A Multi-Probe ISW Study of Dark Energy Models with Negative Energy Density: Galaxy Correlations, Lensing Bispectrum, and Planck ISW-Lensing Likelihood

TL;DR

The paper investigates three dark energy scenarios with potential negative energy densities—CPL, sign-switching $\Lambda_{\mathrm{s}}$CDM, and Omnipotent DE—focusing on late-time cosmological observables tied to evolving gravitational potentials. It employs a multi-probe ISW framework combining ISW-galaxy cross-correlations, the lensing-ISW bispectrum, and Planck ISW-lensing likelihood, alongside CMB and BAO data, to distinguish models. Primary CMB spectra are largely indistinguishable at high $\ell$, but notable differences emerge in the low-$\ell$ ISW plateau and higher-order statistics, with BAO data typically anchoring growth and reducing deviations. Across datasets, no model is decisively favored over $\Lambda$CDM, though the lensing-ISW bispectrum and ISW cross-correlations offer valuable complementary leverage; future high-S/N ISW measurements could be decisive in testing these exotic DE scenarios.

Abstract

We investigate the late-time imprints of three dark energy (DE) models, namely, the Chevallier-Polarski-Linder (CPL) parametrization, $Λ_{\rm s}$CDM, and an Omnipotent DE model, on cosmological observables sensitive to the time evolution of gravitational potentials. While CPL serves as a reference parameterization, the Omnipotent and $Λ_{\rm s}$CDM scenarios were originally proposed as possible solutions to the $H_0$ tension and are selected here because they can yield negative dark energy. These models are examined within a multi-probe framework based on the Integrated Sachs-Wolfe (ISW) effect and the lensing-ISW bispectrum. By analyzing both two- and three-point Cosmic Microwave Background (CMB) correlations, we assess how their late-time dynamics modify the growth and decay of large-scale gravitational potentials compared to the standard $Λ$CDM cosmology. Despite producing nearly indistinguishable CMB angular spectra at high multipoles, these models yield distinctive signatures in the low-$\ell$ ISW plateau as well as in higher-order statistics related to ISW, highlighting the power of both large-scale CMB anisotropies and higher-order CMB statistics in testing dark energy physics. Our results demonstrate that combining complementary ISW probes provides an effective way to discriminate between dark energy scenarios and will be crucial to determine whether negative or sign-switching dark energy is ultimately favored or disfavored by forthcoming data.

Figures (9)

• Figure 1: CMB temperature–temperature angular power spectrum ($C_\ell^{TT}$) for the $\Lambda$CDM (black solid), CPL (red dotted), $\Lambda_{\mathrm{s}}$CDM (blue solid), and Omnipotent DE (orange solid) models, computed using the CMB-only best-fit parameters. Planck 2018 data points with error bars are shown for comparison.
• Figure 2: Ratio of the CMB temperature power spectrum, $(C_\ell^{TT,\Lambda_{\mathrm{s}}\mathrm{CDM}} / C_\ell^{TT,\Lambda\mathrm{CDM}})$, for different values of the transition redshift $z^{\dagger}$ in the $\Lambda_{\mathrm{s}}$CDM model. The highlighted curve corresponds to the best-fit parameter values.
• Figure 3: Ratio of the CMB temperature power spectrum relative to the $\Lambda$CDM prediction, shown as $(C_\ell^{TT,\mathrm{Omnipotent}} / C_\ell^{TT,\Lambda\mathrm{CDM}})$, as a function of multipole moment $\ell$, for different values of the parameters $a_m$ (top), $\alpha$ (middle), and $\beta$ (bottom). The highlighted curves correspond to the best-fit parameter values.
• Figure 4: Matter power spectrum predictions for the dark energy models studied. The orange solid line corresponds to the Omnipotent DE model, the red dotted line to CPL, the blue solid line to $\Lambda_{\rm s}$CDM, and the black solid line to the standard $\Lambda$CDM model. The top panels display the matter power spectra, while the bottom panels show the corresponding ratios relative to $\Lambda$CDM to highlight the deviations more clearly. The left column uses best-fit parameters from the CMB-only analysis, whereas the right column shows results obtained from the combined CMB+BAO best-fit values.
• Figure 5: The ISW–galaxy cross-power spectrum, $C_\ell^{Tg}$, for SDSS (left column) and a Euclid-like survey (right column), computed using the best-fit cosmological parameters from the CMB-only (top row), CMB+BAO (middle row), and CMB+ISW (bottom row) analyses. Predictions are shown for $\Lambda$CDM (black solid line), $\Lambda_{\mathrm{s}}$CDM (blue solid line), Omnipotent DE (orange solid line), and CPL DE (red dotted line) models.