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

Abstract

We investigate the late-time imprints of three dark energy (DE) models, namely, the Chevallier-Polarski-Linder (CPL) parametrization, $\Lambda_{\rm s}$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 $\Lambda_{\rm s}$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 $\Lambda$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.