Galaxy clustering in the DESI Legacy Survey and its imprint on the CMB

We use data from the DESI Legacy Survey imaging to probe the galaxy density field in tomographic slices covering the redshift range $0<z<0.8$. After careful consideration of completeness corrections and galactic cuts, we obtain a sample of $4.9\times 10^7$ galaxies covering 17 739 deg$^2$. We derive photometric redshifts with precision $\sigma_z/(1+z)=0.012 - 0.015$, and compare with alternative estimates. Cross-correlation of the tomographic galaxy maps with Planck maps of CMB temperature and lensing convergence probe the growth of structure since $z=0.8$. The signals are compared with a fiducial Planck $\Lambda$CDM model, and require an overall scaling in amplitude of $A_\kappa=0.901\pm 0.026$ for the lensing cross-correlation and $A_{\rm ISW} = 0.984 \pm 0.349$ for the temperature cross-correlation, interpreted as the Integrated Sachs-Wolfe effect. The ISW amplitude is consistent with the fiducial $\Lambda$CDM prediction, but lies significantly below the prediction of the AvERA model of R\'acz et al. (2017), which has been proposed as an alternative explanation for cosmic acceleration. Within $\Lambda$CDM, our low amplitude for the lensing cross-correlation requires a reduction either in fluctuation normalization or in matter density compared to the Planck results, so that $\Omega_m^{0.78}\sigma_8=0.297\pm 0.009$. In combination with the total amplitude of CMB lensing, this favours a shift mainly in density: $\Omega_m=0.274\pm0.024$. We discuss the consistency of this figure with alternative evidence. A conservative compromise between lensing and primary CMB constraints would require $\Omega_m=0.296\pm0.006$, where the 95% confidence regions of both probes overlap.