Book contents
- Frontmatter
- Contents
- List of exercises
- List of projects
- Preface
- How to use this book
- 1 Special relativity
- 2 Scalar and electromagnetic fields in special relativity
- 3 Gravity and spacetime geometry: the inescapable connection
- 4 Metric tensor, geodesics and covariant derivative
- 5 Curvature of spacetime
- 6 Einstein's field equations and gravitational dynamics
- 7 Spherically symmetric geometry
- 8 Black holes
- 9 Gravitational waves
- 10 Relativistic cosmology
- 11 Differential forms and exterior calculus
- 12 Hamiltonian structure of general relativity
- 13 Evolution of cosmological perturbations
- 14 Quantum field theory in curved spacetime
- 15 Gravity in higher and lower dimensions
- 16 Gravity as an emergent phenomenon
- Notes
- Index
10 - Relativistic cosmology
Published online by Cambridge University Press: 05 June 2012
- Frontmatter
- Contents
- List of exercises
- List of projects
- Preface
- How to use this book
- 1 Special relativity
- 2 Scalar and electromagnetic fields in special relativity
- 3 Gravity and spacetime geometry: the inescapable connection
- 4 Metric tensor, geodesics and covariant derivative
- 5 Curvature of spacetime
- 6 Einstein's field equations and gravitational dynamics
- 7 Spherically symmetric geometry
- 8 Black holes
- 9 Gravitational waves
- 10 Relativistic cosmology
- 11 Differential forms and exterior calculus
- 12 Hamiltonian structure of general relativity
- 13 Evolution of cosmological perturbations
- 14 Quantum field theory in curved spacetime
- 15 Gravity in higher and lower dimensions
- 16 Gravity as an emergent phenomenon
- Notes
- Index
Summary
Introduction
This chapter applies the general theory of relativity to the study of cosmology and the evolution of the universe. Our emphasis will be mostly on the geometrical aspects of the universe rather than on physical cosmology. However, in order to provide a complete picture and to appreciate the interplay between theory and observation, it is necessary to discuss certain aspects of the evolutionary history of the universe. We shall do this in Section 10.6 even though it falls somewhat outside the main theme of development.
The Friedmann spacetime
Observations show that, at sufficiently large scales, the universe is homogeneous and isotropic; that is, the geometrical properties of the three-dimensional space: (i) are the same at all spatial locations and (ii) do not single out any special direction in space.
The geometrical properties of the space are determined by the distribution of matter through Einstein's equations. It follows, therefore, that the matter distribution should also be homogeneous and isotropic. This is certainly not true at small scales in the observed universe, where a significant degree of inhomogeneity exits in the form of galaxies, clusters, etc. We assume that these inhomogeneities can be ignored and the matter distribution may be described by a smoothed out average density in studying the large scale dynamics of the universe.
- Type
- Chapter
- Information
- GravitationFoundations and Frontiers, pp. 452 - 501Publisher: Cambridge University PressPrint publication year: 2010