The baryon acoustic oscillation (BAO) feature was detected at 2–3σ significance in the cross-correlation between galaxy density and galaxy intrinsic ellipticity (the GI correlation) by Xu, Jing, Zhao & Cuesta (2023), yielding a 3–5% measurement of the distance DV/rdD_V/r_d at z = 0.57 and a ~10% improvement when combined with galaxy–galaxy (GG) BAO. Because GI probes the same large-scale modes as density clustering through a spin-2 tidal response, it constitutes an independent standard ruler that could cross-check the sub-percent GG BAO distances of stage-IV surveys — but only if its own methodology is validated and its precision reaches the ~1% level. The open problem is to develop this channel to that precision; the source paper identifies the missing ingredients: (i) BAO reconstruction that coherently processes the galaxy shape field, which density-only reconstruction failed to improve; (ii) realistic mock catalogues containing galaxy shapes, intrinsic-alignment physics and galaxy–halo misalignment for reliable covariances, estimator validation and forecasts; (iii) extension to the full anisotropic GI measurement with redshift-space-distortion and Alcock–Paczynski modeling; and (iv) quantification of misalignment and central/satellite selection effects on the intrinsic-alignment amplitude. Recent work (2023–2026) has advanced anisotropic modeling and measurement and reported a first photometric GI BAO measurement (DES Y3, 0.86σ), but shape-field reconstruction, realistic intrinsic-alignment mocks for GI BAO, and the percent-level precision target all remain open.

Background

Baryon acoustic oscillations (BAO) are sound waves that propagated through the photon–baryon plasma of the early Universe; imprinted on the matter distribution at recombination, they leave a preferred comoving length — the sound horizon, about 150 Mpc — in the clustering of galaxies. This scale, predicted by well-understood early-Universe physics, acts as a 'standard ruler': measuring its apparent size in a galaxy survey determines the distance–redshift relation and hence constrains dark energy. The feature is routinely measured in galaxy–galaxy (GG) density correlations, and 'reconstruction' — using the observed density field to undo the nonlinear smearing of the acoustic peak by large-scale bulk flows (Eisenstein, Seo, Sirko & Spergel 2007) — brings modern surveys such as BOSS (the Baryon Oscillation Spectroscopic Survey) and DESI (the Dark Energy Spectroscopic Instrument) to sub-percent BAO distance precision. Galaxy shapes provide a second tracer of the same structure. A galaxy's two-component ellipticity (γ+\gamma_+, γ×\gamma_×) encodes the orientation and axis ratio of its projected light distribution. Massive galaxies are 'intrinsically aligned' (IA): their major axes preferentially point along the tidal field of the surrounding cosmic web. On large scales this is described by the linear alignment (LA) model of Hirata & Seljak (2004), in which the intrinsic ellipticity field is proportional to the primordial tidal field. IA is best known as a contaminant of weak gravitational lensing, but as a signal it is a direct tracer of the tidal field. The cross-correlation between galaxy positions and the intrinsic ellipticities of those same galaxies — the GI correlation — therefore measures the matter field through a spin-2 tidal response (spin-2 meaning that, like shear, the field transforms with twice the rotation angle when the coordinate frame is rotated) rather than through density. Okumura & Jing (2009) measured this GI correlation for SDSS luminous red galaxies and showed that galaxy–halo misalignment — the angle between a central galaxy and its host dark-matter halo — suppresses the signal by a factor of roughly 2–3 relative to perfect alignment. Theoretically, Okumura, Taruya & Nishimichi (2019) formulated the IA statistics of density and velocity fields and showed that the BAO imprint in the GI correlation function ξg+(r)\xi_{g+}(r) appears as a characteristic dip (trough) at the BAO scale, which van Dompseler, Georgiou & Chisari (2023) explained with a toy model of tidal fields acting on a spherical shell of matter. Taruya & Okumura (2020) forecast that anisotropic IA correlations could tighten geometric and dynamical cosmological constraints by factors exceeding 1.5 over clustering alone. Xu, Jing, Zhao & Cuesta (2023) then reported the first detection of the BAO feature in GI correlations, using the spectroscopic BOSS CMASS sample (a dense sample of massive red galaxies at redshifts around 0.5) cross-matched with shape measurements from the DESI Legacy Imaging Surveys: a 2–3σ BAO dip in the monopole of ξg+\xi_{g+}, a 3–5% constraint on DV/rdD_V/r_d (the angle-averaged distance divided by the sound horizon) at z = 0.57, and a ~10% reduction of the GG+GI distance uncertainty relative to GG alone. The strategic promise they emphasize is systematics control: in next-generation surveys such as DESI and the Rubin Observatory's Legacy Survey of Space and Time (LSST), an independent ~1% GI BAO distance could be compared against sub-percent GG BAO measurements of the same sky, exposing systematics in either. Their analysis was, however, deliberately conservative, and they identified several improvements, each left for future work, needed before this promise can be tested: their reconstruction shifted only galaxy positions, leaving the shape field unchanged, and gave no GI improvement, with shape-field reconstruction 'left for a future study'; the covariance came from jackknife resampling (a scheme that estimates errors by repeatedly dropping spatial subsamples) because realistic mock catalogues with galaxy shapes and IA physics do not exist; only the angle-averaged (monopole) GI signal was used, without modeling of redshift-space distortions (RSD — the apparent anisotropic distortion of correlations by galaxies' peculiar velocities along the line of sight) or of the Alcock–Paczynski effect (the apparent anisotropic stretching of the measured correlation when the assumed cosmology used to convert redshifts and angles into distances is incorrect), although the full two-dimensional ξg+(r)\xi_{g+}(r) contains additional radial and transverse information; and galaxy–halo misalignment, which suppresses the IA amplitude, needs empirical quantification and incorporation into modeling and forecasts, since GI-only constraints came out about three times weaker than GG — well short of the Taruya & Okumura (2020) forecast.

Problem Statement

Determine whether the galaxy density–ellipticity (GI) baryon acoustic oscillation channel can be developed into a validated, systematics-controlled standard ruler precise enough — at roughly 1% BAO-distance precision — to serve as an independent cross-check of sub-percent galaxy–galaxy (GG) BAO distance measurements in stage-IV surveys such as DESI and Rubin LSST, and build the methodology that this requires. The source paper identifies the following methodological gaps, each flagged there as future work serving this single objective: (1) develop and validate a BAO reconstruction that coherently processes the galaxy shape field (or an equivalent technique), settling whether it sharpens the GI BAO feature — including explaining why density-only reconstruction left the GI constraint unchanged or degraded — and, in the anisotropic extension, whether it sharpens the radial and transverse BAO information; (2) produce realistic mock catalogues containing galaxy shapes, intrinsic-alignment physics and galaxy–halo misalignment, and use them to obtain reliable covariance matrices, validate estimators, quantify biases and forecast GI performance, replacing the jackknife and noise-only covariances currently in use; (3) extend the GI BAO analysis from the monopole to the full anisotropic two-dimensional correlation with redshift-space-distortion and Alcock–Paczynski modeling, extracting the BAO-scale radial and transverse information; and (4) empirically quantify the impact of galaxy–halo misalignment and of selection effects such as the composition of central galaxies (those at the center of their dark-matter halo) versus satellite galaxies (those orbiting within it) on IA amplitudes and BAO constraints, incorporating them into the modeling and forecasts. Completion is bounded by the source's own precision criterion: a demonstrated — or rigorously refuted — ability of next-generation GI measurements to reach approximately 1% BAO-distance precision, the level at which, in the source's framing, comparison against sub-percent GG BAO measurements of the same sky provides a check of the systematic bias in the measurements. An answer may legitimately arrive as a validated survey measurement, a mock-based demonstration, or a rigorous infeasibility forecast. Results on the individual components listed above (for example, shape-field reconstruction or realistic IA mocks) constitute partial progress toward this criterion rather than a complete answer.

References

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