On the dissection of degenerate cosmologies with machine learning

Abstract

Based on the DUSTGRAIN-pathfinder suite of simulations, we investigate observational degeneracies between nine models of modified gravity and massive neutrinos. Three types of machine learning techniques are tested for their ability to discriminate lensing convergence maps by extracting dimensional reduced representations of the data. Classical map descriptors such as the power spectrum, peak counts and Minkowski functionals are combined into a joint feature vector and compared to the descriptors and statistics that are common to the field of digital image processing. To learn new features directly from the data we use a Convolutional Neural Network (CNN). For the mapping between feature vectors and the predictions of their underlying model, we implement two different classifiers; one based on a nearest-neighbour search and one that is based on a fully connected neural network. We find that the neural network provides a much more robust classification than the nearest-neighbour approach and that the CNN provides the most discriminating representation of the data. It achieves the cleanest separation between the different models and the highest classification success rate of 59% for a single source redshift. Once we perform a tomographic CNN analysis, the total classification accuracy increases significantly to 76% with no observational degeneracies remaining. Visualising the filter responses of the CNN at different network depths provides us with the unique opportunity to learn from very complex models and to understand better why they perform so well.

Investigating the degeneracy between modified gravity and massive neutrinos with redshift-space distortions

“…The DES Collaboration considers neutrino mass and extensions to GR in the same analysis [36], although they only state the resulting constraints on the MG parameters and not the neutrino masses. There are some promising signs that certain observables may be better at reducing or even breaking this degeneracy, such as higher-order weak lensing statistics [37] and weak lensing tomographic information at multiple redshifts [38]; as well as techniques that are superior at distinguishing models such as machine learning [39,40].…”

An interpretable machine-learning framework for dark matter halo formation

“…Machine learning provides a tool that is well suited to modelling cosmological structure formation, given its ability to learn non-linear relationships. In fact, machine learning tools have already proved useful in the context of structure formation in, for example, distinguishing between cosmological models (Merten et al 2019) or constructing mock dark matter halo catalogues (Berger & Stein 2019). However, understanding the inner workings of machine learning models remains a challenge.…”

Constraining the Neutrino Mass with the Drifting Coefficient of the Field Cluster Mass Function

“…Now that the validity of the analytic model of the field cluster mass function for the f (R) gravity cosmology is confirmed, we repeat the whole process but for the fR4+0.3 eV, fR5+0.15 eV and fR6+0.06 eV cosmologies, which were shown to be degenerate with the GR in the standard statistics including the nonlinear density power spectrum, cluster mass functions and halo bias (Baldi et al 2014;Giocoli et al 2019). Figure 10 (Figure 11) depicts the same as Figure 1 (Figure 2) but for the fR4+0.3 eV, fR5+0.15 eV and fR6+0.06 eV cosmologies.…”

“…Collapsed structures were identified through a FoF finder with a linking length parameter of l c = 0.16 followed by the unbinding procedure implemented in the SUBFIND code to identify the halo center and its spherical overdensity mass and radius for all gravitationally bound objects in each cosmology, similarly to what described above for the CoDECS simulations. For a detailed description of the technical details of the DUSTGRAIN-pathfinder simulations, see Giocoli et al (2019).…”

“…Choosing as a viable MG the f (R) gravity in which the Ricci scalar term, R, in the Einstein-Hilbert action functional is replaced by an arbitrary function, f (R), Baldi et al (2014) numerically investigated a possible cosmic degeneracy between the ΛCDM + GR and the νCDM + f (R), and demonstrated that the two cosmologies cannot be discriminated from each other by several standard diagnostics such as the nonlinear density power spectra, halo bias and cluster mass functions (see also Hagstotz et al 2019;Garcia-Farieta et al 2019). The nonlinear growth rate functions, cluster velocity dispersions, and tomographic higher-order weak lensing statistics were proposed in subsequent works as candidate diagnostics that could be capable of breaking this cosmic degeneracy (Giocoli et al 2019;Hagstotz et al 2019), also employing Machine Learning techniques (Peel et al 2019;Merten et al 2019).…”