Gravitation and Advanced Cosmology

PHYS40972 Gravitation and Advanced Cosmology 15 Semester 2 Undergraduate Level 7 Department of Physics & Astronomy 1 FHEQ level (Framework for Higher Education Qualifications) ' Undefined ' European Credit Transfer & Accumulation System Rating : 7.5 This unit will cover differential geometry, General Relativity, relativistic perturbation theory, and the theoretical foundations of the Standard Cosmological Model.  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:  <ul><li>Employ differential geometry as the mathematical basis of General Relativity</li><li>Explain the physical content of the Einstein equations.</li><li>Analyse the Schwarzschild spacetime and black-hole solutions.</li><li>Formulate relativistic perturbation theory in the contexts of gravitational waves and the inhomogeneous universe.</li><li>Describe the theoretical foundations of the Standard Cosmological Model.</li></ul>  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 principle2. Differential geometry (6 lectures): manifolds; metric and line element; scalars, vectors, and tensors; coordinate transformations; parallel transport and covariant derivatives; geodesics; curvature3. General Relativity (8 lectures): Einstein equations; energy-momentum tensor; Newtonian limit; Schwarzschild and black-hole solutions; FLRW spacetime; gravitational and cosmological redshift4. Relativistic perturbation theory (6 lectures): linearised Einstein equations; gauge fixing; gravitational radiation; cosmological perturbation theory5. 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  1 Written exam 100% <figure class="table"><table><tbody><tr><td>Assessment task </td><td>Length</td><td>How and when feedback is provided</td><td>Weighting within unit (if relevant) </td></tr><tr><td>Written examination </td><td>2 hours</td><td>Examination Marks and Reports </td><td>100%</td></tr><tr><td>Examples classes (self-assessment and formative feedback) </td><td>6 hours</td><td>Model answers provided for examples sheets, with additional feedback provided synchronously in the examples classes and asynchronously via a Canvas discussion board.  </td><td>0%</td></tr></tbody></table></figure> PHYS30392 Cosmology Pre-Requisite Recommended N 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)  Lectures 30 Practical classes & workshops 6 0 114