Theoretical and Observational Cosmology

by Lachieze-Rey, Marc

• ISBN13: 9780792359463
• ISBN10: 0792359461
• Format: Paperback
• Copyright: 1999-09-01
• Publisher: Kluwer Academic Pub

Summary

A complete account of the fundamental techniques of general relativity and their application to cosmology. The book includes reviews of the different cosmological models and their classification, including such topics as causality and horizons, the cosmological parameters, observational tests and constraints of cosmology, symmetries and the large scale topology of space and space-time, and the use of supernovas as cosmological indicators. The perturbations to the cosmological models are discussed throughout the volume. The cosmic microwave background is presented, with an emphasis in secondary distortions in relation to cosmological models and large scale structures. Recent results on dark matter are summarised. A general review of primordial nucleosynthesis is given. Gravitational lensing is discussed in great detail. Most contributions show a balance between theory and observation. Readership: A solid background for students and researchers intending to work in the field of theoretical and observational cosmology.

Table of Contents

Preface	xiii
List of Lecturers	xvii
List of Students	xix
Cosmological Models Cargese Lectures 1998	1	(116)
G.F.R. Ellis
H. Van Helst
Basic relations	1	(2)
1 + 3 covariant description and equations	3	(15)
Variables	4	(4)
1 + 3 covariant propagation and constraint equations	8	(4)
Pressure-free matter (`dust')	12	(1)
Irrotational flow	12	(1)
Implications	13	(3)
Newtonian case	16	(1)
Solutions	17	(1)
Tetrad description	18	(7)
General tetrad formalism	18	(2)
Tetrad formalism in cosmology	20	(4)
Complete set	24	(1)
FLRW universes and observational relations	25	(17)
Coordinates and metric	25	(1)
Dynamical equations	26	(1)
Exact and approximate solutions	27	(3)
Phase planes	30	(1)
Observations	31	(5)
Observational limits	36	(4)
FLRW universes as cosmological models	40	(1)
General observational relations	41	(1)
Solutions with symmetries	42	(17)
Symmetries of cosmologies	42	(3)
Classification of cosmological symmetries	45	(4)
Bianchi Type I universes (s = 3)	49	(4)
Lemaitre-Tolman-Bondi family (s = 2)	53	(3)
Swiss-Cheese models	56	(3)
Bianchi universes (s = 3)	59	(12)
Constructing Bianchi universes	59	(3)
Dynamics of Bianchi universes	62	(2)
Observational relations	64	(1)
Dynamical systems approach	65	(6)
Almost-FLRW universes	71	(16)
Gauge problem	71	(3)
Dynamical equations	74	(1)
Dust	75	(2)
Perfect fluids	77	(4)
Implications	81	(4)
Other matter	85	(1)
Relation to other formalisms	86	(1)
CBR anisotropies	87	(19)
Covariant kinetic theory	87	(2)
Angular harmonic decomposition	89	(2)
Non-linear 1 + 3 covariant multipole equations	91	(5)
Temperature anisotropy multipoles	96	(3)
Almost-EGS-Theorem and its applications	99	(5)
Other CBR calcualtions	104	(2)
Conclusion and open issues	106	(11)
Conclusion	106	(2)
Open issues	108	(9)
Topology of The Universe: Theory and Observation	117	(40)
J.-P. Luminet
B. F. Roukema
Introduction	117	(1)
A Brief History of Cosmological Topology	118	(6)
Mathematical background	124	(13)
Basics of Topology	124	(5)
Two-dimensional manifolds	129	(3)
Three-dimensional manifolds of constant curvature	132	(5)
Topology and Cosmology	137	(4)
Observational methods, candidates and constraints	141	(12)
``Topology'' for the observer	141	(1)
Early work: 100h-1 Mpc	142	(1)
Since 1993: 100h-1 Mpc	143	(9)
Other observational difficulties	152	(1)
Conclusion	153	(4)
Symmetries in General Relativity and Beyond	157	(22)
M. Lachieze-Rey
Introduction	157	(1)
Spaces and manifolds	157	(6)
Basic definition	158	(1)
Vectors and the tangent space	158	(1)
Vector fields	159	(1)
Forms and tensors	159	(2)
The tangent and cotangent bundles	161	(2)
Metric and tetrads	163	(1)
Connections on a manifold	163	(9)
The linear connection	164	(2)
Symmetries of the connection	166	(1)
The metric connection	167	(1)
Lie groups	167	(3)
Connection in the frame bundle	170	(2)
Relativity and the Poincare group	172	(3)
The Cartan - Weyl construction of space	172	(1)
The Poincare group	172	(1)
From the Poincare group to Minkowski spacetime	173	(1)
The teleparallel description of general relativity	174	(1)
Extending	175	(3)
The de Sitter groups	175	(1)
The conformal group	176	(1)
The generator of conformal group	176	(2)
The Wheeler biconformal theory	178	(1)
Conclusion	178	(1)
Gravitational Lenses	179	(32)
F. Bernardeau
Introduction	179	(1)
Physical mechanisms	180	(1)
Born approximation and thin lens approximation	181	(1)
The induced displacement	181	(1)
The case of a point-like mass distribution	181	(4)
Multiple images and displacement field	181	(2)
The amplification matrix	183	(1)
The microlensing experiments	184	(1)
Gravitational lenses in Cosmology	185	(6)
The angular distances	185	(2)
Geometric optics in a weakly inhomogeneous Universe	187	(2)
The linearized equation of geometric optics	189	(2)
Galaxy clusters as gravitational lenses	191	(5)
The isothermal profile	191	(2)
The critical lines for a spherically symmetric mass distribution	193	(1)
The isothermal profile with a core radius	194	(1)
Critical lines and caustics in realistic mass distributions	195	(1)
The weak lensing regime	196	(3)
The mathematical description of the weak lensing regime	196	(1)
The magnification effect	197	(1)
The galaxy shape matrices to measure the distortion field	198	(1)
The construction of the projected mass density	198	(1)
The weak lensing as a probe of the Large-Scale Structures	199	(12)
The large-scale structures	199	(1)
The relation between the local convergence and the local density contrast	200	(1)
The efficiency function	201	(1)
The amplitude of the convergence fluctuations	202	(1)
The expected signal to noise ratio	203	(1)
Separate measurements of Ω and σ8	203	(4)
Prospects	207	(4)
Cosmological Applications of Gravitational Lensing	211	(34)
Y. Mellier
Introduction	211	(1)
Some important quantities and properties	212	(4)
Image multiplicity and Einstein radius	212	(1)
Critical mass	213	(1)
Relation with observable quantities	214	(2)
Academic examples	216	(2)
The singular isothermal sphere	216	(2)
The general case of an axially symmetric lens	218	(1)
Astrophysical examples	218	(22)
Measuring the masses of clusters of galaxies	218	(14)
Measuring the masses of galaxies	232	(8)
Conclusion and future prospects	240	(5)
Measurement of Cosmological Parameters Using Type IA Supernovae	245	(16)
R. Pain
Which cosmological parameters - How ?	245	(3)
A few definitions	245	(1)
Principle of the measurement	246	(2)
Type Ia SNe are excellent cosmological tools	248	(2)
Detection/Follow-up of distant SNe	250	(2)
Strategy	250	(2)
Analysis	252	(1)
Recent results on H0, ΩM and Ω from SNe Ia	252	(4)
Recent determination on H0	252	(2)
Very recent determination of ΩM and Ω	254	(2)
The (near) future	256	(5)
Primordial Nucleosynthesis	261	(44)
K. A. Olive
Introduction	261	(8)
Standard model basics	262	(5)
Historical perspectives	267	(2)
Theory	269	(5)
Abundances	274	(9)
4He	274	(4)
7Li	278	(3)
D	281	(2)
Chemical evolution	283	(6)
Likelihood analysis	289	(6)
Constraints from BBN	295	(6)
Summary	301	(4)
Searches for Dark Matter	305	(12)
J. Rich
Introduction	305	(1)
Wimps	305	(3)
Axions	308	(1)
Neutrinos	309	(2)
Machos	311	(6)
Temperature Anisotropies of the Cosmic Microwave Background	317	(36)
N. Aghanim
Introduction	317	(2)
Temperature fluctuations of the CMB	319	(3)
Primary fluctuations	319	(1)
Secondary fluctuations	320	(2)
Angular power spectrum of the primary anisotropies	322	(4)
The Sunyaev-Zel'dovich effect	326	(16)
Sunyaev-Zel'dovich effect	330	(5)
Observations of the SZ effect	335	(2)
Cosmological applications of the SZ effect	337	(5)
Inhomogeneous re-ionisation	342	(11)
Temperature of the ionised gas	344	(1)
Radius of the ionised region	344	(2)
Optical depth	346	(1)
Induced secondary effects	346	(1)
Generalisation to quasars distribution	346	(1)
Discussion and conclusions	347	(6)
Primordial Galaxies: From Local Hii Galaxies to High Redshift Galaxies	353	(12)
D. Kunth
Introduction	353	(1)
The HII galaxies	354	(1)
The early IUE observations and interpretations	354	(1)
HST observations	355	(1)
The role of the velocity structure of the ISM	356	(3)
The evolution of superbubbles in extended HI halos	359	(3)
Discussion	362	(3)
The relevance of the superbubble model	362	(1)
The galaxies at high redshift	362	(3)
Active Galactic Nuclei	365	(16)
G. Mathez
Short Historic, Basic Properties	365	(2)
Active Galactic Nuclei	365	(1)
Seyfert Galaxies	366	(1)
Quasars	366	(1)
The AGN ZOO	367	(1)
Physical Properties	367	(4)
The continuum spectrum from radio wavelengths to IR, UV, X, γ and TeV	367	(1)
Absorption Lines	368	(1)
Models	369	(1)
Typical Relations	370	(1)
Eddington limit	370	(1)
Unified Model	370	(1)
Statistics	371	(4)
Detection, Surveys, and Catalogues of AGN	371	(2)
High energy samples	373	(1)
Observed evolution of the luminosity function	373	(2)
AGN and Cosmology	375	(1)
Gunn-Peterson test, reionization	375	(1)
Primordial galaxies	375	(1)
Primordial chemistry	375	(1)
AGN and lensing	375	(1)
Geometrical tests	375	(1)
Large Scale Structure	376	(1)
High Energy Backgrounds	376	(1)
Prospects	376	(2)
Bibliography	378	(3)
Cosmic Velocity Fields	381	(1)
J. F. L. Simmons
Introduction	381	(2)
Friedmann models and horizons	383	(2)
The Sunyaev-Zeldovich effect	385	(1)
Statistics and Fourier analysis	386	(3)
Newtonian fluid equations	389	(2)
Method and data	391	(3)
Reconstruction of velocity fields	394