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The BAO linear point as cosmic ruler: tests and applications to the Euclid mission

Ferrari, Angelo Giuseppe

Publisher
Zenodo
DOI
10.5281/zenodo.17747090
Repository
zenodo.org
Language
en

Abstract

Parallel talk presented at the XXI International Workshop on Neutrino Telescopes - Padova 29 September - 3 October 2025 (https://agenda.infn.it/event/44606/) Abstract: The large-scale distribution of galaxies retains imprints of acoustic waves that propagated through the primordial baryon-photon plasma. These waves leave a characteristic signature in the galaxy two-point correlation function, known as the Linear Point (LP). The LP is defined as the midpoint between the peak and dip of the correlation function at scales around 150 Mpc, and in recent years, it has emerged as a novel and robust cosmic ruler. In this talk, I will explain that the Linear Point is a cosmological standard ruler and it crucially enables us to measure cosmic distances without the need to model the impact of non-linearities on the clustering correlation function. The LP maintains its standard ruler properties even in cosmologies with massive neutrinos and thus it is highly relevant for the cosmological inference of the sum of neutrino masses. Recent analyses suggest an unexpected result, that the highest probability region for the sum of the neutrino masses is in the interval m_nu < 0.06 eV. Therefore exploiting complementary observables like the LP is crucial to shed light on such findings. Finally, I will present ongoing work in the context of the Euclid mission. We are assessing the accuracy and expected precision of LP measurements using mock catalogs (dark matter particles, halos, and galaxies) tailored to Euclid’s specifications. This preparatory analysis is crucial for applying the LP method to upcoming Euclid data, ultimately aiming to constrain cosmological parameters and the sum of neutrino masses with Euclid.

Full text

The BAO linear point as cosmic ruler: tests and applications to the Euclid mission Angelo Ferrari 1 BAO 2 From Eisenstein et al. (2007) ❖Imprints of primordial sound waves in the galaxy distribution. ❖Characteristic feature in the 2-point correlation function (2pcf) of galaxies. ❖BAO allow us to measure cosmic distances. ➢Probe the expansion of the Universe, dark energy, curvature and dark matter. ❖Defined as the mid point between the peak and the dip. ❖Geometrical standard ruler (independent of primordial physics). ❖LP position very close to linear theory prediction. ❖Weakly sensitive to Non-Linearities (0.5%) (i.e. non linear gravity, non-linear RSD, scale dependent bias). ❖Used to estimate cosmological distances in a model-independent way. ❖Relevant for ΛCDM, neutrino masses and dark energy models, some modified gravity models. 3 The Linear Point From Anselmi et al. - MNRAS (2016) - arxiv:1508.01170 ❖Weakly sensitive to Non-Linearities. ❖Shift of peak and dip slightly larger, the LP stays fixed at the 0.5% Distance measurements at 0.5% level 4 Dependence on NonLinearities Redshift independent correction to restore agreement with linear prediction at 0.5% at all z From Anselmi et al. - MNRAS (2016) - arxiv:1508.01170 Massive neutrinos add scale dependence already in linear theory but: ❖LP Retains its features as a standard ruler when neutrinos are massive. ❖ ❖In Linear theory LP is z-independent, even with neutrino masses (more stable than peak and dip). ❖ ❖NonLinearities (Gravity and RSD, scale dependent bias): LP position remains in agreement with the linear prediction when neutrinos are assumed to be massive. ✅ ❖ ❖Sensitivity to neutrino masses. 5 LP and massive neutrinos Linear Point Parimbelli et al. - JCAP (2021) 6 Neutrino mass from cosmology SPT results (Camphuis et al 2025) Abdul-Karim et al 2025 How is the LP estimated? 7 MINIMIZE Cosmology agnostic (no cosmology-dependence, no CF template). PEAK AND DIP LP ERROR PROPAGATION FROM POLY COEFFICIENTS TO LP SCALE Best setup for the fit? Order of poly, scale range, binning. Tests on mocks. Either using a 2pcf distribution estimated from mocks or creating one (usually multivariate Gaussian distribution) - Gaussianity of 2pcf (if mocks are used) - Optimal polynomial estimator (consider different orders) - Optimal range of scales on which to perform the fit -Ꭓ2 consistent with expected Ꭓ2 distribution Checks Choice of setup affects bias and errors in the estimate Anselmi et al. - PRD (2018) LP provided distance estimates with statistical uncertainties that are 24% and 18% smaller than the BOSS result for the LOWZ and CMASS samples respectively. LP and distances with BOSS data 8 Anselmi et al. - PRD (2018); Anselmi et al. - PRL (2018) With data one actually measures (exploiting fid. coords): Assuming we know exactly s_LP and r_d we can easily compare with the standard result Cuesta et al. - MNRAS (2016) The Linear Point Standard Ruler with the Euclid galaxy survey 9 Led by S. Anselmi. Collaborators: M. Ballardini, J. Bel, L. Blot, M. A. Breton, S. Casas, P.S. Corasaniti, S. Dusini, M. Lattanzi, M. Magliocchetti, N. Mauri, Y. Rasera, A. Sanchez, C. Sirignano, G. Sirri, L. Stanco, M. Viel, T. Brinckmann, S. Anselmi, A. Renzi, S. Tosi, S. Davini, G. Testera, G. Parimbelli, L. Pagano, A. Troja, A. Ferrari, F. Passalacqua, F. Oppizzi, M. Lembo, A. Begnoni Euclid like z-bins from the narrow lightcone of Raygal 16 DM particles - LP estimates In each bin: ❖Np = 107 ❖Nrandoms = 5x108 (x50) ❖Bin size of 2 Mpc/h from Setup similar to Euclid DR1(redshift bins and area) but with higher number density EUCLID PRELIMINARY ❖Finding the optimal setup for the fit: using different set-ups (scale range – binning –polynomial order). ➢ Fit mock sample of non-linear 2pcf (Zeldovich) assuming they follow a Gaussian multivariate distribution. ❖Perform several tests to decide which setup is optimal: ➢Mock acceptance rate, ➢Goodness of fit, Bias : <E[LP]> vs Fiducial, ➢Minimum statistical uncertainty ❖Actual estimate of LP on (simulated for now) “data” as described before. 17 DM particles - LP estimates Expected agreement within the 0.5% bias uncertainty EUCLID PRELIMINARY Perspectives and next steps 18 ❖Complete the study on the Raygal simulation: ➢Lensed angles for DM particles ➢Halos ❖Study the LP on the lightcone of the Flagship simulation ➢Galaxies ➢Halos ❖Include observational systematics (e.g. interlopers) ❖Covariance and validation with mocks ❖Goal is to be ready to analyze DR1 data To conclude 19 ❖Linear Point is a geometrical standard ruler ❖Stable with respect to Non-Linearities (gravity, RSD, matter tracers) ❖LP estimation procedure knows nothing about cosmology (simple polynomial fit) ❖It can be used to estimate distances in a model independent way with no fixed cosmological parameters and 2pcf templates ❖Relevant for LCDM, dark energy models and neutrino mass ❖It has been shown to estimate distances with smaller errors in the BOSS dataset ❖Within Euclid: ➢1 paper under internal review: Estimates of the LP on the snapshots of the Flagship simulations and several consistency tests on the reliability of the LP for Euclid ➢Current work involving lightcone analysis and study of relativistic effects: starting from RayGal simulation to move to Flagship Data incoming!