Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 2609.25320

Basis function expansions of the two-point correlation function and reconstruction of the cosmological distance scale

Fatima Abd Alrahman·Farnik Nikakhtar·Marcello Musso·Aseem Paranjape·Ravi K. Sheth
View original source ↗Read source document ↗Export metadata ↓

Abstract

The shape of the correlation function of galaxy pairs can be used as a cosmological distance indicator. Most estimators of this shape require that one bin the pair counts, and considerable effort is expended in finding the optimal bin size. Cosmological constraints are then derived, in a separate step, by fitting to the binned pair counts. By projecting the pair counts on a suitable basis set, it is possible to estimate the pair correlation function without binning. Recent work suggests that, in the context of estimating the cosmological distance scale from galaxy clustering data, polynomials and half-integer generalized Laguerre functions are particularly useful bases. We show how to use these bases to measure the correlation function and estimate the reconstructed distance scale in a single step. Our analysis includes the effects of shot-noise and cosmic variance, and highlights the benefits of projecting pair counts onto orthogonal basis functions.

Explore related subjects

astro-ph.CO

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Fatima Abd Alrahman, Farnik Nikakhtar, Marcello Musso, Aseem Paranjape, Ravi K. Sheth. 2026-09-21. Basis function expansions of the two-point correlation function and reconstruction of the cosmological distance scale. https://arxiv.org/abs/2609.25320

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Primordial black hole clustering from spectator fields for interpreting the JWST observations

The observations by the James Webb Space Telescope (JWST) have revealed unexpectedly massive galaxy candidates at high redshifts, posing a significant challenge to the $Λ$CDM model. In this work, we investigate whether primordial black holes (PBHs) with spatial clustering, generated by a light spectator field during inflation, can accelerate early structure formation. We adopt the galaxy candidates with inferred stellar mass $10^9\,M_\odot\leq M_*^{\rm obs}\leq10^{11}\,M_\odot$ at redshift $7 \leq z \leq 10$ reported by the CEERS program as a benchmark. Two different mechanisms are considered, through which PBH clustering can influence structure formation: the PBH-induced isocurvature perturbations that enhance the matter power spectrum on linear scales, and the localized seed formation and accretion by compact PBH clusters on nonlinear scales. We find that, when adopting the cosmic microwave background (CMB) isocurvature constraint $β_{\rm iso}<0.035$ at the benchmark pivot scale $k_*=0.002\,{\rm Mpc}^{-1}$, PBH clustering can produce a cumulative stellar mass density consistent with the JWST observations while satisfying the relevant isocurvature constraint. However, the allowed enhancement of structure formation is strongly suppressed when the constraint at $k_*=0.1\,{\rm Mpc}^{-1}$ is imposed, indicating a significant dependence on the choice of the pivot scale. In contrast, the localized seed effect of compact PBH clusters is strongly constrained by the CMB isocurvature bounds, while isolated supermassive PBHs produce stellar mass densities far below those inferred from the JWST observations. Our results show that PBH clustering induced by a spectator field can substantially accelerate early structure formation, but whether it can fully account for the JWST-inferred stellar mass density depends sensitively on the pivot scale adopted for the CMB isocurvature constraint.

astro-ph.CO↗
arXiv2026

Probing memory-burdened Primordial Black Holes with global 21 cm signal

We investigate the imprints of memory-burdened primordial black holes (PBH) on the global 21 cm signal during the cosmic dawn. Recent studies reopened the possibility of a mass window of PBHs as a compelling candidate for dark matter, particularly in low-mass regimes ($M_{\text {PBH}}< 10^{15}$ g) where conventional constraints from evaporation are being revisited in light of quantum gravitational effects. One such effect, the \textit{memory burden effect}, slows down black hole evaporation by incorporating the backreaction of radiation on the black hole microstates, substantially extending the lifetime of light PBHs and thus modifying their late-time emission spectra. This prolonged emission can dramatically alter the energy injection history in the early universe. By computing the modified energy injection rates into the intergalactic medium and incorporating them into the thermal and ionization evolution of neutral hydrogen, we obtain projected constraints on the fraction of dark matter. The bounds are obtained from the fact that these low mass PBHs, which were thought otherwise evaporated, can modify the absorption amplitude in the global 21-cm signal at redshift $z\approx17$. Considering the two viable scenarios of transition to the memory-burden phase: fast (or instantaneous) and slow (transition with a finite width), we show how the 21 cm bounds are sensitive to different mass ranges. For a broad transition with $δ=10^{-2}$ we find that PBHs in the mass range $M_{\rm PBH}\simeq10^{8}$-$10^{13}$g are excluded at the level of $f_{\rm PBH}\gtrsim10^{-8}$. In contrast, for a fast-transition case with the lowest suppression exponent $k=1$, the evaporation is suppressed so efficiently that no meaningful 21\,cm constraint remains for $M_{\rm PBH}\gtrsim10^{7}$g.

astro-ph.CO↗
arXiv2026

Primordial Black Hole Abundances and Scalar Induced Gravitational Waves from Finite-Width Power Spectra in a Stiff Thermal History

We study the formation of primordial black holes (PBHs) from large primordial perturbations that re-enter the horizon during an epoch with equation of state ${\rm w}\geq1/3$. We consider a log-normal curvature power spectrum of finite width $Δ$ and determine the collapse amplitude by numerical-relativity simulations of a self-gravitating perfect fluid. Threshold scans are performed for five values of $\rm w$ and five spectral widths, and the resulting numerical thresholds are used in the PBH abundance and scalar-induced gravitational-wave (SIGW) calculations. For comparison, we also evaluate the semi-analytical $q$-function prescription. It reproduces the numerical trend close to radiation domination and for nearly monochromatic profiles, but it is not a reliable threshold estimator for generic finite-width profiles in stiffer backgrounds. We show how collapse thresholds increase with both $Δ$ and $\rm w$, changing the curvature amplitude required for PBHs to constitute all of the dark matter and, consequently, the normalization of the accompanying SIGW signal.

astro-ph.CO↗