Direct correlation of line intensity mapping and CMB lensing from evolution along the lightcone

TL;DR

This work demonstrates analytically that lightcone evolution inherently induces line-of-sight mode coupling in line intensity maps, breaking translational invariance and enabling a direct cross-correlation with CMB lensing even when spectrally smooth foregrounds are removed. By developing a flat-sky formalism that retains LOS correlations beyond the Limber approximation, the authors forecast that future wide-sky LIM experiments (e.g., COMAP, CCAT, and potentially CHIME-era surveys) can precisely detect LIM×CMB lensing, with foreground filtering reducing the signal-to-noise ratio only by an order-unity factor. The methodology relies on analytic toy-model intuition, a unifying projection framework, and careful treatment of LOS correlations in the angular spectra, instrumental noise, and filtering, offering a generalizable approach for LIM cross-correlations with any projected field. The results underscore the potential of LIM to probe faint, high-redshift environments and to illuminate the connection between matter and spectral-line emission, with practical implications for planning and interpreting future surveys. Further work could extend to non-linear effects, other lines, and full-sky treatments.

Abstract

Line intensity mapping (LIM) promises to probe previously inaccessible corners of the faint and high-redshift universe. However, confusion with bright foregrounds is a major challenge for current-era pathfinder LIM experiments. Cross-correlation with cosmic microwave background (CMB) lensing is a promising avenue to enable the first LIM detections at high redshifts, a pristine probe of fundamental physics but sparsely populated by faint galaxies, and to further probe the connection between matter and spectral line emission, expanding our understanding of galaxies and the IGM. Previous works have suggested that this direct correlation between LIM and CMB lensing is effectively impossible because smoothly varying modes in the intensity map are lost to bright foregrounds. In this work, we analytically revisit the direct correlation of foreground-filtered line intensity mapping with CMB lensing, highlighting lightcone evolution's previously neglected yet unavoidable and crucial effects. Indeed, the growth of structure and evolution of line emission along the lightcone breaks statistical translational invariance and thus induces mode coupling, even in linear theory, which enables the recovery of the smoothly varying modes lost to bright foregrounds. We compute the effects of these lightcone evolution-induced mode couplings on the LIMxCMB lensing cross-spectrum detectability, predicting that future wider-sky versions of COMAP and CCAT will be able to precisely measure this cross-correlation. Although we focus on the direct correlation of LIM with CMB lensing in this paper, our arguments generalize to the direct correlation of LIM with any projected field.

Figures (22)

• Figure 1: Visualization of the direct correlation between foreground-filtered line intensity maps (Sec. \ref{['sec:LIM']}) and CMB lensing (Sec. \ref{['sec:cmb']}) which we explore analytically in this paper (Sec. \ref{['sec:spectra']}) and argue is a promising observable for future LIM experiments (Sec. \ref{['sec:SNR']}).
• Figure 2: The toy model (Sec. \ref{['sec:toy']}) highlights how lightcone evolution (magenta), inescapable in observation but previously neglected (cyan), distributes information from long-wavelength modes of the linear matter density field into all modes of the line intensity map (Eq. (\ref{['eq:Itoy']})), significantly affecting the direct correlation of LIM with CMB lensing which is sensitive only to long-wavelength modes of the linear matter density field (Eq. (\ref{['eq:ktoy']})). This has dramatic consequences for the detectability of this cross-spectrum (Fig. \ref{['fig:toySNR']}). The computation of all curves are described in App. \ref{['app:toy']} and normalized by the same factor such that the curve accounting for lightcone evolution (magenta) starts at $1$ at the minimum $k$ value plotted.
• Figure 3: Lightcone evolution both (1) increases the detectability of the unfiltered LIM$\times$CMB lensing cross-spectrum and (2) decreases the suppression of detectability due to foreground-filtering (discarding ${k_\parallel}<{\sf \Lambda}$ modes) by distributing information from long--wavelength modes of the linear matter density field into all modes of the line intensity map (see also Fig. \ref{['fig:toyIk']}). The computation of all curves are described in App. \ref{['app:toy']} and normalized by the same factor such that the curve accounting for lightcone evolution (magenta) starts at $1$ when ${\sf \Lambda}=0$.
• Figure 4: Our models for the cosmological signal in line intensity mapping (Sec. \ref{['sec:lim_cosmo']} and App. \ref{['app:luminosity']}) from linear theory compared to the instrumental noise power (Sec. \ref{['sec:lim_noise']}) whose computations are described in App. \ref{['app:experiments']} and summaries are referenced in Table \ref{['tab:experiments']}. For each experiment we also display the range of wave-number sensitivity parallel (cyan) and perpendicular (yellow) to the line of sight which are derived from assumed angular and line-of-sight resolutions reported in Table \ref{['tab:experiments']}. The cosmological signal for each experiment is plotted at the minimum (blue) and maximum (red) accessible redshift.
• Figure 5: The foreground-filtered LIM $\times$ CMB lensing cross-spectrum (Eq. (\ref{['eq:obs']})) computed for each LIM experiment we consider (Table \ref{['tab:experiments']}) using our models described in Sec. \ref{['sec:models']} and summarized in Table \ref{['tab:unify']} for different amounts of filtering. The computation of this cross-spectrum is described in App. \ref{['app:Ik']}. Hatched regions correspond to $\ell$ modes which are inaccessible given the smallest and largest angular scales observed by each experiment.