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Home > MAM4001W > Applied Mathematics Modules > Theoretical Cosmology and Gravity

Theoretical Cosmology and Gravity

Dr Julien Larena
Professor Amanda Weltman
1st and 2nd semester 2020
20 credits / 30 lectures per semester

1st semester (Theoretical Cosmology):

  • What is cosmology? (And what is it not?)
  • The background Universe: kinematics and dynamics in the expanding Friedmann spacetime (metric, lightcones, distances, 4-velocity, 4-wave vector, redshift, energy-momentum tensor, hot Big Bang model, Dark Energy, Inflation)
  • Cosmological perturbation theory: basics (overview of how fluctuations originate and then grow to generate the cosmic microwave background (CMB) anisotropies and galaxies; perturbations in density, velocity and metric potentials)
  • The perturbed Einstein field equations: the evolution of density, velocity and curvature perturbations in the radiation, matter and Dark Energy eras (how modes evolve from Inflation; transfer functions; the effect of Dark Energy; analytical and numerical solutions)
  • The galaxy correlation function and power spectrum (galaxy bias; galaxy number counts and variance; evolution of the power spectrum in the matter and Dark Energy eras)
  • Probing the expansion history and the growth of large-scale structure via galaxy surveys (the BAO feature in the galaxy power spectrum; the growth rate from RSD in the galaxy power spectrum)

2nd semester (Gravity):

This is a course on black holes and gravitational waves. You will learn about the physics and astrophysics of black holes, how they form, what types the universe allows, and how we can understand them using Penrose Diagrams. We will also discuss  how we observe black holes, and neutron stars with modern astronomy and astrophysics. Naturally this requires us to learn about gravitational waves, which are a consequence of general relativity, and one of the hottest topics in physics/astrnomy today. We will be using the book on Gravitational Waves by Michele Maggiore. 

 

The first semester course is not a prerequisite for this module, but it will be helpful in gaining a fuller understanding of cosmology and gravity. 3rd year General Relativity is a prerequisite, and some field theory knowledge will be helpful though not required. You will also be trained in research skills, specifically how to present your research , in written form, in casual conversation and through giving research talks. 

Prerequisites:

The undergraduate module 3GR (General Relativity), or equivalent, is required.