Topological analyses of galaxy distributions have gathered increasing attention in cosmology, as they are able to capture non-Gaussian features of large-scale structures (LSSs) that are overlooked by conventional two-point clustering statistics. We utilize Betti curves, a summary statistic derived from persistent homology, to characterize the multiscale topological features of the LSS, including connected components, loops, and voids, as a complementary cosmological probe. Using halo catalogs from the quijote suite, we develop a coherent and extendable analysis framework that combines Betti-curve measurements, automated machine-learning-based emulators, and Bayesian inference for cosmological parameter estimation. Within this framework, we assess the sensitivity of Betti curves to cosmological parameters and train emulators to model their dependence on cosmology. Our Bayesian inference recovers unbiased estimation of cosmological parameters, notably, $n_{\mathrm{s}}$, ${\sigma }_8$, and ${\mathrm{\Omega }}_{\mathrm{m}}$, while validation on sub-box simulations confirms robustness against cosmic variance. We further investigate the impact of redshift-space distortions (RSDs) on Betti curves and demonstrate that including RSDs enhances sensitivity to growth-related parameters. When combined with the power spectrum, Betti curves break parameter degeneracies and lead to significantly tighter joint constraints than the power spectrum alone on parameters such as $n_{\mathrm{s}}$, ${\sigma }_8$, and $w$. These results establish Betti curves as a viable and complementary topological observable for cosmological parameter inference and motivate further theoretical and observational developments toward their application in future galaxy surveys.

Close

PrevNext

View figure in article

• Cosmological parameters
• Large scale structure of the Universe
• Distances, redshifts, & velocities
• Astrophysical & cosmological simulations