Modern Theoretical and Observational Cosmology: Proceedings of the 2nd Hellenic Cosmology Meeting, held in the National Observatory of Athens , Penteli, 19–20 April 2001

372 Pages·2002·24.37 MB·English

by  Spiros Cotsakis (auth.)

MODERNTHEORETICALANDOBSERVATIONALCOSMOLOGY
ASTROPHYSICS AND
SPACE SCIENCE LIBRARY
VOLUME 276
EDITORIAL BOARD
Chairman
W.B.BURTON,National RadioAstronomyObservatory,Charlottesville, Virginia,U.S.A.
([email protected]); University ofLeiden,The Netherlands([email protected])
ExecutiveCommittee
1.M.E.KUIJPERS,Facultyof Science,Nijmegen.TheNetherlands
E.P.1.VANDEN HEUVEL,Astronomical Institute,Universityof Amsterdam,
TheNetherlands
H.VANDERLAAN,Astronomical Institute, UniversityofUtrecht.
TheNetherlands
MEMBERS
I.APPENZELLER,LandessternwarteHeidelberg-Konigstuhl,Germany
J.N.BAHCALL,TheInstituteforAdvancedStudy,Princeton, U.S.A.
F.BERTOLA,UniversitddiPadova,Italy
J.P.CASSINELLI, Universityof Wisconsin,Madison.U.S.A.
C.J.CESARSKY, Centred'EtudesdeSaclay,Gif-sur-YvetteCedex,France
O.ENGVOLD,InstituteofTheoreticalAstrophysics, University ofOslo,Norway
R.McCRAY, UniversityofColorado,JILA.Boulder,U.S.A.
P.G.MURDIN, Institute ofAstronomy.Cambridge. UiK.
F.PACINI,lstituto AstronomiaArcetri,Firenze.Italy
V.RADHAKRISHNAN,Raman ResearchInstitute,Bangalore,India
K.SATO,School of Science,The Universityof Tokyo,Japan
F.H.SHU, Universityof California.Berkeley, U.S.A.
B.V.SOMOV,Astronomical Institute.Moscow State University. Russia
R.A.SUNYAEV, SpaceResearchInstitute.Moscow,Russia
Y.TANAKA,InstituteofSpace &AstronauticalScience.Kanagawa, Japan
S.TREMAINE,CITA,Princeton University, U.S.A.
N.O.WEISS,UniversityofCambridge, UX
MODERN THEORETICAL
AND OBSERVATIONAL
COSMOLOGY
Proceedings of the 2nd Hellenic Cosmology
Meeting, held in the National Observatory of
Athens, Penteli, 19-20 Apri12001
edited by
MANOLIS PLIONIS
Institute ofA stronomy & Astrophysics,
National Observatory ofA thens, Greece
and
SPIROS COTSAKIS
GEODYSYC, Department of Mathematics,
University of the Aegean, Karlovassi, Greece
SPRINGER-SCIENCE+BUSINESS MEDIA, B.V.
A c.I.P. Catalogue record for this book is available from the Library of Congress.
ISBN 978-94-010-3931-4 ISBN 978-94-010-0622-4 (eBook)
DOI 10.1007/978-94-010-0622-4
Printed on acid-free paper
AII Rights Reserved
© 2002 Springer Science+Business Media Dordrecht
Originally published by Kluwer Academic Publishers in 2002
Softcover reprint of the hardcover 1s t edition 2002
No part of this work may be reproduced, stored in a retrieval system, or transmitted
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Contents
Preface
ManolisPlionis& SpirosCotsakis
Theoretical Cosmology 3
CurrentTrendsinMathematicalCosmology 5
SpirosCotsakis
CasimirEffectContributiontotheCosmologicalConstant 19
E.Elizalde
MassesofCosmologicalStructures 35
N.K. Spyrou
GeometricalAspectsofCosmicMagneticFields 45
ChristosG.Tsagas
GalacticMagneticFieldsasaconsequenceofInflation 53
KonstantinosDimopoulos
RelaxationoftheCosmologicalPrinciple 61
MichaelTsamparlis
ANoteonWavemap-TensorCosmologies 67
Spiros Cotsakis,JohnMiritzis
InflationinStringTheoryandhowyoucangetoutofit 75
E.Papantonopoulos
QuantumCosmologyfortheGeneralBianchiVacuumGeometries 85
T. Christodoulakis & G. O.Papadopoulos
BlackHoleEntropy,TopologicalEntropy,Baum-ConnesConjecture 107
loannisP. Zois
v
vi CURRENTISSUESINCOSMOLOGY
ObservationalCosmology 117
Froth across the Universe 119
RienvandeWeygaert
CosmologicalParameters 259
E.Gaztafiaga
FormingCounterrotatingGalaxies 273
NikosVoglis, MariaHarsoula
CosmologicalParametersfrom theClusteringofAGN 289
SpyrosBasilakos
Large-ScaleEnvironmentalEffects oftheClusterDistribution 299
ManolisPlionis
ScaleDependenceofDarkEnergyAntigravity 313
L.Perivolaropoulos
Probingthe EvolutionofGalaxiesusing RedshiftedHoEmission 323
PaulP. vanderWeif,AlanF. M.Moorwood, LinYan
Gas inthe Universe 339
PadeliPapadopoulos
Summary 347
ReporttoAnaximander 349
RienvandeWeygaert
PREFACE
ManolisPlionis & Spiros Cotsakis
[email protected]
[email protected]
Since the dawn of human civilisation natural phenomena have been subject
toobservation and investigation by the humans who initially ascribed to them
'divine' powers. Godsof'good' and 'evil' werecreatedaccordingtotheuseful
nessornotofsuchunexplained, atthetime, phenomena. Astheirunderstanding
of the world developed and deepened, the divine powers, religious beliefs, su
perstitions and mysticism gavetheirplace totheknowledge, limitedthatitmay
be, of physical reality. However, many issues have been and still are out of
grasp of human understanding. Theseissues have always been atthe centerof
philosophical, theological, and more recently, scientific debate.
Itistousincrediblethat manyoftheconclusions concerning the true scientific
explanation oftheexternal world,towhichtheancient Greeksarrivedpurely on
the basis of abstract thought, came so near to modem scientific ideas and also
form the basis of modem science. Wecannot butstand with amazement atthe
original thoughts ofArchimedes who, among his many extraordinary achieve
mentsinmathematicsandphysics, calculated(cf. TheSandReckoner)themass
density oftheobservable universe andcame upwithafigurethat isincomplete
agreement with current estimates coming from observational cosmology. The
philosopherAnaximanderofMiletus, astudent ofThales, propoundedtheview
that theearth remains inthecenterof the Universe suspended freely and with
out support (contrary to what was thought by most other philosophers of the
time) due to the fact that it is at equal distances from the rest of the Universe.
The atomic theory of Democritus and his teacher Leukipus, the teachings of
Parmenides regarding the spherical shape ofthe earth, that nothing isborn out
ofnothing andthatanything cannotbereduced tonothing (which reminds usof
an energy conservation law), the opinion of Empedocles that light propagates
withfinitevelocity (contrary toAristotlewhobelieved that lightistheoutcome
of a qualitative and instantaneous change of the environment) etc, are only a
1
M.PlionisandS.Cotsakis (eds.),ModemTheoreticalandObservationalCosmology, 1-2.
©2002KluwerAcademicPublishers.
2 CURRENTISSUESIN COSMOLOGY
small,selected fraction of what was known to our ancestors. Furthermore and
despite thedominance ofthe Aristotelian thought, AristarchosofSamos(310
230BC), headofthePeripaticSchool in"-'288BC,wasthefirsttoputforward
the heliocentric hypothesis:
a
"tnfOTi()f.TQ'.l, lapTa j.LEV 11"AQVEQ TWV a(7TpWV saiTOV QAWV j.LEVEu/
aK,iV"lTOV, Tav M,av1I"EP/,cPEPEU()Q/,1I"EpiTOV QAWVK,QTa K,VK,AOV
1I"EP/,cPEPEtQV, b; earu/ EV j.LEUW TW 8poj.Lw K,Eij.LWOC;"
Cosmology, thesciencedealing withthenature, origin, structure andnowadays
theevolution oftheUniverse,isasoldashumancivilisation. Manycivilisations
pursued knowledge inthis subject: Among others the Greeks, the Indians, the
Arabs and much later the Europeans who brought back to light, contrary to
the religious fanaticism ofthe time, the heliocentric system (Copernicus). The
laws of planetary motion formulated byKepler received asound mathematical
justificationwhenthelawofgravitation wasdiscovered byHookeandNewton.
This marks the beginning ofthe modemera of scientific thought.
Modem Cosmology begins with Einstein's discovery ofGeneral Relativity in
1916,and Hubble's discovery in 1929ofthe recession ofdistant galaxies with
velocities proportional to their distance. These two leads, one theoretical and
the other observational, continue to this day to be responsible for the current
interestin this subject.
We initiated several years ago an attempt to bring together once every couple
of years the small but scattered Greek Cosmology Community as well as a
few European Cosmologists, in order to exchange views and opinions and to
generate collaborative efforts. This book contains papers corresponding to
the talks given at the 2nd Hellenic Cosmology Meeting held at the National
Observatory in Athens, in April 19-20, 2001, as well as an invited special
contribution by Rien van de Weygaert. The two themes advanced during the
very lively works of that meeting, one centering around theoretical aspects of
Cosmology andthe other focussing on observational Cosmology, are reflected
inthis volume.
Wewould liketoacknowledge support receivedfromtheDepartmentofMath
ematics,UniversityoftheAegeanandfromtheNational Observatory ofAthens
which madethiseventpossible. WewouldalsoliketothankthestaffofKluwer
for theirkind cooperation and understanding and for their efforts that resulted
inthe fineappearance ofthis volume.
THEORETICAL COSMOLOGY
CURRENT TRENDS INMATHEMATICAL
COSMOLOGY
Spiros Cotsakis
GEODYSYC,DepartmentofMathematics, UniversityoftheAegean,Karlovassi,83200,Greece
[email protected]
Keywords: mathematical cosmology, theories ofgravity(relativistic), spacetime structure,
matterfields.
Abstract Wepresentanelementaryaccountofmathematicalcosmologythroughaseries
ofimportantunsolvedproblems. Weintroducethefundamental notionofacos
mologyandfocusontheissueofsingularitiesasathemeunifyingmanycurrent,
seeminglyunrelatedtrendsofthissubject. Wediscussproblemsassociatedwith
thedefinitionandasymptoticstructureofthenotionofcosmologicalsolutionand
alsoproblemsrelatedtothequalificationofapproximationsandtotherangesof
validityofgivencosmologies.
1. Introduction
Circumstantialevidenceisaverytrickything.Itmayseemtopointverystraight
toonething,butifyoushiftyourownpointofviewalittle,youmayfinditpointing
inanequallyuncompromisingmannertosomethingentirelydifferent. (Sherlock
Holmes)
Inanyfieldofapplied mathematics onestartsbycarefully identifying thebasic
object ofstudy,onethatcontains theessential parameters oftheproblem, tobe
determined by later analysis. The mathematical methods of cosmology which
promise to be useful, even essential to the nature of problems one typically
encounters come from two different sources, namely, differential geometry
and dynamical systems theory. Indeed, mathematical cosmology, a largely
unexploredbuthighlyinterestingandpromisingareaofresearch, maybeloosely
defined as that separate discipline in applied mathematics which lies in the
differentiable world of geometry and dynamical systems borrowing heavily
from both areas and contributing back constantly new problems and ideas not
onlytoboth ofthese mathematical fieldsbutalsototheclosely related physical
and observational cosmology.
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M.PlionisandS.Cotsakis(eds.),ModemTheoreticalandObservational Cosmology, 5-17.
©2002KluwerAcademicPublishers.