A new probe of the high-redshift Universe: nulling CMB lensing with interloper-free "LIM-pair" lensing

Intermediate redshifts between galaxy surveys and the cosmic microwave background (CMB) remain unexplored territory. Line intensity mapping (LIM) offers a way to probe the $z\gtrsim 1$ Universe, including the epoch of reionization and the dark ages. Via exact nulling of the lensing kernel, we show that LIM lensing, in combination with galaxy (resp., CMB) lensing, can uniquely probe the $z\gtrsim 1$ (resp., pre-reionization) Universe. However, LIM foregrounds are a key hurdle to this futuristic technique. While continuum foregrounds can be controlled by discarding modes perpendicular to the line of sight (low $k_\parallel$ modes), interloper foregrounds haven't been addressed in the context of LIM lensing. In this paper, we quantify the interloper bias to LIM lensing for the first time, and derive a ''LIM-pair'' estimator which avoids it exactly after cross-correlating with CMB lensing. This new quadratic lensing estimator works by combining two intensity maps in different lines, from the same redshift, whose interlopers are uncorrelated. As a result, this foreground avoidance method is robust to even large changes in the amplitude of the interloper power and non-Gaussianity. The cross-spectrum of the LIM-pair estimator with CMB lensing is thus robust to the currently large theoretical uncertainties in LIM modeling at high redshift.