(ed.). Gravitational waves (IOP, 2001)(422s).

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References 279References[1] Taylor J H and Weisberg J M 1989 Astrophys. J. 345 434[2] Jantzen R T, Carini P and Bini D 1992 Ann. Phys. 215 1[3] Bini D, Carini P and Jantzen R T 1997a Int. J. Mod. Phys. D 6 1[4] Bini D, Carini P and Jantzen R T 1997b Int. J. Mod. Phys. D 6 143[5] Misner C W, Thorne K S and Wheeler J A 1973 Gravitation (New York: Freeman)[6] de Felice F and Clarke C J S 1990 Relativity on Curved Manifolds (Cambridge:Cambridge University Press)[7] de Felice F 1978 J. Phys. A: Math. Gen. 12 1223
Chapter 16Elementary introduction to pre-big bangcosmology and to the relic gravitonbackgroundMaurizio GasperiniDipartimento di Fisica, Università di Bari, Via G. Amendola 173,70126 Bari, Italy and Istituto Nazionale di Fisica Nucleare,Sezione di Bari, Bari, ItalyThis is a contracted version of a series of lectures for graduate and undergraduatestudents given at the ‘VI Seminario Nazionale di Fisica Teorica’ (Parma,September 1997), at the Second International Conference ‘Around VIRGO’ (Pisa,September 1998), and at the Second SIGRAV School on ‘Gravitational Wavesin Astrophysics, Cosmology and String Theory’ (Center ‘A. Volta’, Como, April1999). The aim is to provide an elementary, self-contained introduction tostring cosmology and, in particular, to the background of relic cosmic gravitonspredicted in the context of the so-called ‘pre-big bang’ scenario. No specialpreparation is required besides a basic knowledge of general relativity and ofstandard (inflationary) cosmology. All the essential computations are reportedin full details either in the main text or in the appendices. For a deeper and morecomplete approach to the pre-big bang scenario the interested reader is referred tothe updated collection of papers available at http://www.to.infn.it/∼gasperin/.16.1 IntroductionThe purpose of these lectures is to provide an introduction to the background ofrelic gravitational waves expected in a string cosmology context, and to discussits main properties. To this purpose, it seems to be appropriate to include a shortpresentation of string cosmology, in order to explain the basic ideas underlying280
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GRAVITATIONAL WAVES
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c IOP Publishing Ltd 2001All righ
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viContents4 Astrophysics of gravita
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viiiContents11.3 Gravitational wave
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xContents16.5 Cosmological perturba
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PrefaceGravitational waves today re
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2 Gravitational waves, theory and e
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10 Gravitational waves, theory and
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SynopsisGravitational waves and the
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Chapter 2Elements of gravitational
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Using the TT gauge to understand gr
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Interaction of gravitational waves
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Analysis of beam detectors 21This d
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Exercises for chapter 2 232. Show t
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Gravitational-wave detectors 25indi
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Gravitational-wave observables 27th
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The physics of interferometers 29
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The physics of interferometers 31Dr
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The physics of interferometers 33Fi
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The physics of resonant mass detect
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The physics of resonant mass detect
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A detector in space 39LISA has been
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Gravitational and electromagnetic w
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Chapter 4Astrophysics of gravitatio
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Sources detectable from ground and
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Variational principles and the ener
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Variational principles and the ener
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Practical applications of the Isaac
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Exercises for chapter 5 57(f)This s
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Expansion for the far field of a sl
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Application of the TT gauge to the
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6.4.1 Mass-quadrupole radiationEner
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Chapter 7Source calculationsNow tha
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The r-modes 73As we mentioned in ch
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The r-modes 75instability. In an id
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The r-modes 77Table 7.1. Gravitatio
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The r-modes 79evolution turns out t
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ReferencesWe have divided the refer
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References 83[19] van der Klis M 19
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Solutions to exercises 85For this p
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Solutions to exercises 87The gauge
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Chapter 8Resonant detectors for gra
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Sensitivity and bandwidth of resona
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8.2 Sensitivity for various GW sign
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Sensitivity for various GW signals
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Recent results obtained with the re
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Discussion and conclusions 101Figur
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Chapter 9The Earth-based large inte
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Introduction 105Figure 9.1. The sim
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h(sqrt(1/Hz))10 −610 −810 −10
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18.5 cmThe SA suspension and requir
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A few words about the Low Frequency
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Conclusion 113Figure 9.7. The R and
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Chapter 10LISA: A proposed joint ES
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Description of the LISA mission 117
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Expected gravitational-wave results
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References 149[8] Folkner W M 1998
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References 151[68] Miralda-Escuda J
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Introduction 153detect GWs with a s
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Testing theories of gravity 155•
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0Testing theories of gravity 157the
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Taking the scalar product we findGr
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Gravitational wave radiation in the
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The hollow sphere 169and introduced
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Scalar-tensor cross sections 171mon
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Scalar-tensor cross sections 173Tab
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Scalar-tensor cross sections 175Tab
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References 177Frossati G and Coccia
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Chapter 12Generalities on the stoch
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Introduction 183contribution to the
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Definitions 185The value of H 0 is
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Definitions 18712.2.2 The character
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Definitions 189or, dividing by the
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The overlap reduction function 191O
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The overlap reduction function 193T
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The overlap reduction function 195F
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Achievable sensitivities to the SGW
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Observational bounds 207Table 12.10
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equation gives immediately(ρgwρ
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Chapter 13Sources of SGWBHere we re
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Topological defects 213This correla
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Topological defects 215It can be sh
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Topological defects 217(i)A loop ra
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Topological defects 219• A peak n
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Topological defects 22113.1.2 Hybri
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Inflation 223Hubble radius and when
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Inflation 225as a first approximati
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Inflation 227the lower bound to the
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Page 248 and 249: Astrophysical sources 237which is t
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Page 252 and 253: References 241[39] Liddle A R 2000
Page 254: PART 4THEORETICAL DEVELOPMENTSHerma
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330 Elementary introduction to pre-
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Chapter 17Post-Newtonian computatio
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340 Post-Newtonian computation of b
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PART 5NUMERICAL RELATIVITYEdward Se
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362 Numerical relativityspite of mo
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364 Numerical relativityterms, of m
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366 Numerical relativityHere we hav
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368 Numerical relativityinformation
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370 Numerical relativityThe Palma,
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372 Numerical relativityHyperbolic
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374 Numerical relativityEinstein di
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376 Numerical relativityare the abi
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378 Numerical relativityeach cell i
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380 Numerical relativityFigure 18.1
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382 Numerical relativity1D code [45
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384 Numerical relativityfunctions,
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386 Numerical relativityto a very a
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388 Numerical relativity18.5 Comput
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390 Numerical relativitynumerics an
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392 Numerical relativityinitial dis
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396 Numerical relativityof these re
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400 Numerical relativityof Einstein
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402 Numerical relativity18.9.5.2 Co
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404 Numerical relativity[23] Ashby
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406 Numerical relativity[101] Shapi
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408 Numerical relativity(Singapore:
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410 IndexEhlers Lagrangian, 254Eins
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412 Indexscalarspherical harmonics,
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