Persistent homology in cosmic shear II: A tomographic analysis of DES-Y1

Abstract

We demonstrate how to use persistent homology for cosmological parameter inference in a tomographic cosmic shear survey. We obtain the first cosmological parameter constraints from persistent homology by applying our method to the first-year data of the Dark Energy Survey. To obtain these constraints, we analyse the topological structure of the matter distribution by extracting persistence diagrams from signal-to-noise maps of aperture masses. This presents a natural extension to the widely used peak count statistics. Extracting the persistence diagrams from the cosmo-SLICS, a suite of N -body simulations with variable cosmological parameters, we interpolate the signal using Gaussian Processes and marginalise over the most relevant systematic effects, including intrinsic alignments and baryonic effects.We find for the structure growth parameter S8 = 0.747 +0.025 −0.031 , which is in full agreement with other late-time probes. We also constrain the intrinsic alignment parameter to A = 1.54 ± 0.52, ruling out the case of no intrinsic alignments at a 3σ-level.

KiDS-1000 cosmology: Constraints from density split statistics

“…6, which shows that the mean aperture numbers with baryons are slightly lower. Different to our studies of baryonic feedback such as Heydenreich et al (2022) or Harnois-Déraps et al ( 2021), the inclusion of baryons in the sources has only a minor impact on the DSS, but as expected, becoming more important at small scales. In light of this, we can safely neglect the impact of baryons in our real data analysis.…”

“…This can be constructed either from simulations (see, e.g., Harnois-Déraps et al 2021;Zürcher et al 2022, for examples of simulation-based inference using the lensing peak count) or from analytical calculations, where for instance Reimberg & Bernardeau (2018) and Barthelemy et al (2021) made use of large deviation theory (LDT) to model the reduced-shear correction to the aperture mass probability distribution function (PDF). Another approach to access higher-order moments is discussed in Halder et al (2021), Halder & Barreira (2022), and Heydenreich et al (2022), where third-order cosmic shear statistics were modelled directly from the bispectrum. Although, the simulation-based approach has advantages regarding the numerical incorporation of critical systematic effects such as the intrinsic alignment (IA) of galaxies (see, e.g.…”

Cosmology from the integrated shear 3-point correlation function: simulated likelihood analyses with machine-learning emulators

“…their eqs. (30)(31)(32)). Reference [56] does not provide a detailed derivation of their expressions, which keeps us from inspecting this issue further.…”

“…Further complications arise by the need to account for baryonic feedback effects, as well as systematics effects such as photometric redshift uncertainties, shear multiplicative bias and galaxy intrinsic alignments (IA). This helps explain why existing real-data constraints using higher-order shear information are based not on the full 3-point correlation function, but on other statistics including aperture moments [17][18][19][20][21], lensing peaks [22][23][24], density-split statistics [25][26][27][28][29] and persistent homology of cosmic shear [30,31]. The shear 3PCF was recently measured using DES Year 3 (Y3) data [20], although only in patches over the survey and not over the whole footprint as that would be too computationally demanding.…”

Fitting covariance matrix models to simulations

“…Large collaborations, such as Euclid, are already preparing to exploit these statistics. More complex observables have also been explored, such as various topological measures [9][10][11][12], synthetic tracers such as voids [13] or galaxies marked by local density, morphology or stellar mass [14][15][16], etc. This implies that data vectors will soon have hundreds of components.…”