Cℓestial harmonics - Applications of Angular Power Spectra to Problems in Astroparticle and Cosmological Physics

The overarching topic of this thesis is the use of angular power spectra formalisms in the spherical harmonic space, aimed at inferring information on observables relevant to astroparticle physics and cosmology applications. Part I describes the work I developed at the University of Turin under the supervision of Prof. Nicolao Fornengo and Prof. Stefano Camera, collected in (Rubiola et al., 2024, 2025). It focuses on the astroparticle-cosmological topic of indirect detection techniques for Dark Matter particle candidates belonging to the Weakly Interacting Massive Particle (WIMP) class, endowed with masses spanning the GeV-TeV energy scale. The subject is dealt with in terms of a statistical cross-correlation formalism between the 2MRS galaxy clustering spectroscopic sample and the unresolved gamma-ray background (UGRB), which was modelled including observational features based on the Fermi-LAT satellite measured performances. The nature of the UGRB sources has been under scrutiny long since (Camera et al., 2013, 2015; Fornengo & Regis, 2014), for it possibly conceals, next to the emission coming from astrophysical processes such as different classes of Active Galactic Nuclei (AGNi) and of Star Forming Galaxies (SFGs), signatures of Beyond the Standard Model (BSM) particle signals – in particular, those coming from the potential annihilation of WIMP particles. This general physical endeavour is complemented with a number of innovations at the crossroad between the statistical and the physical levels – namely, the application of the multi-tracer formalism and of a signal filtering analogous to the one known as Wiener filter. The use of the Wiener filter can be understood as the introduction of a theoretical Ansatz concerning the connection between the halos hosting the galaxies and the halos hosting the astrophysical and dark matter UGRB sources. This first idea is combined with the use of a multi-tracer analysis aimed at simultaneously exploiting the constraining power coming from the galaxy autocorrelation signal, the galaxy-UGRB cross-correlation signal and the UGRB autocorrelation signal. Multiple strategies are described, eventually translated in a discussion of the smallest measurable annihila- tion cross-section for WIMP candidates at different masses comprised in the interval from 10 GeV to 1 TeV, capable of ensuring the detection of an excess dark matter signal against the irreducible astrophysical background at the 2σ level in the explored statistical configurations. We find that the multi-tracer innovation is particularly effective for light WIMP candidates (10 ≤ mχ ≤ 100 GeV): the sensitivities to the bounds on the annihilation cross-section are forecast to attain values more than an order of magnitude lower than the thermal WIMP cross-section rate and up to about a factor of five below the results obtained with standard cross-correlation approaches. On the other hand, the features of the Wiener filter chiefly improve the detectability of signals at the high-mass end of the discussed WIMP mass interval. The second part of this work (Part II) is instead a fundamental cosmology study based on the research work developed under the supervision of Prof. David Alonso, Dr Carlos García García and Dr Matteo Zennaro, during my visits at the Department of Physics of the University of Oxford (May–September 2024 and June–August 2025), whose outcome is published in (Rubiola et al., 2025). The project concentrated on measuring the growth factor of cosmic structures and on constraining the two parameters of the ΛCDM Ωm and σ8 as well as their combination, the parameter S8 . By doing so, we were able to elaborate on the so-called “σ8 tension” (also known as “S8 tension”, the precise distinction will be exposed in the text), that is, the 2-3σ mismatch between the variance of the density perturbations with respect to the average cosmic matter density as measured in the low-redshift Universe, chiefly reported by some main observational campaigns focusing on measuring cosmic shear signals (Asgari et al., 2021; Doux et al., 2022; Dalal et al., 2023), once the results are compared with the value obtained from the Planck mission observations of the Cosmic Microwave Background. The situation is made more unclear because other probes of the Large Scale Structure provide mixed evidence on potential divergences between high-redshift and low-redshift measurements on those parameters, spanning from a 2-3σ tension to full agreement with Planck (Di Valentino et al., 2025). The community is thus pondering different alternative answers to this potential inconsistency, spanning from statistical fluctuations, modelling and instrumental systematics affecting the power spectrum at the smallest scales and particularly severe in the case of cosmic shear statistics, up to interpreting such divergence as a signature of a falsification of the ΛCDM requiring the introduction of new physics in terms of additional fields or modifications of the gravitational interaction. Taking a rather agnostic stance, oriented in the first place to properly measuring the relevant quantities, we build upon a number of previous works, in particular, on (García-García et al., 2021; Sailer et al., 2025a), that laid out tomographic and multi-tracer analyses combining CMB lensing, galaxy clustering and weak lensing / cosmic shear observables from several surveys. These and other works indeed identified the shear signal as the main source of the tension, driving the discrepancy to a value as high as ∼ 3.5σ, a value which gets typically reduced when cosmic shear samples are excluded from the same analysis configurations and only galaxy clustering signals are retained. Altogether, the onset of the divergence between the predictions based on the ΛCDM model having the cosmological parameters set at the values provided by Planck (Aghanim et al., 2020) and the predictions calculated starting from the measurement of the same parameters from Large Scale Structure (LSS) statistics was identified in the redshift interval 0.25 ≤ z ≤ 0.5, while, at higher redshifts, the measurements based on the LSS appear more consistent with the CMB-based prediction. Building on these conclusions, constraints are presented in my work, focusing on measuring the amplitude of matter perturbations using statistics on the clustering of galaxies and in cross-correlation with the gravitational lensing signal of the cosmic microwave background (CMB): we developed a low-redshift analysis (z ≲ 0.3), in order to complement the results in the extant literature we mentioned above. This allowed us to complement the redshift intervals explored by extant tomographic analyses by covering almost all of the remaining epochs: we worked indeed with three redshift bins derived from the data of the 2MASS photometric survey (2MPZ) and the WISE×SuperCOSMOS galaxy survey having as average redshifts zm,1 ∼ 0.07, zm,2 ∼ 0.18, zm,3 ∼ 0.32, combined with the CMB lensing maps from Planck: next to completing extant available results, we could thus concentrate on a regime particularly sensitive to Dark Energy models different from the baseline cosmological constant assumed by the ΛCDM model. The combined study of low redshifts and small scales allowed us to achieve sufficient constraining power on the parameters of interest just by using the well-understood galaxy clustering data without introducing cosmic shear observable that, as mentioned, might be more problematic to handle: we strived to have all potential systematics under control, in order to introduce cosmic shear in future analysis having already predisposed the clearest and cleanest analysis conditions. After having set all the other cosmological parameters at mutually compatible LSS-based and CMB-based values – our data would not be able to constrain the whole set of ΛCDM parameters independently –, we considered two main strategies: by imposing a prior on Ωm derived from the DESI measurements of the baryon acoustic oscillation (BAO), we measure S8 = 0.79 ± 0.06, sufficiently in agreement with Planck constraints and recover the Ωm value corresponding to the prior. When instead this prior is not included, we find a value of S8 = 0.82 ± 0.07 – compatible with Planck – and Ωm = 0.245 ± 0.024, 2.8σ lower than the value reported by Planck. We interpret the somehow different results on Ωm (although of course no incompatibility or tension can be claimed) in terms of the fact that, in absence of the BAO prior, the measurement of this quantity is driven by the general functional form of the galaxy auto-correlation power spectrum (its “broadband ” shape), more sensitive to theoretical uncertainties in the power spectrum models and with a relatively loose constraining power, whilst, in presence of a prior on Ωm , the value is tightly controlled by the very specific sensitivity of this quantity to the BAO, from whose measurement the prior was derived. Also in analogy with (García-García et al., 2021; Sailer et al., 2025a), the low-redshift growth history is reconstructed: we recover substantial agreement with the Planck predictions, as well as with other reported results using the lensing tomography technique. Both research topics reserve specific attention to intermediate and small scales of the Large Scale Structure of the Universe, whose appropriate modelling calls for going beyond the linear perturbation theory: analytic tools spanning from the halo model to the use of emulators and of the Hybrid Effective Field Theory Lagrangian Perturbation Theory (HEFT LPT) calculations, devised to more accurately describe the non-linear matter field as well as that of biased tracers such as galaxy clustering signals are discussed. In particular, the 2MPZ-CMB lensing data are also used in order to test the phenomenology of non-linear galaxy bias terms and their coevolution relations, that is, the possibility of expressing the higher-order bias terms as functions of the well-understood and directly measurable linear galaxy bias term. By comparing our measurements of the bias parameters for our galaxy samples with analogous measurements available in the literature, we find a qualitative agreement among them and consistency with the available empirical coevolution scaling laws. Eventually, computational techniques concerning more efficient marginalisation over nuisance parameters in the likelihood MCMC sampling process, as well as the development of extrapolation schemes aimed at extending the dynamic ranges of the baccoemu emulator, were also implemented, thus complementing my research with specific technical and computational aspects.