An unexpected explanation for neutrino mass, Dark Matter (DM) and Dark Energy (DE) from genuine Quantum Chromodynamics (QCD) of the Standard Model (SM) is proposed here, while the strong CP problem is resolved without any need to account for fundamen
tal axions. We suggest that the neutrino sector can be in a double phase in the Universe: i) relativistic neutrinos, belonging to the SM; ii) non-relativistic condensate of Majorana neutrinos. The condensate of neutrinos can provide an attractive alternative candidate for the DM, being in a cold coherent state. We will explain how neutrinos, combining into Cooper pairs, can form collective low-energy degrees of freedom, hence providing a strongly motivated candidate for the QCD (composite) axion.
In a topological description of elementary matter proposed by Bilson-Thompson, the leptons and quarks of a single generation, together with the electroweak gauge bosons, are represented as elements of the framed braid group of three ribbons. By ident
ifying these braids with emergent topological excitations of ribbon networks, it has been possible to encode this braid model into the framework of quantum geometry provided by loop quantum gravity. In the case of trivalent networks, it has not been possible to generate particle interactions, because the braids correspond to noiseless subsystems, meaning they commute with the evolution algebra generated by the local Pachner moves. In the case of tetravalent networks, interactions are only possible when the models original simplicity, in which interactions take place via the composition of braids, is sacrificed. We demonstrate that it possible to preserve both the original classification of fermions, as well as their interaction via the braid product, if we embed the braid in a trivalent scheme, and supplement the local Pachner moves, with a non-local and graph changing 1-handle attachment. Moreover, we use Kauffman-Lins recoupling theory to obtain invariants of braided networks that distinguish topological configurations associated to particles in the Bilson-Thompson model.
Our work intends to show that: (1) Quantum Neural Networks (QNN) can be mapped onto spinnetworks, with the consequence that the level of analysis of their operation can be carried out on the side of Topological Quantum Field Theories (TQFT); (2) Deep
Neural Networks (DNN) are a subcase of QNN, in the sense that they emerge as the semiclassical limit of QNN; (3) A number of Machine Learning (ML) key-concepts can be rephrased by using the terminology of TQFT. Our framework provides as well a working hypothesis for understanding the generalization behavior of DNN, relating it to the topological features of the graphs structures involved.
