MPhys Physics with Theoretical Physics / Course details

This unit will cover differential geometry, General Relativity, relativistic perturbation theory, and the theoretical foundations of the Standard Cosmological Model. 

This unit aims to: give students a grounding in differential geometry, general relativity, and the theoretical foundations of cosmology. 

On the successful completion of the course, students will be able to:  

• Employ differential geometry as the mathematical basis of General Relativity
• Explain the physical content of the Einstein equations.
• Analyse the Schwarzschild spacetime and black-hole solutions.
• Formulate relativistic perturbation theory in the contexts of gravitational waves and the inhomogeneous universe.
• Describe the theoretical foundations of the Standard Cosmological Model.

Syllabus (S2, 30 lectures + 6 examples classes)  

1. Preliminaries and motivation (2 lectures): Cartesian tensors; variational calculus; Newtonian mechanics and gravity; review of Special Relativity; Einstein's lift experiment; weak and strong equivalence principle

2. Differential geometry (6 lectures): manifolds; metric and line element; scalars, vectors, and tensors; coordinate transformations; parallel transport and covariant derivatives; geodesics; curvature

3. General Relativity (8 lectures): Einstein equations; energy-momentum tensor; Newtonian limit; Schwarzschild and black-hole solutions; FLRW spacetime; gravitational and cosmological redshift

4. Relativistic perturbation theory (6 lectures): linearised Einstein equations; gauge fixing; gravitational radiation; cosmological perturbation theory

5. Theory foundations of the Standard Cosmological Model (8 lectures): power spectra; Cosmic Microwave Background physics; structure formation; inflation; slow-roll dynamics; reheating/preheating

+ 6 hours of examples classes 

Lectures; example classes; online material, collated on Canvas 

Cheng, T. P., Relativity, Gravitation and Cosmology: A Basic Introduction (second edition, Cambridge University Press, 2010)

D'Inverno, R. Introducing Einstein's Relativity, (Oxford University Press, 1992)

Hartle, J. B. An Introduction to Einstein's General Relativity, (Addison Wesley, 2004)

Hobson, M. P., Efstathiou, G. & Lasenby, A. N. General Relativity: An Introduction for Physicists (Cambridge University Press, 2006)

Baumann, D., Cosmology (Cambridge University Press, 2022)

Lambourne, R. J. A., Relativity, Gravitation and Cosmology (Cambridge University Press, 2010)

Gorbunov D.S. & Rubakov V.A. Introduction to the Theory of the Early Universe: Cosmological Perturbations and Inflationary Theory, (World Scientific, 2011) 
Mukhanov, V.F. Physical Foundations of Cosmology, (Cambridge University Pre, 2005) 
Weinberg, S. Cosmology (Oxford University Press, 2008)