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 spectroscopically calibrated luminous red galaxies (LRGs) from the Dark Energy Spectroscopic Instrument (DESI). We detect this cross-correlation at a significance of 38$σ$; combining our measurement with the Planck Public Release 4 (PR4) lensing map, we detect the cross-correlation at 50$σ$. 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 $0.4 \le z \le 1.0$ to constrain the amplitude of matter density fluctuations through the parameter combination $S_8^\times = σ_8 \left(Ω_m / 0.3\right)^{0.4}$. 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 $k_{\rm max}=0.6$ $h/{\rm Mpc}$, we obtain a 3.3% constraint on $S_8^\times = σ_8 \left(Ω_m / 0.3\right)^{0.4} = 0.792^{+0.024}_{-0.028}$ from ACT data, as well as constraints on $S_8^\times(z)$ 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 1.2$σ$. Jointly fitting ACT and Planck lensing cross-correlations we obtain a 2.7% constraint of $S_8^\times = 0.776^{+0.019}_{-0.021}$, which is consistent with the Planck early-universe extrapolation within 2.1$σ$, 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 $Λ$CDM model over cosmic time.