A cosmic ruler gets distorted by magnified galaxies

A map of galaxies is more than a catalogue of points: the way galaxies cluster across enormous distances carries clues about the Universe’s history. One feature of that clustering is a broad peak, or “turnover,” in the matter power spectrum—the mathematical description of how matter is distributed across scales. Its characteristic scale reflects the transition from radiation-dominated to matter-dominated expansion in the early Universe. That makes it a potential cosmic ruler, complementary to the better-known baryon acoustic oscillation (BAO) ruler.

The challenge considered in this study is that a survey does not observe galaxy positions in isolation. Gravity from foreground matter bends and magnifies light from more distant galaxies. In a flux-limited survey, magnification can change which galaxies enter the sample. The resulting correction to the observed galaxy power spectrum depends on scale and can alter the turnover’s shape. If analysts fit the data without that correction, the inferred ruler may shift.

Testing the effect with mock surveys

Yolanda Dube and colleagues calculate the lensing contribution to the observed galaxy power-spectrum monopole, a summary of clustering averaged over direction. They model two survey designs: one resembling Euclid’s Hα galaxy survey, covering redshifts from 0.9 to 1.8, and one resembling the proposed MegaMapper Lyman-break galaxy survey, spanning 2.1 to 5.

The team calculates power spectra and their statistical covariances for the survey models, then fits the turnover in redshift bins. They compare lensing-corrected predictions with a standard treatment that neglects lensing, and quantify shifts relative to the precision forecast for combining bins without lensing. The analysis uses a specified cosmological model and estimated survey properties, including how galaxy counts change with brightness—a quantity called magnification bias.

The turnover shifts, and can disappear from view

In both survey designs, the calculated lensing contribution grows in importance with redshift. For the Euclid-like case, the largest shift in an individual bin is about 0.3 times the forecast uncertainty of the stacked, no-lensing measurement. The turnover remains present across the modelled redshift range.

For the MegaMapper-like case, the shift becomes larger than that reference uncertainty at about redshift 2.9 in the study’s fiducial setup. At higher redshifts, lensing boosts power on very large scales enough to wash out the peak used to identify the turnover. The authors find that it disappears at roughly redshift 3.7 under their chosen definition and assumptions. These are not universal thresholds: changing the assumed magnification bias by 20% can move the point where the shift exceeds the reference uncertainty to roughly redshift 2.7–3.3, and can move the disappearance point from about 3.3 to beyond 4.5.

There is an important distinction between a large shift within a particular bin and the bias in a result obtained by stacking many bins. In the fiducial MegaMapper-like example, analysing lensed bins as if lensing were absent produces a stacked bias of about 0.93 times the no-lensing uncertainty when bins up to redshift 3.6 are combined. The study’s warning is not that every high-redshift measurement fails, but that treating the turnover as unchanged across redshift bins becomes unsafe unless lensing is modelled.

The paper also presents a tentative calculation for DESI’s DR1 quasar sample. Using the sample’s estimated magnification bias, the authors find a small predicted turnover shift and describe lensing as likely negligible for those estimates. They emphasize that this is an illustration, not a complete analysis of the evolving catalogue.

Forecasts, not a measurement from survey data

These results are forecasts based on noiseless mock power-spectrum data—not a detection of a shifted turnover in observed survey data. The authors use a Gaussian covariance and leave out effects such as the survey window, which can reshape measured clustering and correlate neighbouring scales, as well as super-sample covariance and observational selection systematics. The turnover fit also depends on the range of scales used; alternative fitting choices affect the recovered value and, in some cases, the redshift at which the feature is deemed to vanish.

The practical message is conditional but useful: lensing and magnification bias should be included when interpreting high-redshift galaxy clustering as a measurement of the turnover ruler. The forecasts show why that correction may matter, particularly for MegaMapper-like observations. Realistic analyses of survey data will be needed to establish the effect in practice. This article is based on an arXiv preprint; the supplied source does not establish whether it has undergone peer review.