MMath&Phys Mathematics and Physics

Year of entry: 2023

Course unit details:
Early Universe

Course unit fact file
Unit code PHYS40772
Credit rating 10
Unit level Level 4
Teaching period(s) Semester 2
Offered by
Available as a free choice unit? No

Overview

Early Universe (M)

Pre/co-requisites

Unit title Unit code Requirement type Description
Cosmology PHYS30392 Pre-Requisite Compulsory
Gravitation PHYS40771 Pre-Requisite Compulsory

Aims

Development of the cosmological model, its problems and their possible resolution within the framework of relativistic gravity and modern particle physics.

Learning outcomes

On completion successful students will be able to:


1. formulate the linear theory of structure formation in the CDM model, obtain solutions in simple model cases of a one component universe.
2. explain the problems of big bang cosmology and the way to solve them in inflationary theory.
3. calculate basic cosmological parameters in inflationary slow roll models.
4. indicate the relations of the Cosmic Microwave Background Radiation and cosmological parameters.
5. discuss the evidence for an accelerating universe and the possible role of dark energy.

Syllabus

1.   Standard model of cosmology:  Review
Review of FRW universe; Natural units; Distance measures in FRW and conformal time; Basic observational facts; Neutrino decoupling and the radiation density; A brief history of time.

2.   Structure formation
Overview of structure formation; Relativistic perturbation theory; Synchronous and Conformal Newtonian gauges; Evolution of vector and tensor perturbations; Scalar perturbations in one component universe; Adiabatic and isocurvature perturbations; Power spectra; Suppression of power on small scales due to baryons and neutrinos.

3.   Cosmic microwave background
Basic features of the angular power spectrum; Recombination and photon decoupling; Density and velocity fluctuations; Sachs-Wolfe effects.

4.   Inflation
Horizon and Flatness puzzles, primordial perturbations; Definition of inflation and its solution of the horizon and flatness puzzles; Potential formulation and slow roll dynamics; reheating and the transition to radiation domination; Klein-Gordon field as a simple worked example; Fluctuations generated during inflation; Model zoo: large field, small field and hybrid models; Connecting observations with theory; Preheating and the transition to radiation domination.

Assessment methods

Method Weight
Written exam 100%

Feedback methods

Will be available on students’ individual written solutions to examples sheets, model answers will be issued. Several review sessions will be suggested during the semester.

Recommended reading

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, (CUP, 2005)
Weinberg, S. Cosmology (OUP)

Study hours

Scheduled activity hours
Assessment written exam 1.5
Lectures 23
Independent study hours
Independent study 75.5

Teaching staff

Staff member Role
Jeffrey Forshaw Unit coordinator

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