Topics in Physics Beyond the Standard Model

General Introduction to the course: cosmological constant problem, electroweak hierarchy problem, dark matter -Introduction to cosmology: homogeneous and isotropic universes, FRW metric, Friedmann equations, energy momentum tensor for matter and radiation, solution to Friedmann equations, cosmological constant, de Sitter universe -Brief history of the Universe: BBN, CMB, structure formation -Horizon and Flatness Problems

Inflation as a solution to the horizon and flatness problems – Classical dynamics of inflation from a single scalar field – preview of quantum effects during inflation (quantum fluctuations, power spectra, estimate of the power spectrum from dimensional analysis) – general treatment of cosmological perturbations over a homogeneous and isotropic background: symmetries of the problem and their consequences, gauge redundancy of General Relativity and gauge invariant quantities

Computation of quantum fluctuations during inflation – Minimum number of e-folds to solve horizon and flatness problem – Observables in the CMB

Introduction to effective field theories – Dimensional analysis and selection rules of broken symmetries of the SM - Precise statement of the hierarchy problems (cosmological constant and Higgs boson mass) - Symmetries and hierarchy problems – Introduction to supersymmetry – Higgs and cosmological constant in supersymmetry

Direct and indirect constraints on solutions to the hierarchy problems – Introduction to landscapes - Abbott solution to the cosmological constant (CC) problem – Relaxion explanation of the Higgs mass

More on the relaxion - introduction to 2- and 3-form fields – Brown-Teitelboim solution to the CC problem - Bousso-Polchinski solution to the cosmological constant (CC) problem – Multiverse – Weinberg’s argument – anthropic solutions to the CC problem

Anthropic solution to the Higgs mass hierarchy – Dynamical selection mechanisms for the Higgs mass – Scale invariance for Higgs and cosmological constant – Symmetry and Landscapes, general philosophy and split supersymmetry.

Thermodynamics in an expanding universe – equilibrium distributions from maximum entropy – limiting forms for relativistic and non-relativistic particles – Boltzmann Equation

Relic density calculations – Weakly Interactive Massive Particle (WIMP) dark matter - models of thermal dark matter production beyond WIMPs

General constraints on thermal dark matter: Neff bounds, small scale structure, matter radiation equality and CMB peaks – ultralight dark matter production via the misalignment mechanism

QCD theta angle – calculation in chiral perturbation theory of pion masses and neutron EDM with a theta angle – strong CP problem – solutions (mu=0, P, CP, axion) – axion potential – axion cosmology – axion as dark matter

Approximate symmetries of inflation - conformal invariance - symmetries of inflationary correlators - In-In formalism for cosmological correlators – Imprints on non-gaussianities of massive particles during inflation (cosmological collider physics)