MC1. Cosmological Singularities
Spiros Cotsakis
| Cosmologies
The spacetime metric Derivatives Transport and geodesics Conjugate points and geodesic congruences Causal structure Globalization Singularity theorems Cosmological applications Bibliography S.W. Hawking, G.F.R. Ellis: The large-scale structure of space-time, (CUP, 1973) R.W. Wald: General relativity, (Chicago, 1984), chapters 8, 9 B. O'Neill: Semi-Riemannian geometry, (Academic Press, 1983) R. Penrose: Techniques of differential topology in relativity, (SIAM, 1972) J.K. Beem et al: Global lorentzian geometry, (Dekker, 1996) S. Cotsakis: Current trends in mathematical cosmology, gr-qc/0107090. |
MC2. Constraints and Evolution in Cosmology
Yvonne Choquet-Bruhat
| I will first recall the standard n+1 decomposition of the Riemann and
Ricci tensor of a lorentzian metric on a manifold V of the type
MxR
with respect to a field of frames with time axes orthogonal to the manifolds
M_{t}~ Mx{t} and space axis tangent to it. The Einstein equations split
then into constraints geometrically defined, and evolution equations.
The choice of equations considered as determining the evolution of the spacetime metric is not unique. They are well posed as partial differential equations, and satisfy the causality naturally required of a classical field theory, only under appropriate choice of ''gauges''. We will discuss some recently obtained well posed causal systems and their use for the study of the time of existence of solutions of the Cauchy problem (analytically and numerically). In a second part we will consider the ''cosmological'' case, where the spacetime is endowed with a family of privileged observers, i.e. of time lines. We will give the n+1 decomposition in a family of orthonormal frames with time axis tangent to the given time lines. One then obtains for the Riemann tensor metric and connection a symmetric first order system of partial differential equations. Moreover a system of the same type can be obtained through the use of the Euler equations of a perfect fluid whose flow lines the privileged observers time lines (a similar system, but with spurious characteristics has been written recently by H. Friedrich). We will discuss possible applications of the new system, which is not as well adapted as the old one to the solution of the Cauchy problem. |
MC3. Cosmological Dynamical Systems
Giannis Miritzis
| We study homogeneous and isotropic cosmologies in different gravity
theories with one or two fluids and/or one scalar field as matter source.
We give a brief review of the basic mathematical formalism of the theory
of finite dynamical systems. We write the field equations in a form suitable
for the dynamical system approach and analyze the general properties of
the system of DEs describing the evolution of the models. Finally we discuss
without technical details the dynamical system approach to the study of
Bianchi type models.
Bibliography Perko L. (1991), Differential Equations and Dynamical Systems, Springer-Verlag Wainwright J. and Ellis G.F.R. (1997), Dynamical Systems in Cosmology, Cambridge University Press Wainwright J. (1996), Relativistic Cosmology, in Proceedings of the 46th Scottish Universities Summer School in Physics, eds. G. Hall and J. Pulham, Institute of Physics Publishing Coley A. (1999), Dynamical Systems in Cosmology, gr-qc/ 9910074. |
MC4. Exact Cosmological Solutions
Sotiris Bonanos
| After a short historical introduction emphasizing the observational
facts (Olbers' paradox, Hubble recession, microwave background radiation)
and assumptions (cosmological principle) that lead to our present picture
of the universe, we will discuss in detail the possible cosmological
models that are allowed within the framework of general relativity. The
emphasis will be on the mathematical derivation and the mathematical /
physical properties peculiar to each model. The level will be that
of an introductory General Relativity textbooks given below.
Bibliography Malcolm Ludvigsen, General Relativity - A Geometric Approach, 1999, Cambridge U. Press. Ray d'Inverno, Introducing Einstein's Relativity, 1992, Oxford U. Press. |
PHYSICAL COSMOLOGY
PC1. Large Scale Structure
Manolis Plionis
| Basics of Dynamical Cosmology (Redshift, magnitudes, Friedman
Equations)
Thermal History of the Universe The Microwave Background Building Blocks of the Universe (Galaxies, clusters, filaments, voids) and statistics of the Large Scale Structure (correlation functions, shape statistics, topological measurers etc) Measuring the Universe (Extragalactic Distance scale, Large-Scale Dynamics and Velocity fields, Determination of Cosmological Parameters). Bibliography J.V.Narlikar "Introduction to Cosmology", Cambridge Univ. Press Rowan-Robinson, "Cosmology", Clarendon Press-Oxford Combes et al "Galaxies & Cosmology", A&A Library, Springer (Chapters 11, 12, 13) J. Peacock "Cosmological Physics", Cambridge Univ. Press (Part 2, 5 and 6). |
PC2. Observational Cosmology
Giannis Georgantopoulos
| Galaxies and their Evolution: multiwavelenght observations of galaxies,
Luminosity functions, number counts,the Hubble Deep Field AGN (Seyferts galaxies, QSOs): evolution and their space distribution the X-ray and Infrared Backgrounds Clusters of galaxies and their Evolution: X-ray observations, mass-temperature relation, luminosity function and evolution of clusters, clusters at high redshift, groups of galaxies. Bibliography B.Peterson, "Active Galactic Nuclei", Cambridge Univ. press Charles & Seward, "Exploring the X-ray Universe", Cambridge Univ. Press (Chapters 6, 13, 14) J. Peacock, "Cosmological Physics", Cambridge Univ. Press (Part 5, sections 13, 14). |
PC3. Cosmological Parameters from Large
Scale Structure and CMB Data
Giorgos Efstathiou
| Introduction to the CMB, explaining the origin of peaks in the power
spectrum.
Summarize the latest CMB results, implications for cosmological parameters, and future experiments (polarization,MAP,Planck). Surveys of large-scale structure with emphasis on the 2dF survey. Results from the 2dF survey. Combined analysis of the 2dF and CMB. Implications for fundamental physics. Bibliography J. Peacock, "Cosmological Physics", Cambridge Univ. Press J. Peacock et. al, Nature 410 (2001) 169. |
PC4. Cosmological Perturbations
Christos Tsagas
| It is widely believed that the galaxies and the cluster of galaxies
that fill our universe started from weak, infinitesimal, perturbations
on an otherwise homogeneous and isotropic cosmic fluid. These small deviations
from uniformity grew slowly, through gravitational instability, to form
the large-scale structure we observe today. The aim of the course is to
provide a brief but comprehensive introduction to structure formation theory.
The course is divided into two main sections. In the first, it provides
the mathematical framework necessary to analyse linear cosmological perturbations
both in the Newtonian and in the relativistic framework. The second part
addresses the so-called non-linear regime, namely the evolution of perturbations
that have grown too strong for the linear analysis to apply. This late-time
stage is actually the one that gives rise to the non-linear structures,
such as the galaxies and the cluster of galaxies, we observe in the universe
today.
Bibliography Structure Formation in the Universe, T. Padmanabhan, Cambridge University Press (1993) Cosmology: The Origin and Evolution of Cosmic Structure, P. Coles and F. Lucchin, Wiley (1995) Principles of Physical Cosmology, P.J.E. Peebles, Princeton University Press (1993) Cosmological Inflation and Large-Scale Structure, A.R. Liddle and D.H. Lyth, Cambridge University Press (2000) Cosmological Physics, J.A. Peacock, Cambridge. |
STRING AND PARTICLE COSMOLOGY
SPC1. Inflation
Giorgos Lazarides
| The standard big bang cosmological model and the history of the early
universe according to the grand unified theories are summarized. The shortcomings
of this cosmological model and their resolution by inflation are discussed.
Inflation and the subsequent oscillation and decay of the inflaton field
are then studied in detail. The density perturbations produced during inflation
and their evolution during the matter dominated era are presented.
The temperature fluctuations of the cosmic background radiation are summarized. The hybrid inflationary model is introduced in the context of a concrete supersymmetric grand unified theory based on the Pati-Salam gauge group. Two `natural' extensions of supersymmetric hybrid inflation which avoid the cosmological disaster encountered in the standard hybrid inflationary scenario from the overproduction of monopoles at the end of inflation are discussed. It is shown that successful `reheating' which satisfies the gravitino constraint takes place after the end of inflation. The scenario of baryogenesis via a primordial leptogenesis is considered in some detail and shown that it can operate consistently with the solar and atmospheric neutrino oscillation data as well as the SU(4)_c symmetry. The mu-term is generated via a Peccei-Quinn symmetry and proton is practically stable. Bibliography E.W. Kolb and M.S. Turner, The Early Universe (Addison-Wesley, Redwood City, CA, 1990) A.D. Linde, Particle Physics and Inflationary Cosmology (Harwood Academic Publishers, London, 1990) G. Lazarides, hep-ph/9802415 G. Lazarides, hep-ph/9904428 [Springer Tracts Mod. Phys. 163(2000)227] G. Lazarides, hep-ph/9904502 [PRHEP-corfu98/014] G. Lazarides, hep-ph/0011130. |
SPC2. Particle Cosmology
Kyriakos Tamvakis
| Gauge Theories and Unification
Global and Local Supersymmetry Gauge Theories at finite temperature Symmetry Breaking and Phase Transitions. Monopoles, Baryon Asymmetry, etc. Inflationary Models Effective Superstring Theories Effective Four-Dimensional Theories from Branes. Bibliography G. G. Ross, Grand Unified Theories, 1984 Addison-Wesley H. P. Nilles, Physics Reports 110 (1984) 1 A. B. Lahanas and D. V. Nanopoulos, Physics Reports 145 (1987) 1 R. Brandenberger, Reviews of Modern Physics 57 (1985) 1. M. B. Breen, J. H. Schwarz and E. Witten, Superstring Theory, 1987 Cambridge University Press M. Kaku, Introduction to Superstrings, 1988 Springer-Verlag V. A. Rubakov, hep-ph/0104152. |
SPC3. String Cosmology
Nikos Mavromatos
| ``Old ‘’ String Theory is a theory of one-dimensional extended
objects, whose vibrations correspond to excitations of various target-space
field modes including gravity. It is for this reason that strings present
the first, up to now, mathematically consistent framework for quantum gravity,
unified with the rest of fundamental interactions in nature.
In these lectures I will give an introduction to Effective Target-Space Actions derived from conformal invariance conditions of the underlying sigma models in string theory, or equivalently , corresponding to on-shell S-matrix amplitudes for the various string modes. For brevity we shall restrict ourselves to bosonic strings with some hints on the extension to supersymmetric strings. In this context I shall discuss cosmology, emphasizing the role of the dilaton field in inducing inflationary scenaria and in general expanding string universes. Specifically, I shall discuss first the concept of dimensional reduction (and the associated Kaluza-Klein excitations) in string theory. Then I will proceed in analysing some exact solutions of string theory with a linear dilaton, and discuss their role in inducing expanding Robertson-Walker Universes. I will also mention briefly pre-Big-Bang scenaria of String Cosmology, in which the dilaton plays a crucial role. In view of recent claims on experimental evidence (from diverse astrophysical sources) on the existence of cosmic acceleration in the universe today , with a positive non-zero cosmological constant (de Sitter type) I shall also discuss difficulties of incorporating such Universes (with eternal acceleration) in the context of critical string theory. Bibliography M. Green J. Schwarz and E. Witten , "Superstring Theory" , Vols I and II (Cambridge University Press 1987) I. Antoniadis, C. Bachas, J. Ellis and D.V. Nanopoulos, Nuclear Physics B328 (1989), 117 G Veneziano , Lectures given at 71st Les Houches Summer School Jul 1999, Published in *Les Houches 1999, The primordial universe* 581-628, hep-th/0002094 E. Witten, hep-th/0106109. |
SPC4. Brane Cosmology
Lefteris Papantonopoulos
| The introduction of branes in physics, had offered another novel
way of describing our Universe. According to the "Brane-World" scenario,
we are living on a D3-brane, which is embedded in a higher dimensional
space, the so called "bulk".
After reviewing the embedding of a D-brane in a D+1 dimensional space, we discuss the cosmology we get on the brane.We describe the cosmological evolution of the brane-universe in two (equivalent) ways. In the first approach the branes are static solutions of the underlying theory, and the cosmological evolution is due to the time evolution of the energy density of the brane. In the second approach, the cosmological evolution of our universe is due to the motion of the brane in the background gravitational field of the bulk. Bibliography T. Shiromizu, K. Maeda and M. Sasaki, "The Einstein Equations on the 3-Brane World", Phys. Rev. D62 (2000) 024012, gr-qc/9910076, P. Binetruy, C. Deffayet and D. Langlois, "Nonconventional Cosmology from a Brane Universe", Nucl. Phys. B 565 (2000) 269, hep-th/9905012, H. A. Chamblin and H. S. Reall, "Dynamic Dilatonic Domain Walls", Nucl. Phys. B 562 (1999) 133, hep-th/9903225. |
SPC5. Quantum Cosmology
Theodosis Christodoulakis
| The imposition of Spatial Homogeneity reduces Einstein's
Field Equations to a Classical Mechanical system with configuration
space variables the components of the scale factor matrix, the lapse function
and the shift vector of some anisotropic Bianchi Type model. Among these
variables there are constraints which reflect the covariance of the theory
under general coordinate transformations. The connecting link is provided
by the automorphisms of the Lie Algebra of the isometry group characterising
the Bianchi Type. The generators of these automorphisms are the momentum
constraints and (at occasion) some classical integrals of motion. Their
quantum versions reduce the space in which the wave function-- obeying
the Wheeler-DeWitt Equation -- lives.
Bibliography K. Sundermeyer, Constrained Dynamics, Lecture Notes in Physics, Vol. 169, Springer-Verlag (1982) Quantum Gravity, Quantum Cosmology and Lorentzian Geometry, Springer-Verlag, (1994) C. J. Isham, Canonical Quantum Gravity and the Problem of Time, gr-qc/9210011 J. Halliwell, S. Hawking, Quantum Cosmology-Beyond Minisuperspace, Cambridge Univeristy Press (1985) J. J. Haliwell, A Bibliography of papers on Quantum Cosmology, Int. J. Mod. Phys, A5, 2473-2494 (1990). |
SPC6. Dark Matter
Thanasis Lahanas
| There are a number of different observations which indicate the presence
of Dark Matter (DM), one of the biggest mysteries of modern Cosmology.
Recent cosmological observations suggest that the Matter-Energy density
of the Universe is close to its critical density, Ù = 1, whose large amount
( ~70 % ) is Dark Energy of uknown origin. The baryonic density comprises
only the ~ 5 % while the rest is due to Dark Matter of unknown composition.
Modern particle physics theories, notably String
Theories, should address to the question who ordered both Dark Energy and Dark Matter. In the framework of Supersymmetric theories the yet undiscovered in accelerator experiments ``neutralinos" can be good candidates for Cold Dark Matter. Their relic density today can be in agreement with astrophysical data, putting severe constraints on supersymmetric models. These are of relevance to next run experiments offering the guarantee that Supersymmetry will be discovered at future planned accelerators. Bibliography S. Weinberg, ``Gravitation and Cosmology", J. Wiley, New York 1972 G. Jungman,M. Kamionkowski and K. Griest, Phys. Reports 187 (1996) 195 E. W. Kolb and M. S. Turner ``The Pocket Cosmology" European Physical Journal C 15 (2000) 1, available on the PDG WWW pages, http://pdg.lbl.gov/. |
HISTORY OF COSMOLOGY
HC. History of Cosmology
Andreas Paraskevopoulos
| Our historical survey starts with the scientific inquiry that occurred
in the sixth century BC with the concepts emerged by the Greek philosophers,
particularly Thales, and through Epicurus we pass on to the universal principles
capable of accounting for the observed universe of Aristotle. We then analyse
the heliocentric cosmology of Aristarchus and the geocentric cosmology
of Ptolemy based on his epicycle theory. Finally, we consider cosmological
aspects of the works of Copernicus, Kepler, Galileo, Newton, and Herschel
before passing on to issues of modern cosmology. Here the theories of Einstein,
de Sitter, Friedmann and Lemaitre as well as important developments in
observational cosmology are presented and we round off with current trends
in the field such as those of chaotic and inflationary cosmologies and
the emerging ideas of quantum, string and M-theory cosmology.
Bibliography E. Harrison, Cosmology (2nd ed.) (CUP, 2000) J.D. North, The measure of the Universe. A History of Modern Cosmology (Dover, 1990) J.D. North, The Fontana History of Astronomy and Cosmology (Fontana Press, 1994) A. Lightman and R. Brawer, Origins: the lives and worlds of modem cosmologists . |