We introduce the Galaxy Intensity Mapping cross-COrrelation estimator (GIMCO), which is a new tomographic estimator for the gravitational lensing potential, based on a combination of intensity mapping (IM) and galaxy number counts. The estimator can be written schematically as IM$(z_f)times$galaxy$(z_b)$ $-$ galaxy$(z_f)times$IM$(z_b)$ for a pair of distinct redshifts $(z_f,z_b)$; this combination allows to greatly reduce the contamination by density-density correlations, thus isolating the lensing signal. As an estimator constructed only from cross-correlations, it is additionally less susceptible to systematic effects. We show that the new estimator strongly suppresses cosmic variance and consequently improves the signal-to-noise ratio (SNR) for the detection of lensing, especially on linear scales and intermediate redshifts. %This makes it particularly valuable for future studies of dark energy and modified gravity. For cosmic variance dominated surveys, the SNR of our estimator is a factor 30 larger than the SNR obtained from the correlation of galaxy number counts only. Shot noise and interferometer noise reduce the SNR. For the specific example of the Dark Energy Survey (DES) cross-correlated with the Hydrogen Intensity mapping and Real time Analysis eXperiment (HIRAX), the SNR is around 4, whereas for Euclid cross-correlated with HIRAX it reaches 52. This corresponds to an improvement of a factor 4-5 compared to the SNR from DES alone. For Euclid cross-correlated with HIRAX the improvement with respect to Euclid alone strongly depends on the redshift. We find that the improvement is particularly important for redshifts below 1.6, where it reaches a factor of 5. This makes our estimator especially valuable to test dark energy and modified gravity, that are expected to leave an impact at low and intermediate redshifts.
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