Quantifying the accuracy of the Alcock-Paczyński scaling of baryon acoustic oscillation measurements

Abstract

We investigate -in a generic setting -the regime of applicability of the Alcock-Paczyński (AP) scaling conventionally applied to test different cosmological models, given a fiducial measurement of the baryon acoustic oscillation (BAO) characteristic scale in the galaxy 2-point correlation function. We quantify the error in conventional AP scaling methods, for which our ignorance about the true cosmology is parameterised in terms of two constant AP scaling parameters. We propose a new, and as it turns out, improved version of the constant AP scaling, also consisting of two scaling parameters.The two constant AP scaling methods are almost indistinguishable when the fiducial model used in data reduction and the "true" underlying cosmology are not differing substantially in terms of metric gradients, but are otherwise expected to differ. Our new methods can be applied to existing analyses through a reinterpretation of the results of the conventional AP scaling. This reinterpretation might be important in model universes where curvature gradients above the scale of galaxies are significant.We test our theoretical findings on ΛCDM mock catalogues. The conventional constant AP scaling methods are surprisingly successful for pairs of large-scale metrics, but eventually break down when toy models allowing for large metric gradients are tested. The new constant AP scaling methods proposed in this paper are efficient for all test models examined. We find systematic errors of ∼1% in the recovery of the BAO scale when the true model is distant from the fiducial, which cannot be attributed to any constant AP approximation. The level of systematic uncertainty is robust to the exact fitting method employed. This indicates that caution must be taken with the error budget when extrapolating the BAO acoustic scale measurements obtained in the standard literature. 4 The Alcock-Paczyński scaling and the BAO feature 13 5 Testing the predicted shift of the BAO feature with mock catalogues 15 5.1 The mock catalogues 15 5.2 The likelihood function and the fitting procedure 16 5.3 Large-scale model cosmologies 18 5.4 Toy models with large metric gradients 24 6 Discussion 29 Appendix A The 2-point correlation function and the Landy-Szalay estimators 31 A.1 The 2-point correlation 31 A.2 The Landy-Szalay estimators 33 Appendix B Conjecture of improved AP scaling 35 Appendix C Bounds on the AP error terms 38 C.1 Bounds on the magnitude of ∆ α 38 C.2 Bounds on the magnitude of ∆ 39 -1 -The distribution of gravitationally-bound matter in space serves as an important probe of large-scale dynamics of the Universe. In the Lambda Cold Dark Matter (ΛCDM) cosmology -or indeed any Friedmann-Lemaître-Robertson-Walker (FLRW) model beginning in a hot big bang -the primordial plasma exhibits sound waves which are imprinted as a characteristic scale in the matter distribution after the decoupling of the baryons from the photons [1, 2]. This characteristic baryon acoustic oscillation (BAO) scale is predicted to be seen as an excess in the autocorrelation o...

Constraining early dark energy with large-scale structure

“…First, the use of the Alcock-Paczynski scaling parameters [47] to extract the BAO frequency from the three-dimensional galaxy distribution is accurate if the Universe has a local Friedman-Robertson-Walker geometry (see, e.g., Refs. [48][49][50]), which clearly holds true in the EDE model. Second, the BAO frequency can be extracted from the postreconstruction position space correlation function (or the power spectrum) by fitting the BAO peak (or Fourier-space BAO wiggles) with a simple Gaussian (or harmonic) template, which does not rely on any cosmology-specific information.…”

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“…However, it is more convenient to switch to the geodesic distances between galaxies and consider the "deprojected" three-dimensional power spectrum instead of the two-dimensional angular power spectrum [76]. In practice, the change of coordinates is realized by means of the so-called Alcock-Paczynski scaling parameters that are based on some trial fiducial cosmology [77][78][79][80]. Importantly, if the trial cosmology is different from the correct one, the reconstructed 3D power spectrum appears distorted compared to the true one [81].…”

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