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Programme & Unit Catalogues

## PH40112: Relativistic cosmology

Owning Department/School: Department of Physics
Credits: 6      [equivalent to 12 CATS credits]
Notional Study Hours: 120
Level: Masters UG & PG (FHEQ level 7)
Period:
Semester 2
Assessment Summary: EX 100%
Assessment Detail:
• Examination (EX 100%)
Supplementary Assessment:
Like-for-like reassessment (where allowed by programme regulations)
Requisites: Before taking this module you must take PH30043 OR ( take PH30101 AND take PH30111 )
Description: Aims:
This unit aims to develop a mathematically rigorous description of general relativity and cosmology, including derivation of the Einstein field equations and the exploration of the Friedmann-Robertson-Walker solution, which forms the basis for modern cosmological models. The unit also aims to provide an overview of observational cosmology, and the techniques and observations that have constrained current cosmological models.

Learning Outcomes:
After taking this unit the student should be able to:
* show proficiency in calculations involving tensors (inner and outer products, contraction, parallel transport);
* understand the basics of geometric/coordinate-free vector and tensor analysis;
* perform covariant differentiation of tensor quantities in curved space;
* provide a physical explanation of the Einstein field equations;
* show how the Friedmann-Robertson-Walker metric is an exact solution to the Einstein equations;
* describe the key ideas behind cosmology and the expanding universe;
* describe the observations and techniques used to establish the accelerating expansion of the universe, including systematics and sources of uncertainty;
* describe the observation and analysis of the Cosmic Microwave Background Radiation, including systematics and sources of uncertainty;
* describe current state of the art cosmology experiments, how their results compare to each other, and current open questions that they address.

Skills:
Numeracy T/F A, Problem Solving T/F A.

Content:
Vectors, one-forms and tensors. Vector spaces, manifolds and tangent spaces. Einstein summation convention. Curvilinear coordinates. Tensor operations, covariant differentiation. Review of special relativity, spacetime metric and geodesics. Local coordinates. Locally inertial frames.
The Riemann tensor. The Bianchi identity, The Ricci tensor. Curvature scale. The Stress-energy tensor. Energy as the source of gravity. The dynamics of a pressureless dust. Conservation laws. Perfect fluids.
The Einstein field equations. The Einstein tensor. The cosmological constant. Interpreting the field equations. The Friedmann-Robertson-Walker metric. Cosmological dynamics.
Inflationary cosmology. Observations of the Cosmic Microwave Background Radiation. Observations and analysis of the extragalactic distance ladder. Sources of systematic and measurement uncertainty in cosmology.
Comparison of results from different cosmological experiments. Current state of the art experiments. Open questions in the field and potential implications.
Programme availability:

#### PH40112 is Compulsory on the following programmes:

Department of Physics
• USPH-AFM10 : MPhys(Hons) Physics with Astrophysics (Year 4)
• USPH-AFM11 : MPhys(Hons) Physics with Astrophysics with Research placement (Year 4)
• USPH-AAM10 : MPhys(Hons) Physics with Astrophysics with Study year abroad (Year 4)

#### PH40112 is Optional on the following programmes:

Department of Physics
• USPH-AFM02 : MPhys(Hons) Physics (Year 4)
• USPH-AFM04 : MPhys(Hons) Physics with Research placement (Year 4)
• USPH-AAM03 : MPhys(Hons) Physics with Study year abroad (Year 4)
• USPH-AKM03 : MPhys(Hons) Physics with Professional Placement (Year 5)
• USPH-AKM04 : MPhys(Hons) Physics with Professional and Research Placements (Year 5)
• USXX-AFM01 : MSci(Hons) Mathematics and Physics (Year 4)
• USXX-AAM01 : MSci(Hons) Mathematics and Physics with Study year abroad (Year 5)
• USXX-AKM01 : MSci(Hons) Mathematics and Physics with Year long work placement (Year 5)

 Notes: This unit catalogue is applicable for the 2018/19 academic year only. Students continuing their studies into 2019/20 and beyond should not assume that this unit will be available in future years in the format displayed here for 2018/19. Programmes and units are subject to change in accordance with normal University procedures. Availability of units will be subject to constraints such as staff availability, minimum and maximum group sizes, and timetabling factors as well as a student's ability to meet any pre-requisite rules. Undergraduates: Find out more about these and other important University terms and conditions here. Postgraduates: Find out more about these and other important University terms and conditions here.