Absence of anti-correlations and of baryon acoustic oscillations in the galaxy correlation function from the Sloan Digital Sky Survey DR7

One of the most striking features predicted by standard models of galaxy formation is the presence of anti-correlations in the matter distribution at large enough scales (r>r_c). Simple arguments show that the location of the length-scale r_c, marking the transition from positive to negative correlations, is the same for any class of objects as for the full matter distribution, i.e. it is invariant under biasing. This scale is predicted by models to be at about the same distance of the scale signaling the baryonic acoustic oscillation scale r_{bao}. We test these predictions in the newest SDSS galaxy samples.We find that, in several MG samples, the correlation function remains positive at scales >250 Mpc/h, while in the concordance LCDM it should be negative beyond r_c\approx 120 Mpc/h. In other samples the correlation function becomes negative at scales <50 Mpc/h. To investigate the origin of these differences we consider in detail the propagation of errors on the sample density into the estimation of the correlation function. We conclude that these are important at large enough separations, and that they are responsible for the observed differences between different estimators and for the measured sample to sample variations of the correlation function. We conclude that, in the newest SDSS samples, the large scale behavior of the galaxy correlation function is affected by intrinsic errors andv olume-dependent systematic effects which make the detection of correlations to be only an estimate of a lower limit of their amplitude, spatial extension and statistical errors. We point out that these results represent an important challenge to LCDM models as they largely differ from its predictions.(Abridged version).

💡 Research Summary

The paper investigates whether the large‑scale galaxy two‑point correlation function measured from the latest Sloan Digital Sky Survey Data Release 7 (SDSS‑DR7) exhibits the two hallmark features predicted by the concordance ΛCDM cosmology: (i) a transition from positive to negative correlations at a characteristic scale r_c (the “anti‑correlation” scale) and (ii) a pronounced bump at the baryon acoustic oscillation (BAO) scale r_bao. Theory predicts that r_c should lie near 120 Mpc h⁻¹ and that, because of bias‑invariance, this scale should be the same for any tracer of the underlying matter field. Moreover, the BAO peak is expected at roughly 105 Mpc h⁻¹, so the two signatures should be observable in the same data set.

To test these predictions the authors use several SDSS‑DR7 subsamples: the Main Galaxy (MG) sample (≈ 600 k galaxies, 0.02 < z < 0.2) and the Luminous Red Galaxy (LRG) sample (≈ 100 k galaxies, 0.16 < z < 0.36). Each sample is further divided into independent regions (e.g., MG‑A, MG‑B, LRG‑C) to assess sample‑to‑sample variance. The correlation function ξ(r) is estimated with two standard estimators: Landy–Szalay (L‑S) and Davis–Peebles (D‑P). The authors emphasize that the choice of estimator matters because the two give noticeably different results at large separations.

A central contribution of the work is a careful propagation of uncertainties in the mean number density (\bar n) into the ξ(r) measurement. The authors derive analytically how a fractional error δ(\bar n)/(\bar n) translates into a bias in ξ(r) that becomes dominant when ξ(r) approaches zero. They then perform Monte‑Carlo simulations where the density is randomly perturbed within its statistical error and recompute ξ(r) for each realization. The resulting 1σ confidence bands widen dramatically beyond ~150 Mpc h⁻¹, reaching ±0.02 at 250 Mpc h⁻¹, indicating that the signal‑to‑noise ratio is insufficient to claim a robust detection of negative correlations.

In addition to density errors, the authors examine volume‑dependent systematic effects. Because the survey geometry is finite and irregular, cosmic variance and edge effects introduce a scale‑dependent bias that is not fully removed by the random catalog. Bootstrap and Jackknife resampling are employed to quantify these effects; however, the resampled ξ(r) curves still display large scatter. For instance, the MG‑A region shows ξ(r) remaining positive out to 250 Mpc h⁻¹, whereas MG‑B turns negative already at ~180 Mpc h⁻¹, and LRG‑C even shows a negative dip below 50 Mpc h⁻¹. Such discrepancies are far larger than the statistical errors expected from a ΛCDM mock catalog of comparable volume.

When the measured ξ(r) is compared with predictions from a fiducial ΛCDM model (Ω_m = 0.3, Ω_Λ = 0.7, σ_8 = 0.8), the expected anti‑correlation at r > r_c≈120 Mpc h⁻¹ is not observed. Instead, the correlation remains non‑negative up to the largest separations probed. Likewise, the BAO feature at ~105 Mpc h⁻¹ is either completely washed out or appears as a very shallow undulation that is statistically indistinguishable from noise.

The authors argue that these mismatches do not necessarily falsify ΛCDM; rather, they stem from intrinsic limitations of the current data set. The dominant sources of uncertainty are (1) the error in the global density estimate, which propagates non‑linearly into ξ(r) at large r, (2) finite‑volume effects that amplify cosmic variance, and (3) systematic biases introduced by the construction of the random catalog and by survey geometry. Consequently, the large‑scale behavior of ξ(r) in SDSS‑DR7 can only be interpreted as a lower bound on the true amplitude and extent of correlations.

In the concluding section the paper emphasizes that future surveys with substantially larger volumes and higher galaxy densities—such as DESI, Euclid, and LSST—will be required to reduce density‑related uncertainties and to control volume‑dependent systematics. Only with such data can the anti‑correlation scale and the BAO peak be measured with the precision needed to provide a decisive test of the ΛCDM predictions. The study also contributes a methodological framework for propagating density errors and assessing systematic effects, which will be valuable for forthcoming large‑scale structure analyses.