Preface
1 Effective potential and phase transitions 11.1 Coleman-Weinberg one loop effective potential . . . . . . . . . . 11.1.1 One-loop effective potential of, Á4 theory . . . . . . . . 31.1.2 Dimensional regularization . . . . . . . . . . . . . . . . . . 41.1.3 Renormalization scheme independence of the effective potential . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51.2 Standard model Higgs potential . . . . . . . . . . . . . . . . . . . . 61.3 Higgs vacuumstability . . . . . . . . . . . . . . . . . . . . . . . . . 61.4 Effective potential at finite temperature . . . . . . . . . . . . . . . 61.5 Phase transitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2 GravitationalWaves 92.1 Linearised gravity . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92.2 Energy loss by gravitational radiation frombinary neutron stars or black holes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122.3 Waveformof gravitational waves from binary mergers . . . . . . 152.4 Gravitational waves from phase transitions . . . . . . . . . . . . . 152.5 Gravitational waves andMulti-messenger astronomy . . . . . . . 18
3 Black Holes 193.0.1 Kerr black hole . . . . . . . . . . . . . . . . . . . . . . . . . 193.0.2 Photon orbit around Kerr black holes . . . . . . . . . . . . 193.0.3 Massive particle orbits around Kerr black holes . . . . . . 193.0.4 Frame dragging and Lens-Thirring precession of gyroscopes 193.0.5 Space-time structure of Kerr black hole . . . . . . . . . . . 193.0.6 Penrose process . . . . . . . . . . . . . . . . . . . . . . . . . 193.0.7 Super-radiance . . . . . . . . . . . . . . . . . . . . . . . . . 19
4 High energy cosmic rays 214.1 Sources of high energy cosmic rays . . . . . . . . . . . . . . . . . . 214.1.1 High energy positrons from the galaxy . . . . . . . . . . . 214.1.2 High energy gamma ray observations . . . . . . . . . . . . 214.1.3 Ultra-High energy neutrino observations . . . . . . . . . . 21
5 DarkMatter 235.1 Equilibriumdistribution of collision-less particles . . . . . . . . . 235.1.1 Detection of dark matter . . . . . . . . . . . . . . . . . . . 255.1.2 Interaction of dark matter with standard model particles 255.1.3 Higgs portal . . . . . . . . . . . . . . . . . . . . . . . . . . . 255.1.4 Vector portal . . . . . . . . . . . . . . . . . . . . . . . . . . 255.1.5 Axion portlal . . . . . . . . . . . . . . . . . . . . . . . . . . 255.1.6 Neutrino portal . . . . . . . . . . . . . . . . . . . . . . . . . 255.2 Dark matter signals in high energy photons, positrons and neutrinos observations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 265.3 Effective DM-nucleon interaction operators . . . . . . . . . . . . 265.3.1 Direct detection experiments . . . . . . . . . . . . . . . . . 275.3.2 Collider searches for dark matter . . . . . . . . . . . . . . 275.4 Dark matter at cosmological scales . . . . . . . . . . . . . . . . . . 275.5 Boltzmann equation . . . . . . . . . . . . . . . . . . . . . . . . . . 275.6 Relic density . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 315.6.1 Relic density of Cold DarkMatter by Freeze-Out . . . . . 335.6.2 Cold dark matter relic by Freeze-In . . . . . . . . . . . . . 365.7 Relic density of SIMP dark matter . . . . . . . . . . . . . . . . . . 395.8 Relic density ofWarmdark matter . . . . . . . . . . . . . . . . . . 395.9 St