<div>Preface</div><div><br></div><div>1 Effective potential and phase transitions 1</div><div>1.1 Coleman-Weinberg one loop effective potential . . . . . . . . . . 1</div><div>1.1.1 One-loop effective potential of ¸Á4 theory . . . . . . . . 3</div><div>1.1.2 Dimensional regularization . . . . . . . . . . . . . . . . . . 4</div><div>1.1.3 Renormalization scheme independence of the effective potential . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5</div><div>1.2 Standard model Higgs potential . . . . . . . . . . . . . . . . . . . . 6</div><div>1.3 Higgs vacuumstability . . . . . . . . . . . . . . . . . . . . . . . . . 6</div><div>1.4 Effective potential at finite temperature . . . . . . . . . . . . . . . 6</div><div>1.5 Phase transitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6</div><br><div>2 GravitationalWaves 9</div><div>2.1 Linearised gravity . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9</div><div>2.2 Energy loss by gravitational radiation frombinary neutron stars or black holes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12</div><div>2.3 Waveformof gravitational waves from binary mergers . . . . . . 15</div><div>2.4 Gravitational waves from phase transitions . . . . . . . . . . . . . 15</div><div>2.5 Gravitational waves andMulti-messenger astronomy . . . . . . . 18</div><div><br></div><div>3 Black Holes 19</div><div>3.0.1 Kerr black hole . . . . . . . . . . . . . . . . . . . . . . . . . 19</div><div>3.0.2 Photon orbit around Kerr black holes . . . . . . . . . . . . 19</div><div>3.0.3 Massive particle orbits around Kerr black holes . . . . . . 19</div><div>3.0.4 Frame dragging and Lens-Thirring precession of gyroscopes 19</div><div>3.0.5 Space-time structure of Kerr black hole . . . . . . . . . . . 19</div><div>3.0.6 Penrose process . . . . . . . . . . . . . . . . . . . . . . . . . 19</div><div>3.0.7 Super-radiance . . . . . . . . . . . . . . . . . . . . . . . . . 19</div><div><br></div><div>4 High energy cosmic rays 21</div><div>4.1 Sources of high energy cosmic rays . . . . . . . . . . . . . . . . . . 21</div><div>4.1.1 High energy positrons from the galaxy . . . . . . . . . . . 21</div><div>4.1.2 High energy gamma ray observations . . . . . . . . . . . . 21</div><div>4.1.3 Ultra-High energy neutrino observations . . . . . . . . . . 21</div><div><div><br></div><div>5 DarkMatter 23</div><div>5.1 Equilibriumdistribution of collision-less particles . . . . . . . . . 23</div><div>5.1.1 Detection of dark matter . . . . . . . . . . . . . . . . . . . 25</div><div>5.1.2 Interaction of dark matter with standard model particles 25</div><div>5.1.3 Higgs portal . . . . . . . . . . . . . . . . . . . . . . . . . . . 25</div><div>5.1.4 Vector portal . . . . . . . . . . . . . . . . . . . . . . . . . . 25</div><div>5.1.5 Axion portlal . . . . . . . . . . . . . . . . . . . . . . . . . . 25</div><div>5.1.6 Neutrino portal . . . . . . . . . . . . . . . . . . . . . . . . . 25</div><div>5.2 Dark matter signals in high energy photons, positrons and neutrinos observations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26</div><div>5.3 Effective DM-nucleon interaction operators . . . . . . . . . . . . 26</div><div>5.3.1 Direct detection experiments . . . . . . . . . . . . . . . . . 27</div><div>5.3.2 Collider searches for dark matter . . . . . . . . . . . . . . 27</div><div>5.4 Dark matter at cosmological scales . . . . . . . . . . . . . . . . . . 27</div><div>5.5 Boltzmann equation . . . . . . . . . . . . . . . . . . . . . . . . . . 27</div><div>5.6 Relic density . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31</div><div>5.6.1 Relic density of Cold DarkMatter by Freeze-Out . . . . . 33</div><div>5.6.2 Cold dark matter relic by Freeze-In . . . . . . . . . . . . . 36</div><div>5.7 Relic density of SIMP dark matter . . . . . . . . . . . . . . . . . . 39</div><div>5.8 Relic density ofWarmdark matter . . . . . . . . . . . . . . . . . . 39</div><div>5.9 Structure formation in cold darkmatter . . . . . . . . . . . . . . . 39</div><div>5.10 Structure formation in warmdarkmatter . . . . . . . . . . . . . . 39</div><div>5.11 Structure formation in SIMP dark matter . . . . . . . . . . . . . . 39</div><div>5.12 Fuzzy dark matter . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39</div><div>5.13 Primordial black holes as dark matter . . . . . . . . . . . . . . . . 39</div><div><br></div><div>6 Axions 43</div><div>6.1 The Strong CP problem . . . . . . . . . . . . . . . . . . . . . . . . . 43</div><div>6.2 Models of axions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43</div><div>6.3 Axion darkmatter . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43</div><div>6.4 Direct detection of axions . . . . . . . . . . . . . . . . . . . . . . . 43</div><div><br></div><div>7 Supersymmetry 45</div><div>7.1 Lorentz transformations of fields . . . . . . . . . . . . . . . . . . . 45</div><div>7.1.1 Weyl, Dirac andMajorana fermions . . . . . . . . . . . . . 46</div><div>7.1.2 Dotted and undotted indices . . . . . . . . . . . . . . . . . 48</div><div>7.2 Grassmann variables . . . . . . . . . . . . . . . . . . . . . . . . . . 49</div><div>7.3 Supersymmetric transformations of fields . . . . . . . . . . . . . 50</div><div>7.3.1 Generators of SUSY transformations . . . . . . . . . . . . 52</div><div>7.4 Supersymmetry as translations in superspace . . . . . . . . . . . 53</div><div>7.5 SUSY invariant Lagrangian . . . . . . . . . . . . . . . . . . . . . . . 58</div><div>7.6 SUSY gauge theories . . . . . . . . . . . . . . . . . . . . . . . . . . . 60</div><div>7.6.1 Abelian SUSY gauge theory . . . . . . . . . . . . . . . . . . 60</div><div>7.6.2 Non-abelian SUSY gauge theory . . . . . . . . . . . . . . . 63</div><div>7.7 MSSM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67</div><div><div>7.8 Higgs potential inMSSM . . . . . . . . . . . . . . . . . . . . . . . . 67</div><div>7.8.1 Gauge boson masses . . . . . . . . . . . . . . . . . . . . . . 70</div><div>7.8.2 Higgs masses . . . . . . . . . . . . . . . . . . . . . . . . . . 71</div><div>7.8.3 Higgs couplings . . . . . . . . . . . . . . . . . . . . . . . . . 75</div><div>7.9 Neutralino mass . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77</div><div><br></div><div>8 Grand Unified Theories 79</div><div>8.1 SU(5) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79</div><div>8.2 SO(10) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79</div><div><br></div><div>9 Particle physics models of Inflation 81</div><div>9.1 Starobinsky model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81</div><div>9.2 Supergravity models . . . . . . . . . . . . . . . . . . . . . . . . . . . 81</div><div>9.3 CosmicMicrowave Background . . . . . . . . . . . . . . . . . . . 81</div><div>9.4 Constraints of InflationModels from CMB . . . . . . . . . . . . . 81</div><div>9.5 Constrains on NeutrinoMass from CMB and LSS . . . . . . . . . 81</div></div></div>