CDM.

Abstract

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 $Λ$CDM cosmology. Through a comprehensive likelihood analysis, we derive best-fit values and 68\% confidence intervals for key cosmological parameters, finding $Ω_{\rm m} = 0.322^{+0.027}_{-0.030}$ and $σ_8 = 0.735^{+0.045}_{-0.035}$ for $Λ$CDM, with deviations in alternative models consistent within $1σ$. For the thawing model, we consider an exponential potential with slope $λ= 0.736^{+0.270}_{-0.227}$, 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 $λ_1 = 0.405^{+0.293}_{-0.322}$ and $λ_2 = 23.226^{+7.975}_{-7.258}$. 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 $χ^2_{\rm min}$ among the tested scenarios, and highlight the need for future high-precision measurements to distinguish between quintessence models and $Λ$CDM.

Figures (11)

• Figure 1: Different scalar field dynamics has been shown. Left figure shows the thawing dynamics while middle and the right figures show the tracker and scaling-freezing dynamics, respectively.
• Figure 2: Left Panel: Angular power spectrum of the Integrated Sachs-Wolfe (ISW)–thermal Sunyaev-Zeldovich (tSZ) effect, with uncertainties shown as an error band (dodgerblue) and error bars (grey). The data is presented in Table 1 of Ibitoye24. The theoretical angular power spectra for various cosmological models are plotted alongside the observed data. An inset log-log plot (top-right) highlights the detailed fit of each model to the data, demonstrating that the $\Lambda$CDM model provides a better statistical fit compared to the thawing, tracker, and scaling-freezing dynamics models. $D^{\rm y-ISW}_{\ell}=10^{14} \ell(\ell+1)C^{\rm y-ISW}_{\ell}/2\pi$. Right Panel: Ratios of the $\Lambda$CDM matter power spectrum ($P_{\rm m}^{\Lambda \rm CDM}$) to the matter power spectra computed for quintessence dynamics at redshifts $z = 0.0$, $z = 0.1$, $z = 1.0$, and $z = 5.0$. Different line styles and colors distinguish the thawing, tracker, and scaling-freezing dynamics models.
• Figure 3: Final Estimates of Model Parameters with Uncertainties. Final estimates of our model parameters are computed as the marginalized 1D (M1D) values from their respective posterior distributions. Each panel corresponds to an individual cosmological parameter ($\Omega_b$, $\Omega_m$, $h$, and $\sigma_8$), displaying the best-fit values grouped by the models, while error bars depict the lower and upper uncertainties associated with each estimate.
• Figure 4: Posterior distributions from MCMC with the full covariance matrix for the seven free parameters in our Quintessence model. The figures show the joint constraints for all parameter pairs and the marginalized distributions for each parameter along the table diagonal.
• Figure 5: The posterior distributions and correlations of key cosmological parameters from Thawing Dynamics of Quintessence Models Compared to the $\Lambda{\rm CDM}$ Framework. The constraints includes the Thawing dynamics sensitive parameters. The filled contours represent the 68% and 95% confidence regions for the Thawing Dynamics (green) and $\Lambda{\rm CDM}$ (navy) models, illustrating the differences in parameter estimates and their uncertainties, as well as the impact of different dynamical behaviors on cosmological constraints.