The Linear Point Standard Ruler with DESI DR1 and DR2 Data

TL;DR

This work revisits the linear point, a purely geometric feature in the monopole of the two-point correlation function, as a standard ruler in the era of precision cosmology. Using DESI DR1/DR2 data and AbacusSummit mocks, the authors quantify how the linear point performs relative to traditional template-based BAO analyses, showing that post-reconstruction measurements have markedly smaller uncertainties and are closer to unity once a sample-dependent correction for nonlinear damping is applied. They define a dimensionless LP quantity, $\\alpha_\mathrm{iso,LP}$, and demonstrate excellent agreement with isotropic BAO results after accounting for smearing via a correction to the fiducial linear point $s_\mathrm{LP}^\mathrm{fid}$, though this introduces a controlled cosmology dependence. The study also explores alternatives such as Laguerre reconstruction and discusses the implications for future cosmological inferences that combine LP measurements with standard BAO pipelines. Overall, the linear point emerges as a valuable complement to template-based BAO analyses, particularly when reconstruction is employed and damping corrections are properly incorporated.

Abstract

The linear point, a purely geometric feature in the monopole of the two-point correlation function, has been proposed as an alternative standard ruler. Compared to the peak in the correlation function, it is more robust to late-time nonlinear effects at the percent level. In light of improved simulations and high quality data, we revisit the robustness of the linear point and use it as an alternative to template-based fitting approaches typically used in BAO analyses. We present the linear point measurements on galaxy samples from the first and second data releases (DR1 and DR2) of the DESI survey. We convert the linear point into a dimensionless parameter $α_{iso,LP}$, defined as the ratio of the linear point in the fiducial cosmology and the observed value, analogous to the isotropic BAO scaling parameter $α_{iso}$ used in previous BAO measurements. Using the 2nd generation of AbacusSummit mock catalogs, we find that linear point measurements are more precise when calculated in the post-reconstruction regime with 15-60% smaller uncertainties than those pre-reconstruction. We find a systematic shift in the linear point measurements compared against the isotropic BAO measurements in mocks; we attribute this to the isotropic damping parameter responsible for smearing the linear point in the nonlinear regime. We propose a sample-dependent correction that mitigates the impact of late-time nonlinear effects. While this introduces a cosmology dependence in an otherwise model-independent measurement, this is necessary given the sub-percent precision dictated by current cosmological surveys. Comparing $α_{iso,LP}$ with isotropic BAO measurements made on the DESI DR1 and DR2 galaxy samples, we find excellent agreement after applying this correction, particularly post-reconstruction. We discuss future scope regarding cosmological inference with linear point measurements.

Figures (17)

• Figure 1: Average two point correlation function of the 25 LRG1Abacus- 2 mocks in the typical BAO fitting range of 50-150 $h^{-1}\mathrm{Mpc}$. The solid line represents the best-fit DESI BAO template to the points, whereas the inset plot shows a narrower range of 70-115 $h^{-1}\mathrm{Mpc}$ in which the correlation function can be approximated as an odd degree polynomial. A fifth degree polynomial fit is shown as a dotted-dashed line in the inset, and the vertical line indicates the location of the linear point.
• Figure 2: The mean isotropic BAO dilation parameter, $\alpha_\mathrm{iso,BAO}$, compared to the mean ratio of the fiducial linear point to the measured linear point, defined in Eq. \ref{['eq:qiso_lp']} as $\alpha_\mathrm{iso,LP}$, computed on LRG and ELGAbacus- 2 mock catalogs pre- (left) and post-reconstruction (right). Both panels have he same $x$-axis and $y$-axis range to illustrate the difference in size of error bars pre- and post-reconstruction.
• Figure 3: Same as Figure \ref{['fig:qiso_bao_lp_mocks_uncorrected']}, but using the "corrected" $\alpha_\mathrm{iso,LP}$ values after taking into account the smearing in the fiducial linear point due to late-time nonlinear evolution. The correction only shifts the $y$-axis coordinates to lower values and slightly increases the size of error bars.
• Figure 4: Two-point correlation functions for different DESI DR1 tracers before (open circles) and after reconstruction (solid triangles). The overplotted curves are the best fit polynomial interpolations over the linear point fitting range (70 $h^{-1}\mathrm{Mpc}$$<s<$ 115 $h^{-1}\mathrm{Mpc}$) before (dashed lines) and after reconstruction (dotted-dashed lines). The pre-reconstruction (gray) post-reconstruction (colored) linear point measurements are shown as vertical lines with the shaded region representing the $1\sigma$ error bar. We also plot, as a dotted vertical line, the linear point in the unsmeared linear theory correlation function obtained from CLASS for the DESI fiducial cosmology (same in all panels). Note that we were unable to measure the linear point on the pre-reconstruction BGS correlation function; the first panel is therefore missing the gray vertical line and shaded band.
• Figure 5: The linear point measurements on DR1 tracers, converted to $\alpha_\mathrm{iso,LP}$, plotted against the BAO measurements made in desi2024_iii, pre- (left) and post-reconstruction (right).