Lecturers

Primordial black holes in the early universe

Juan Garcia-Bellido

Instituto de Fisica Teorica (IFT), Madrid, Spain

 Topics to be covered in this course:

• Introduction to PBH (dark matter)

• Formation mechanisms (type I and II)

• Inflationary Perturbations (single/multi fields)

• Quantum Diffusion during inflation (delta N formalism)

• Primordial Non-Gaussianity

• Gravitational Collapse during radiation (thresholds/thermal history/PBH mass function)

• Clustering of PBH (Poisson versus PNG) / cluster dynamics

• Early/Late PBH Binaries Merging Rates

• Close Hyperbolic Encounters (CHE) in dense clusters (spin and mass distributions)

• Stochastic Gravitational Wave Background (at formation, scalar-induced, mergers, CHE)

• PBH Constraints (limits with caveats): evaporation, microlensing, accretion, dynamical effects, GW

• Future Detectability (GWO, microlensing, Gaia, spectral distortions CMB) 

• Present Evidences of their existence 

Black Hole mechanics and thermodynamics in effective field theories of gravity 

Nilay Kundu 

Indian Institute of Technology (IIT), Kanpur

Topics to be covered in this course:

• Black hole (BH) thermodynamics in two-derivative theories - event horizon and horizon adapted coordinates. Stationary BH, and non-stationary perturbations - Killing vectors. Raychaudhuri equation and area theorem.

• Diffeomorphism invariant theories of gravity. BH entropy as Wald entropy in such theories. The Noether charge approach to BH entropy to be discussed with examples. First law in higher derivative theories.

• The second law for BH mechanics in higher-derivative theories - perturbative approach in the fluctuations around the stationary BH. Linearized second law.

• Physical process version of the first law in higher derivative theories of gravity.

• Treating Higher derivative theories of gravity as corrections to Einstein’s two derivative general relativity in an Effective Field Theory (EFT) setup. Extending the second law to non-linear orders. Zeroth law of BH thermodynamics.

 Neutrinos in Structure formation and Cosmology 

 Arka Banerjee 

 Indian Institute of Science Education and Research (IISER), Pune 

Topics to be covered in this course:

• The impact of neutrinos on the evolution of the Universe, and conversely, how measurements of the observable Universe can constrain properties of neutrinos. 

• How neutrinos affect the evolution of the background, and their contributions to the energy density of the Universe at various epochs. 

• Effects of neutrinos on the evolution of fluctuations in the Universe, at the time of the CMB, and then at late times.

• Linear perturbation theory and techniques used to study the problem at fully nonlinear level in density perturbations. 

• Surveying the different cosmological observables that are currently expected to best constrain the properties of neutrinos in the next decades, with a focus on measuring the sum of neutrino masses. 

Effective field theory approach and post-Minkowskian expansion in general relativity  

Alok Laddha

Chennai Mathematical Institute (CMI), Chennai

Topics to be covered in this course:

• Effective field theory(EFT) for  hyperbolic gravitational Scattering -1 

• EFT for hyperbolic gravitational scattering - 2 

• Mapping hyperbolic scattering to bound orbits 

• Introduction to gravitational scattering amplitudes (on-shell approach) 

• Mapping on-shell observables in QFT to EFT results