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This volume is composed of extensive and detailed notes from the lectures given at the 40th Karpacz Winter School. This school focussed on quantum gravity phenomenology with emphasis on its relation to observational astrophysics and cosmology. These notes have been carefully edited with the aim to give advanced students and young researchers a balanced and accessible introduction to an rather heavily mathematical subject.

Quantum gravity --- Cosmology --- Astrophysics --- Gravité quantique --- Cosmologie --- Astrophysique --- Congresses. --- Congrès --- Physics. --- Relativity (Physics). --- Relativity and Cosmology. --- Physics beyond the Standard Model. --- Atomic Physics --- Physics --- Astronomy & Astrophysics --- Physical Sciences & Mathematics --- Natural philosophy --- Philosophy, Natural --- Quantum field theory. --- String theory. --- Gravitation. --- Classical and Quantum Gravitation, Relativity Theory. --- Quantum Field Theories, String Theory. --- Models, String --- String theory --- Nuclear reactions --- Relativistic quantum field theory --- Field theory (Physics) --- Quantum theory --- Relativity (Physics) --- Matter --- Antigravity --- Centrifugal force --- Properties

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Application of the concepts and methods of topology and geometry have led to a deeper understanding of many crucial aspects in condensed matter physics, cosmology, gravity and particle physics. This book can be considered an advanced textbook on modern applications and recent developments in these fields of physical research. Written as a set of largely self-contained extensive lectures, the book gives an introduction to topological concepts in gauge theories, BRST quantization, chiral anomalies, supersymmetric solitons and noncommutative geometry. It will be of benefit to postgraduate students, educating newcomers to the field and lecturers looking for advanced material.

Topology. --- Geometry. --- Mathematical physics. --- Topologie --- Géométrie --- Physique mathématique --- Physics. --- Global differential geometry. --- Mathematical Methods in Physics. --- Physics beyond the Standard Model. --- Differential Geometry. --- Topology --- Geometry --- Mathematical physics --- Applied Physics --- Physics - General --- Engineering & Applied Sciences --- Physics --- Physical Sciences & Mathematics --- Physical mathematics --- Analysis situs --- Position analysis --- Rubber-sheet geometry --- Natural philosophy --- Philosophy, Natural --- Mathematics --- Differential geometry. --- Quantum field theory. --- String theory. --- Quantum Field Theories, String Theory. --- Geometry, Differential --- Differential geometry --- Models, String --- String theory --- Nuclear reactions --- Relativistic quantum field theory --- Field theory (Physics) --- Quantum theory --- Relativity (Physics) --- Physical sciences --- Dynamics

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The theory of quantum chromo dynamics (QCD), an organic part of the standard model (SM) of particle physics, has been validated by many theoretical and experimental studies. The strongly coupled QCD dynamics controls colored particles’ (quarks and gluons) collective motion at large spacetime separations and the formation of colorless composite states (hadrons). While QCD theory and the related phenomenology aspects are being intensively studied in laboratory measurements, the possible connections of this important layer of knowledge to cosmology remain rather vague and largely unexplored. No doubt, the physical vacuum has been transformed many times throughout the lifetime of the universe and has affected its history through a sequence of events, such as the cosmic inflation, phase transitions, and the dark-energy-dominated expansion. Strong interactions could play an important role in some of these cosmological events. In particular, the emergence of a new state of matter called the quark-gluon plasma at the LHC is often suggested to provide an important source of empirical knowledge to what the universe looked like in the first few moments after the Big Bang. This Special Issue aims at creating an overview of the recent progress in these directions by focusing on the novel implications of quantum chromo, or more generally, Yang–Mills (YM) dynamics, to the physics of the early universe and critical phenomena in cosmology.

Research & information: general --- Physics --- dynamics of phase transitions --- spinodal instability --- heavy-ion collisions --- neutron stars --- dark energy --- non-Abelian gauge theory --- condensate --- QCD --- DGLAP equations --- physics beyond the standard model --- tensorgluons --- extended DGLAP equations --- tensorgluon splitting functions --- neutron star --- equation of state --- many-body methods of nuclear matter --- neutron-skin thickness --- GW170817 --- Weyl gravity --- renormalization group --- inflation --- light scalar fields --- axial anomaly --- SU(2) Yang–Mills thermodynamics --- de-percolation of axionic lumps --- cosmological and galactic dark-matter densities --- cosmology --- particle physics --- particle symmetry --- stable particles --- dark matter --- cosmic rays --- QCD in the early universe --- phase transitions --- hydrodynamical evolution --- equation of state of super-dense matter --- classical Yang-Mills fields --- Dark Energy --- Dark Matter --- gluon condensate --- effective Yang-Mills action --- cosmic inflation --- n/a --- SU(2) Yang-Mills thermodynamics --- Research. --- Physics.