The Atacama Cosmology Telescope: High-redshift measurement of structure growth from the cross-correlation of Quaia quasars and CMB lensing from ACT DR6 and $\textit{Planck}$ PR4

We measure the amplitude of matter fluctuations over a wide range of redshifts by combining CMB lensing observations from ACT DR6 and $\textit{Planck}$ PR4 with the overdensity of quasars from Quaia, a $\textit{Gaia}$ and $\textit{unWISE}$ quasar catalog. Our analysis includes the CMB lensing power spectrum from ACT DR6, the auto-correlation of two Quaia quasar samples centered at $z \simeq 1.0$ and $z \simeq 2.1$, and their cross-correlations with CMB lensing from both ACT DR6 and $\textit{Planck}$ PR4. By performing a series of contamination and systematic null tests, we find no evidence for contamination in the lensing maps, contrary to what was suggested in previous Quaia cross-correlation analyses using $\textit{Planck}$ PR4 CMB lensing data. From the joint analysis of the quasar auto- and cross-correlations with CMB lensing, and including BOSS BAO data to break the degeneracy between $Ω_m$ and $σ_8$, we obtain $σ_8 = 0.802^{+0.045}_{-0.057}$, consistent with $Λ$CDM predictions from $\textit{Planck}$ primary CMB measurements. Combining the CMB lensing auto-spectrum with the cross-correlation measurement improves the constraint on $σ_8$ by $12\%$ relative to the lensing auto-spectrum alone, yielding $σ_8 = 0.804 \pm 0.013$. This dataset combination also enables a reconstruction of structure growth across redshifts. We infer a $12\%$ constraint on the amplitude of matter fluctuations at $z > 3$, with a measurement at the median redshift of the signal of $σ_8(\tilde{z}=5.1) = 0.146^{+0.021}_{-0.014}$, consistent with $\textit{Planck}$ at the $1.4σ$ level. These results provide one of the highest redshift constraints on the growth of structure to date.