Cosmological Structure Analysis Using Correlation Functions

Cosmological structure analysis seeks to characterise the large-scale distribution of matter in the universe, probing the imprint of fundamental physics on galaxy clustering and cosmic expansion. Central to this endeavour are correlation functions, statistical measures that quantify how density fluctuations at different points are related. The two-point correlation function and its Fourier counterpart, the power spectrum, capture the bulk of information in the quasi-linear regime, revealing phenomena such as baryon acoustic oscillations and the growth rate of structures. Extending beyond Gaussian statistics, three-point correlation functions and the bispectrum probe non-linear gravitational collapse and primordial non-Gaussianity. Advances in methodology now enable the extraction of information on smaller, highly non-linear scales through forward modelling and simulation-based inference, while environment-dependent statistics exploit the cosmic web—voids, walls, filaments and nodes—to lift parameter degeneracies. Such techniques are complemented by marked statistics, which weight regions by local density, and by higher-order estimators like skew spectra. Together, these tools refine constraints on matter density, dark energy properties, neutrino masses and the amplitude of density fluctuations, thereby deepening our understanding of cosmological parameters and the physics of structure formation.

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Cosmological Structure Analysis Using Correlation Functions publication trend

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Technical terms

Two-point correlation function: A measure of the excess probability of finding pairs of density fluctuations separated by a given distance, relative to a random distribution.

Power spectrum: The Fourier transform of the two-point correlation function, describing the distribution of clustering power as a function of spatial frequency (wavenumber).

Bispectrum: The Fourier analogue of the three-point correlation function, quantifying the coupling of modes and capturing non-Gaussian information in the density field.

Non-linear scale: A spatial scale at which density perturbations have grown sufficiently for linear theory to break down and mode coupling becomes significant.

Redshift-space distortions: Anisotropies in the observed clustering pattern arising from galaxy peculiar velocities along the line of sight, which modify inferred distances from redshift measurements.

References

1. A forward modeling approach to analyzing galaxy clustering with SimBIG. Proceedings of the National Academy of Sciences of the United States of America (2023).
2. Cosmology with cosmic web environments. Astronomy & Astrophysics (2023).
3. Cosmological Information in the Marked Power Spectrum of the Galaxy Field. The Astrophysical Journal (2023).
4. Cosmological information in skew spectra of biased tracers in redshift space. Journal of Cosmology and Astroparticle Physics (2023).