Book contents
- Frontmatter
- Contents
- Preface
- Part 1 Foundations
- Part 2 Relativistic cosmological models
- 4 Kinematics of cosmological models
- 5 Matter in the universe
- 6 Dynamics of cosmological models
- 7 Observations in cosmological models
- 8 Light-cone approach to relativistic cosmology
- Part 3 The standard model and extensions
- Part 4 Anisotropic and inhomogeneous models
- Part 5 Broader perspectives
- Appendix: Some useful formulae
- References
- Index
4 - Kinematics of cosmological models
from Part 2 - Relativistic cosmological models
Published online by Cambridge University Press: 05 April 2012
- Frontmatter
- Contents
- Preface
- Part 1 Foundations
- Part 2 Relativistic cosmological models
- 4 Kinematics of cosmological models
- 5 Matter in the universe
- 6 Dynamics of cosmological models
- 7 Observations in cosmological models
- 8 Light-cone approach to relativistic cosmology
- Part 3 The standard model and extensions
- Part 4 Anisotropic and inhomogeneous models
- Part 5 Broader perspectives
- Appendix: Some useful formulae
- References
- Index
Summary
In cosmology, the matter components allow us to make a physically motivated choice of preferred motion. For example, we could choose the CMB frame, in which the radiation dipole vanishes, or the frame in which the total momentum density of all components vanishes. Such a choice corresponds to a preferred 4-velocity field ua that generates a family of preferred world lines. We can then make a 1+3 split relative to ua, in order to relate the physics and geometry to the observations. In this chapter we discuss how to do this for the kinematics of cosmological models; the following chapter will consider the dynamics.
The (real or fictitious) observers are comoving with the matter-defined 4-velocity ua, and we can call the observers and the 4-velocity ‘fundamental’. If we change our choice of fundamental 4-velocity, the kinematics and dynamics transform in a well-defined way, as discussed in the following chapter.
Comoving coordinates
To describe the spacetime geometry it is convenient to use comoving (Lagrangian) coordinates, adapted to the fundamental world lines. These are locally defined as follows.
(1) Choose a surface S that intersects each world line once only (note that no unique choice is available in general). Label each world line where it intersects this surface; as the surface is three-dimensional, three labels yi, (i =1,2,3), are required to label all the world lines.
(2) Extend this labelling off the surface S by maintaining the same labelling for the world lines at later and earlier times.
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- Relativistic Cosmology , pp. 73 - 88Publisher: Cambridge University PressPrint publication year: 2012