PHYM432 Relativity and Cosmology

2007-2008

Aims

The module aims to introduce the student to the special and general theories of relativity, and to illustrate the latter theory with a description of the three historical tests of the theory: the precession of the perihelion of mercury, the bending of light passing close to the sun and the gravitational red shift. Application of the general theory to the standard cosmological model is also included in the course. Although the course avoids the use of advanced mathematical topics and emphasises the concepts behind the theory, students will require a good level level of mathematical fluency and intuition in order to engage with material.

Intended Learning Outcomes

After successfully completing this module, the student will able to:

Module Specific Skills

• give coherent explanations of the principles associated with: special relativity, general relativity, and cosmology;
• interpret observational data in terms of the Standard Model of the evolution of the universe;
• describe experiments and observational evidence to test the general theory of relativity, explain how these support the general theory and can be used to criticise and rule-out alternative possibilities;
• apply tensors to the description of curved spaces;
• solve problems by applying the principles of relativity;
• deduce the Friedmann equations describing the evolution of the Universe.
• explain what is meant by: intrinsic and extrinsic curvatures, the curvature of space, local inertial reference frame, and Riemannian coordinates/geometry.
• describe world lines of particles and photons in a curved space-time;
• describe the Cosmological Principle and the Robertson-Walker metric.

Discipline Specific Skills

• locate, retrieve and evaluate relevant information from the WWW.

Personal and Key Skills

• meet deadlines for completion of work to be discussed in class by developing appropriate time-management strategies;
• explain to non-specialists the basis of one of the corner-stones of 20th century Physics.

Learning and Teaching Methods

Lectures (20×1hr), discussions and problems classes (2×1hr), e-learning resources.

Assignments

The student is expected to work through a set of problems published on the WWW.

Assessment

One 90-minute examination (100%).

Syllabus Plan and Content

1. Introduction
2. Key aspects of special relativity
   1. Galilean and Lorentz transformations
   2. Length contraction and time dilation
   3. Doppler effect
   4. Relativistic mechanics
3. Accelerated reference frames
   1. The person in the lift
   2. Inertial forces
   3. Tidal forces
4. Curved spaces
   1. Euclidean spaces
   2. Curvature in one and two dimensions
   3. Intrinsic and extrinsic curvature
   4. Riemannian curvature
   5. Introduction to tensors
5. Application to space-time physics
   1. The equivalence principle
   2. Tidal forces and local inertial frames
   3. Equations for world lines of free particles and photons
   4. Schwarzschild metric
   5. Black holes
6. Experimental tests of general relativity
   1. Advance of perihelion of mercury
   2. Bending of light
   3. Gravitational red shift
7. Cosmology
   1. The cosmological principle
   2. Robertson-Walker metric
   3. Red-shift distance relation
   4. The Friedmann equations
   5. Cosmic microwave background
   6. Helium production

Core Text

Supplementary Text(s)

Formative Mechanisms

Progress in the set problems will be reviewed weekly.

Evaluation Mechanisms

The module will be evaluated using information gathered via the student representation mechanisms, the staff peer appraisal scheme, and measures of student attainment based on summative assessment.