The lack of positive evidence for Weakly Interacting Massive Particles (WIMPs) as well as the lack of discovery of supersymmetric (SUSY) particles at the LHC may appeal to a non-supersymmetric solution for the Standard Model problem of the Higgs boson mass divergence, the origin of the electroweak energy scale and the physical nature of the cosmological dark matter in the approach of composite Higgs boson. If the Higgs boson consists of charged constituents, their binding can lead to stable particles with electroweak charges. Such particles can take part in sphaleron transitions in the early Universe, which balance their excess with baryon asymmetry. Constraints on exotic charged species leave only stable particles with charge $-2n$ possible, which can bind with n nuclei of primordial helium in neutral dark atoms. The predicted ratio of densities of dark atoms and baryonic matter determines the condition for dark atoms to dominate in the cosmological dark matter. To satisfy this condition of the dark-atom nature of the observed dark matter, the mass of new stable $-2n$ charged particles should be within reach of the LHC for their searches. We discuss the possibilities of dark-atom binding in multi-atom systems and present state-of-the-art quantum mechanical descriptions of dark-atom interactions with nuclei. Annual modulations in such interactions with nuclei of underground detectors can explain the positive results of DAMA/NaI and DAMA/LIBRA experiments and the negative results of the underground WIMP searches.

New heavy particles with electroweak charges arise in extensions of the standard model. They should take part in sphaleron transitions in the early Universe, which balance baryon asymmetry with the excess of new charged particles. If electrically charged with charge $-2n$, they bind with n nuclei of primordial helium in dark atoms of dark matter. This makes it possible to find the ratio of densities of asymmetric dark matter and baryonic matter. Examples of the model with new, successive, and stable generation of quarks and leptons and the minimal walking technicolor model are considered.

The new stable fermion family, with Standard Model electroweak (EW) charges, should take part in sphaleron transitions in the early Universe before breaking of the EW symmetry. The conditions of balance between the excess of new fermions (additional generation of new superheavy U, D quarks and new E, N leptons) and baryon asymmetry, were considered at temperatures above, and below, the phase transition, using a system of equations for chemical potentials.

The dark atoms $XHe$ are the composite Thomson like atomic dark matter candidates. We address two cosmological problems of this model. The excess of new superheavy particles with even negative charge $X^{-2n}$ over the corresponding antiparticles is balanced by sphaleron transitions with baryon asymmetry and the mass range of $X$ particles should be specified at which this excess can provide dominance of dark atoms in the dark matter density. The other problem is possible capture of light nuclei by dark atoms, which can lead to formation of anomalous isotopes. The possibility of formation of multi dark atom systems at the nucleosynthesis stage is also studied. We approach these open questions of dark atom cosmology in the present work.

The multi-messenger exploration of dark matter and physics beyond the Standard Model has emerged as a central direction in modern astro-particle physics, particularly following the discovery of gravitational waves. In this work, we present a comprehensive review and forward-looking perspective on machine-learning-enhanced multi-messenger approaches, combining information from gravitational waves, cosmic rays, gamma rays, neutrinos, and collider experiments. We summarize the current state of the field, discuss recent methodological developments, and outline a coherent research program aimed at integrating heterogeneous datasets within a unified inference framework. We collaboratively propose a plan for forthcoming analyses aiming at extracting information on the properties and interactions of dark matter, and finally on its genesis, combining multi-messenger astronomy techniques and inputs from laboratory physics. The main objectives planned in this line of research comprise: (i) the multi-messenger analysis of new physics in cosmology, including mainly, but not only, several different models of dark matter; (ii) the phenomenology of new physics signatures in ground-based cosmic rays experiments, with cross-correlation to the corresponding physical, astrophysical and cosmological observations; (iii) the development of machine learning methods for data analysis in ground-based cosmic rays experiments, in light of the new physics signatures. We note that several groups have explored the use of multi-messenger observations, including gravitational waves, to probe alternative dark matter candidates. The present work builds on these developments by focusing on the role of machine learning in integrating heterogeneous datasets. We foresee that a cross-fertilizing approach combining the information that arises from very different experimental methodologies will represent the right and successful path to extract information about the very elusive dark matter particles and provide answers to the main questions that are left in fundamental physics.