The Atacama Cosmology Telescope DR6 and DESI: structure formation over cosmic time with a measurement of the cross-correlation of CMB lensing and luminous red galaxies

We present a high-significance cross-correlation of CMB lensing maps from the Atacama Cosmology Telescope (ACT) Data Release 6 (DR6) with luminous red galaxies (LRGs) from the Dark Energy Spectroscopic Instrument (DESI) Legacy Survey spectroscopically calibrated by DESI. We detect this cross-correlation at a significance of 38σ; combining our measurement with the Planck Public Release 4 (PR4) lensing map, we detect the cross-correlation at 50σ. Fitting this jointly with the galaxy auto-correlation power spectrum to break the galaxy bias degeneracy with σ ₈, we perform a tomographic analysis in four LRG redshift bins spanning 0.4 ≤ z ≤ 1.0 to constrain the amplitude of matter density fluctuations through the parameter combination S ₈^× = σ ₈ (Ω_m / 0.3)^0.4. Prior to unblinding, we confirm with extragalactic simulations that foreground biases are negligible and carry out a comprehensive suite of null and consistency tests. Using a hybrid effective field theory (HEFT) model that allows scales as small as k _max = 0.6 h/ Mpc, we obtain a 3.3% constraint on S ₈^× = σ ₈ (Ω_m / 0.3)^0.4 = 0.792^+0.024_-0.028 from ACT data, as well as constraints on S ₈^×(z) that probe structure formation over cosmic time. Our result is consistent with the early-universe extrapolation from primary CMB anisotropies measured by Planck PR4 within 1.2σ. Jointly fitting ACT and Planck lensing cross-correlations we obtain a 2.7% constraint of S ₈^× = 0.776^+0.019_-0.021, which is consistent with the Planck early-universe extrapolation within 2.1σ, with the lowest redshift bin showing the largest difference in mean. The latter may motivate further CMB lensing tomography analyses at z < 0.6 to assess the impact of potential systematics or the consistency of the ΛCDM model over cosmic time.