Multiprobe constraints on early and late time dark energy

We perform a multiprobe analysis combining cosmic microwave background (CMB) data from and the Atacama Cosmology Telescope (ACT), ACT CMB lensing, and large-scale structure (LSS) measurements from the Dark Energy Spectroscopic Instrument (DESI), including DESI Legacy Imaging Survey (LS) galaxies and baryon acoustic oscillations (BAOs). We present the first 5 × 2     pt analysis of ACT DR6 lensing, DESI LS, and Integrated Sachs-Wolfe (ISW). Within Λ CDM , this yields S 8 = σ 8 ( Ω m / 0.3 ) 0.5 = 0.819 ± 0.016 , in good agreement with primary CMB inferences and provides a sound-horizon-free Hubble constant constraint of H 0 = 70.0 ± 4.4     km   s − 1     Mpc − 1 . Then, combining with CMB primary and BAO, we reconfirm a CMB–BAO discrepancy in the Ω m – D v r d plane, which is heightened when combining BAO with the 5 × 2     pt data vector. We explore two dark-energy extensions that may reconcile this: an early-time modification, early dark energy (EDE), and late-time dynamical dark energy (DDE) parametrized by w 0 w a . For CMB primary + BAO + 5 × 2     pt , we find a 3.3 σ preference for DDE over Λ CDM , while EDE is modestly favored at 2.3 σ . The models address different shortcomings of Λ CDM : DDE relaxes the neutrino mass bound ( M ν < 0.17     eV vs < 0.050     eV under Λ CDM ), making it compatible with neutrino oscillation measurements, while EDE raises the Hubble constant to H 0 = 70.5 ± 1.2     km   s − 1   Mpc − 1 , easing the discrepancy with SH0ES. However, neither model resolves both issues simultaneously. Our analysis indicates that both DDE and EDE remain viable extensions of Λ CDM within current uncertainties and demonstrates the capacity of combined probes to place increasingly stringent constraints on cosmological parameters.