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

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String cosmology 231HPre-big bangPost-big bang0.0Figure 13.5. Qualitative behaviour of H in the suggested cosmological model. Brokencurves indicate the lowest order solution singular at t = 0. At around t = 0 a regularevolution interpolating between the two phases is displayed.0.0tfields):R(η) =− 1H s η s( η − (1 − α)ηsαη s) −α, (13.32)andφ(η) = φ s − γ ln η − (1 − α)η s,η swhere η is the conformal time (see section 13.2) ranging between −∞ and η s < 0,α = ( √ 3 − 1)/2, and γ = √ 3.At a value η = η s the curvature becomes of order of the string scale and thelowest order effective action does not give any more a good description of physics:we enter a ‘full stringy’ regime. One expects that higher order corrections to theeffective action tame the growth of the curvature, and both H and dφ/dt stayapproximatively constant. In terms of conformal time this meansR(η) =− 1H s η , φ(η) = φ s − 2β ln η η s, (13.33)where β is a free parameter which measures the growth of the dilaton in thisphase, which lasts for η s
232 Sources of SGWBdominated phase characterized byR(η) = 1H s η12 (η − 2η 1 ), φ = φ 0 . (13.34)The time-dependent component of a metric perturbation h ν µ can be expressed asin equation (13.20), where ψ obeys the Schrödinger-like equation (13.21) withpotential given, in this case, by:V (η) = eφ/2Rd 2dη 2 (Re−φ/2 ).Taking into account equations (13.32) and (13.34) one finds⎧1 4ν 2 − 1⎪⎨ 4 [η − (1 − α)η s )] 2 , −∞
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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
Page 192 and 193: Chapter 12Generalities on the stoch
Page 194 and 195: Introduction 183contribution to the
Page 196 and 197: Definitions 185The value of H 0 is
Page 198 and 199: Definitions 18712.2.2 The character
Page 200 and 201: Definitions 189or, dividing by the
Page 202 and 203: The overlap reduction function 191O
Page 204 and 205: The overlap reduction function 193T
Page 206 and 207: The overlap reduction function 195F
Page 208 and 209: Achievable sensitivities to the SGW
Page 218 and 219: Observational bounds 207Table 12.10
Page 220 and 221: equation gives immediately(ρgwρ
Page 222 and 223: Chapter 13Sources of SGWBHere we re
Page 224 and 225: Topological defects 213This correla
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Page 228 and 229: Topological defects 217(i)A loop ra
Page 230 and 231: Topological defects 219• A peak n
Page 232 and 233: Topological defects 22113.1.2 Hybri
Page 234 and 235: Inflation 223Hubble radius and when
Page 236 and 237: Inflation 225as a first approximati
Page 238 and 239: Inflation 227the lower bound to the
Page 240 and 241: String cosmology 22913.3 String cos
Page 244 and 245: String cosmology 233Figure 13.6. h
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Page 248 and 249: Astrophysical sources 237which is t
Page 250 and 251: References 239of [71]). However, fo
Page 252 and 253: References 241[39] Liddle A R 2000
Page 254: PART 4THEORETICAL DEVELOPMENTSHerma
Page 257 and 258: 246 Infinite-dimensional symmetries
Page 279 and 280: Chapter 15Gyroscopes and gravitatio
Page 281 and 282: 270 Gyroscopes and gravitational wa
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282 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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