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

@misc{alrahman2026basis,
  title = {{Basis function expansions of the two-point correlation function and reconstruction of the cosmological distance scale}},
  author = {Fatima Abd Alrahman and Farnik Nikakhtar and Marcello Musso and Aseem Paranjape and Ravi K. Sheth},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.25320},
  eprint = {2609.25320},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.25320},
}

TY  - UNPB
TI  - Basis function expansions of the two-point correlation function and reconstruction of the cosmological distance scale
AU  - Fatima Abd Alrahman
AU  - Farnik Nikakhtar
AU  - Marcello Musso
AU  - Aseem Paranjape
AU  - Ravi K. Sheth
PY  - 2026
DA  - 2026/09/21
PB  - arXiv
DO  - 10.48550/arxiv.2609.25320
UR  - https://arxiv.org/abs/2609.25320
AB  - 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.
ER  -