Table of Contents

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 Structure formation in cold darkmatter . . . . . . . . . . . . . . . 395.10 Structure formation in warmdarkmatter . . . . . . . . . . . . . . 395.11 Structure formation in SIMP dark matter . . . . . . . . . . . . . . 395.12 Fuzzy dark matter . . . . . . . . . . . . . . . . . . . . . . . . . . . . 395.13 Primordial black holes as dark matter . . . . . . . . . . . . . . . . 39
6 Axions 436.1 The Strong CP problem . . . . . . . . . . . . . . . . . . . . . . . . . 436.2 Models of axions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 436.3 Axion darkmatter . . . . . . . . . . . . . . . . . . . . . . . . . . . . 436.4 Direct detection of axions . . . . . . . . . . . . . . . . . . . . . . . 43
7 Supersymmetry 457.1 Lorentz transformations of fields . . . . . . . . . . . . . . . . . . . 457.1.1 Weyl, Dirac andMajorana fermions . . . . . . . . . . . . . 467.1.2 Dotted and undotted indices . . . . . . . . . . . . . . . . . 487.2 Grassmann variables . . . . . . . . . . . . . . . . . . . . . . . . . . 497.3 Supersymmetric transformations of fields . . . . . . . . . . . . . 507.3.1 Generators of SUSY transformations . . . . . . . . . . . . 527.4 Supersymmetry as translations in superspace . . . . . . . . . . . 537.5 SUSY invariant Lagrangian . . . . . . . . . . . . . . . . . . . . . . . 587.6 SUSY gauge theories . . . . . . . . . . . . . . . . . . . . . . . . . . . 607.6.1 Abelian SUSY gauge theory . . . . . . . . . . . . . . . . . . 607.6.2 Non-abelian SUSY gauge theory . . . . . . . . . . . . . . . 637.7 MSSM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 677.8 Higgs potential inMSSM . . . . . . . . . . . . . . . . . . . . . . . . 677.8.1 Gauge boson masses . . . . . . . . . . . . . . . . . . . . . . 707.8.2 Higgs masses . . . . . . . . . . . . . . . . . . . . . . . . . . 717.8.3 Higgs couplings . . . . . . . . . . . . . . . . . . . . . . . . . 757.9 Neutralino mass . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
8 Grand Unified Theories 798.1 SU(5) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 798.2 SO(10) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
9 Particle physics models of Inflation 819.1 Starobinsky model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 819.2 Supergravity models . . . . . . . . . . . . . . . . . . . . . . . . . . . 819.3 CosmicMicrowave Background . . . . . . . . . . . . . . . . . . . 819.4 Constraints of InflationModels from CMB . . . . . . . . . . . . . 819.5 Constrains on NeutrinoMass from CMB and LSS . . . . . . . . . 81

About the Author

Dr. Subhendra Mohanty obtained his Ph.D from University of Wisconsin-Madison and, after a few post-doctoral stints at CERN, ICTP and other institutions, has been at the Physical Research Laboratory (India) where he is currently a Senior Professor. He has also been a Visiting Professor at Universitat Autonoma of Barcelona. Dr. Mohanty has given numerous courses on various aspects of particle physics and cosmology at his home institution and outside, being an early adopter of the genre of Astroparticle Physics. He has published more than hundred research papers with his local and international collaborators and has trained numerous PhD students and young researchers in the field.