Multiprobe constraints on early and late time dark energy

We perform a multiprobe analysis combining cosmic microwave background (CMB) data from Planck 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 $5\times2$pt analysis of ACT DR6 lensing, DESI LS, and Planck ISW. Within $\Lambda$CDM, this yields $S_8 = \sigma_8(\Omega_m/0.3)^{0.5} = 0.819 \pm 0.016$, in good agreement with primary CMB inferences and provides a sound-horizon-free Hubble constant constraint of $H_0 = 70.0 \pm 4.4$ km s$^{-1}$ Mpc$^{-1}$. Then, combining with CMB primary and BAO, we reconfirm a CMB-BAO discrepancy in the $\Omega_m$-$\frac{D_v}{r_d}$ plane, which is heightened when combining BAO with the $5\times2$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) parameterized by $w_0w_a$. For CMB primary+BAO+$5\times2$pt, we find a $3.3\sigma$ preference for DDE over $\Lambda$CDM, while EDE is modestly favoured at $2.3\sigma$. The models address different shortcomings of $\Lambda$CDM: DDE relaxes the neutrino mass bound ($M_\nu<0.17$eV vs. $<0.050$eV under $\Lambda$CDM), making it compatible with neutrino oscillation measurements, while EDE raises the Hubble constant to $H_0=70.5\pm1.2\,\mathrm{km\,s^{-1}\,Mpc^{-1}}$, easing the discrepancy with SH0ES. However, neither model resolves both issues simultaneously. Our analysis indicates that both DDE and EDE remain viable extensions of $\Lambda$CDM within current uncertainties and demonstrates the capacity of combined probes to place increasingly stringent constraints on cosmological parameters.