1. Stochastic gravitational wave and its spectral property
Hyung Won Lee, Inje University
11 June, 2013
4th Japan-Korea Workshop, Osaka University

2. 4th Japan-Korea Workshop, 10-11 June 2013
Contents
Introduction
Characters of stochastic GWs
Sources of stochastic background of GWs
Detection
Remarks
4th Japan-Korea Workshop, June 2013

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GW Observatories
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4. 4th Japan-Korea Workshop, 10-11 June 2013
Introduction
New window onto the Universe
Large scale Laser interferometer detector for Gravitational Wave(GW)
LIGO, EGO-Virgo, GEO600, KAGRA
LISA, ET, BBO
Detecting known astrophysical sources
Expect real detection around 2020
Possibly detect stochastic GW of cosmological origin
A new window to study very early universe
4th Japan-Korea Workshop, June 2013

5. Gravitational wave generation
Triple time variation of quadruple moment
Sources
Man-made source (not possible to detect)
Astrophysical Objects
Burst from collapse
Pulsar
Binary system
Quasinormal mode of black hole
Stochastic background
Cosmological background
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6. Astrophysical Sources
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Gravitational wave
Two polarization mode
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Detection of GW
Large scale interferometer
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Matched filter
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Sensitivity
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Detection range
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Data Analysis
GW detector is Omni-directional : all-sky search
Interferometer is broad band
GW is polarized : correlation measurement required
Measure phase of GW
Computationally intense
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13. Characterization of stochastic backgrounds of GWs
Isotropic, stationary, unpolarized
Frequency spectrum is main property
Energy density per unit log frequency, ℎ 0 2 Ω 𝐺𝑊 (𝑓)
Spectral density of ensemble average the Fourier component of the metric, 𝑆 ℎ (𝑓)
Characteristic amplitude of the stochastic background, ℎ 𝑐 (𝑓)
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14. Energy density parameter
Definition Ω 𝐺𝑊 𝑓 = 1 𝜌 𝑐 𝑑 𝜌 𝐺𝑊 𝑑 ln 𝑓
𝜌 𝑐 = 3 𝐻 𝜋𝐺 , 𝐻 2 = 8𝜋𝐺 3 𝜌 (1st Hubble equation)
𝐻 0 = ℎ 0 ×100km/s∙Mpc, 0.5< ℎ 0 <0.65
ℎ 0 2 Ω 𝐺𝑊 (𝑓) independent of ℎ 0
Total density parameter for GW Ω 𝐺𝑊 = 0 ∞ Ω 𝐺𝑊 𝑓 𝑑 ln 𝑓
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15. Sources of stochastic background of GWs(Allen, 1996)
Inflation : Allen, et al.
Cosmic String network : Vilenkin, et al.
Bubbles from Phase transition : Kamionkowski, et al.
Modified f(R) gravity : Capozziello, et al.
Modified Chaplygyn Gas : Bouhmadi-Lopez, et al.
New Idea?
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Spectrum by Inflation
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17. Spectrum by Cosmic String
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18. Spectrum by Bubbles from Phase tr.
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Modified f(R) gravity
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20. Modified Chaplygin Gas
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New Idea?
Transplakian mechanism
Quantum gravity effect
Black body like spectrum for GWs
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22. Detectability with Single Detector
Noise spectrum
Detectable if
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23. Detection with Correlation
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Sensitivity curve
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Stochastic signal
From LIGO homepage
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Remarks
GW open a new window onto the Universe
Hard to detect
Specialized treatment for data
Cross correlation between detectors
Thermalisation like black-body radiation?
Model dependent
We need to see real GW data
4th Japan-Korea Workshop, June 2013