1 Wei-Tou NI Center for Gravitation and Cosmology (CGC) Department of Physics, National Tsing Hua University Hsinchu, Taiwan, ROC Dark energy, co-evolution of massive black holes with galaxies, and ASTROD-GW, Adv. Space Res. (2012), arXiv: Int. J. Mod. Phys. D 22 (2013) DISTINGUISHING DARK ENERGY MODELS VIA GRAVITATIONAL-WAVE (GW) MEASUREMENTS Dark 2012Dark Energy via GW Measurements W-T Ni

Bounds on massive gravity theories Dark 2012 Dark Energy via GW Measurements W-T Ni 2

Outline Introduction -- dark energy talks Luminosity distance vs redshift to test and to determine the dark energy models Determining the source parameters with GW observations Classification of GWs and methods of detection Gravitational-wave missions – NGO/eLISA, ASTROD-GW, DECIGO Distinguishing dark energy models and the lensing effects Discussion and Outlook Dark 2012 Dark Energy via GW Measurements W-T Ni 3

Dark Energy Talks COSMIC ACCELERATION: Dark energy and modified theories Mohammad Sami (CTP, Jamia Millia Islamia/Nagoya University) Interacting holographic dark energy Xin Zhang (Northeastern) Finite-time future singularities and cosmologies in modified gravity Kazuharu Bamba (KMI, Nagoya) Vainshtein mechanism in the most general scalar-tensor theories Ryotaro Kase (Tokyo University of Science)* Model for neutrino masses and dark matter with a discrete gauge symmetry Chi-Fong Wong (NTHU)* F(R) bigravity Shin'ichi Nojiri (Nagoya University) The vacuum bubbles: revisited Bum-Hoon Lee (Sogang University) Massive Scalar Field Quantum Cosmology Sang Pyo Kim (Kunsan U) ………… Dark 2012 Dark Energy via GW Measurements W-T Ni 4

Space GW detectors and Dark energy Luminosity Distance-Redshift relation In the solar system, the equation of motion of a celestial body or a spacecraft is given by the astrodynamical equation a = a N + a 1PN + a 2PN + a Gal-Cosm + a GW + a non-grav In the case of scalar field models, the issue becomes what is the value of w(  ) in the scalar field equation of state: w(  ) = p(  ) / ρ(  ), where p is the pressure and ρ the density. For cosmological constant, w = -1. From cosmological observations, our universe is close to being flat. In a flat Friedman-Lemaître-Robertson-Walker (FLRW) universe, the luminosity distance is given by d L (z) = (1+z) ∫ 0 → z (H 0 ) -1 [Ω m (1+z′) 3 + Ω DE (1+z′) 3(1+w) ] -(1/2) dz′, where w is assumed to be constant Dark 2012 Dark Energy via GW Measurements W-T Ni 5

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Dark 2012 Dark Energy via GW Measurements W-T Ni 9 Catalogs of GW sources Typical binaries: sky positions, distance, orbit orientation, orbit separation, chirp mass for the system, spin magnitude and orientation, merger time (if appropriate) Sources with subtantial orbital evolution: masses of the individual objects Most favorable cases: masses, spins and distances to 1 %

Extreme Mass Ratio Inspirals (EMRIs) EMRIs are GW sources for space GW detectors. The NGO/eLISA sensitive range for central MBH masses is M . The expected number of NGO/eLISA detections over two years is 10 to 20; 18 for LISA, a few tens; 18 for ASTROD-GW, similar or more with sensitivity toward larger central BH’s and with better angular resolution (Sec. 4.3) Dark 2012 Dark Energy via GW Measurements W-T Ni 10

Massive Black Hole Binaries The expected rate of MBHB sources is 10 yr -1 to 100 yr -1 for NGO/eLISA and 10 yr -1 to 1000 yr -1 for LISA. 18 For ASTROD-GW, similar number of sources but with better angular resolution (Sec. 4.3) Dark 2012 Dark Energy via GW Measurements W-T Ni 11

Space GW detectors and Dark energy In the solar system, the equation of motion of a celestial body or a spacecraft is given by the astrodynamical equation a = a N + a 1PN + a 2PN + a Gal-Cosm + a GW + a non-grav In the case of scalar field models, the issue becomes what is the value of w(  ) in the scalar field equation of state: w(  ) = p(  ) / ρ(  ), where p is the pressure and ρ the density. For cosmological constant, w = -1. From cosmological observations, our universe is close to being flat. In a flat Friedman Lemaître-Robertson-Walker (FLRW) universe, the luminosity distance is given by d L (z) = (1+z) ∫ 0 → z (H 0 ) -1 [Ω m (1+z′) 3 + Ω DE (1+z′) 3(1+w) ] -(1/2) dz′, where w is assumed to be constant Dark 2012 Dark Energy via GW Measurements W-T Ni 12

Earlier GW Classification (Thorne 1995); (Ni 1997) (i) High-frequency band (1-10 kHz); (ii) Low-frequency band (100 μ Hz - 1 Hz)  (100 nHz – 1 Hz); (iii) Very-low-frequency band (1 nHz nHz)  (300 pHz – 100 nHz); (iv) Extremely-low-frequency band (1 aHz - 1 fHz  1 aHz - 10 fHz) Dark 2012 Dark Energy via GW Measurements W-T Ni 13

Complete GW Classification (Modern Physics Letters A25, 922, 2010; ArXiv ; Dark 2012 Dark Energy via GW Measurements W-T Ni 14

15 B F Schutz ASTROD 5: GW Sources11 July 2012 Sensitivity and BH Science 10 6 M z=1, SNR= M z=20, SNR= M z=5, SNR=15 eLISA ASTROD

16 B F Schutz ASTROD 5: GW Sources11 July 2012 Sensitivity and BH Science 10 6 M z=1, SNR= M z=20, SNR= M z=5, SNR=15 eLISA ASTROD Unresolved binary systems

Dark 2012 Dark Energy via GW Measurements W-T Ni 17 The Gravitational Wave Background from Cosmological Compact Binaries Alison J. Farmer and E. S. Phinney (Mon. Not. RAS [2003]) Optimistic (upper dotted), fiducial (Model A, lower solid line) and pessimistic (lower dotted) extragalactic backgrounds plotted against the LISA (dashed) single- arm Michelson combination sensitivity curve. The ‘ unresolved ’ Galactic close WD – WD spectrum from Nelemans et al. (2001c) is plotted (with signals from binaries resolved by LISA removed), as well as an extrapolated total, in which resolved binaries are restored, as well as an approximation to the Galactic MS – MS signal at low frequencies. ASTROD-GW Region DECIGO BBO Region

Strain noise power spectra of ASTROD-GW as compared with LISA and NGO/eLISA 東吳 Classification and Detection of Gravitational Waves W.-T. Ni 18

Complete GW Classification (I) Ultra high frequency band (above 1 THz): Detection methods include Terahertz resonators, optical resonators, and ingenious methods to be invented. Very high frequency band (100 kHz – 1 THz): Microwave resonator/wave guide detectors, optical interferometers and Gaussian beam detectors are sensitive to this band. High frequency band (10 Hz – 100 kHz): Low-temperature resonators and laser-interferometric ground detectors are most sensitive to this band. Middle frequency band (0.1 Hz – 10 Hz): Space interferometric detectors of short armlength ( km). Low frequency band (100 nHz – 0.1 Hz): Laser-interferometer space detectors are most sensitive to this band Dark 2012 Dark Energy via GW Measurements W-T Ni 19

Complete GW Classification (II) Very low frequency band (300 pHz – 100 nHz): Pulsar timing observations are most sensitive to this band. Ultra low frequency band (10 fHz – 300 pHz): Astrometry of quasar proper motions are most sensitive to this band. Extremely low (Hubble) frequency band （ 1 aHz – 10 fHz): Cosmic microwave background experiments are most sensitive to this band. Beyond Hubble frequency band (below 1 aHz): Inflationary cosmological models give strengths of GWs in this band. They may be verified indirectly through the verifications of inflationary cosmological models Dark 2012 Dark Energy via GW Measurements W-T Ni 20

東吳 Classification and Detection of Gravitational Waves W.-T. Ni 21

Comparison of current and planned GW detectors 東吳 Classification and Detection of Gravitational Waves W.-T. Ni 22

Space GW detectors as dark energy probes Luminosity distance determination to 1 % or better Measurement of redshift by association From this, obtain luminosity distance vs redshift relation, and therefore equation of state of dark energy Dark 2012 Dark Energy via GW Measurements W-T Ni 23

Space GW Detectors Space interferometers (eLISA, ASTROD-GW, DECIGO) for gravitational-wave detection hold the most promise with signal-to- noise ratio. eLISA (evolved Laser Interferometer Space Antenna) is aimed at detection of low-frequency (10 -4 to 1 Hz) gravitational waves with a strain sensitivity of 4 × /(Hz) 1/2 at 1 mHz. There are abundant sources for eLISA, and ASTROD-GW: galactic binaries (neutron stars, white dwarfs, etc.). Extra-galactic targets include supermassive black hole binaries, supermassive black hole formation, and cosmic background gravitational waves. LISA Pathfinder will Launch in 2015; DECIGO Pathfinder will bid for a selection in A date of eLISA launch is hoped for Dark 2012 Dark Energy via GW Measurements W-T Ni 24

eLISA/NGO: evolved Laser Interferometer Space Antenna / New Gravitational Wave Observatory Dark 2012 Dark Energy via GW Measurements W-T Ni 25 Variations of the arm lengths, the velocities in the line of sight direction, and the angle between barycentre of S/Cs and Earth in 1000 days for the S/C configuration

ASTROD-GW Mission Orbit Considering the requirement for optimizing GW detection while keeping the armlength, mission orbit design uses nearly equal arms. 3 S/C are near Sun-Earth Lagrange points L3 、 L4 、 L5 ， forming a nearly equilateral triangle with armlength 260 million km （ AU ）. 3 S/C ranging interferometrically to each other Dark 2012 Dark Energy via GW Measurements W-T Ni 26 (L 3 ) S/C 2 S/C 3 (L 5 ) S/C 1 (L 4 ) L 1 L 2 60  Sun Earth

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Determination of Dark Energy Equation is limited by gravitational lensing Dark 2012 Dark Energy via GW Measurements W-T Ni 29 Better resolution may help to resolve and lessen the gravitational lensing effects; further study on this is needed.

Space GW detectors as a dark energy probe For LISA, the accuracy of luminosity distance determination for MBH-MBH mergers is expected to be 1-2 % for redshifts z < 3, degrading to ≈ 5 % for z ≈ 5 one has to obtain redshifts of the host galaxies. High signal to noise ratio gives high angular resolution which facilitates the determination of optical association and redshift. Arun et al. (2007) showed that when higher signal harmonics are included in assessing the parameter estimation problem, the angular resolution increases by more than a factor of 10, making it possible for LISA to identify the host galaxy/galaxy cluster Dark 2012 Dark Energy via GW Measurements W-T Ni 30

ASTROD-GW ASTROD-GW will be able to determine this equation to 1 % or better through z to 20 with the only limitation coming from weak lensing. Self-calibration methods may apply; however, the weak lensing may limit the accuracy to % for z = With more study and observation, the limitation from weak lensing will be clearer and hopefully suppressed to certain extent Dark 2012 Dark Energy via GW Measurements W-T Ni 31

Weak Lensing Limit As investigated in Kocsis et al. (2006), at z=1, the weak lensing error in determining the redshift is about 2-3 %; at z=2, the weak lensing error is about 10 %; at z=3, the weak lensing error is about 20 %; at z=4, the weak lensing error is about 30 %. Gunnarsson et al. (2006) used the observed properties of the foreground galaxies along the line of sight to the source to delense and reduce the dispersion due to lensing for source at z = 1.5 from about 7% to < 3% Dark 2012 Dark Energy via GW Measurements W-T Ni 32

Weak Lensing Limit (2) Shapiro et al. (2010) proposed to use mapping shear and flexion of galaxy images to reduce the lensing error. They estimated that delensing with a 2D mosaic image from an Extremely Large Telescope could reduce distance errors by about 25–30 per cent for an MBHB at z=2. Including an additional wide shear map from a space survey telescope could reduce distance errors by nearly a factor of 2. Saini et al. (2010) proposed to use self-calibration to reduce systematic uncertainties in determining distance- redshift relation via gravitational radiation from merging binaries Dark 2012 Dark Energy via GW Measurements W-T Ni 33

Current Expectation Binaries as distance indicators Detection, LCGT, adLIGO, adVirgo: 2016 PTAs: about 2020 ET sensitivities Space detectors for Gravitational Waves Dark energy equation via binary GW observations Dark 2012 Dark Energy via GW Measurements W-T Ni 34

ASTROD’s GW gaols -- dedicated to GW detection Larger Arm Length  More Sensitivity to Lower Frequency and Larger Wavelength Better S/N to massive BH events  Better accuracy for cosmic distance measurement and probe deeper into larger redshift and earlier Universe. Better probe to dark energy. More sensitive to primordial gravitational waves if foreground GWs can be separated Dark 2012 Dark Energy via GW Measurements W-T Ni 35

Weak-Light Phase Locking To 2 pW A.-C. Liao, W.-T. Ni and J.-T. Shy, On the study of weak-light phase-locking for laser astrodynamical missions, Publications of the Yunnan Observatory 2002, (2002); IJMPD (2002). To 40 fW G. J. Dick, M., D. Strekalov, K. Birnbaum, and N. Yu, IPN Progress Report (2008) Dark 2012 Dark Energy via GW Measurements W-T Ni 36

Orbit configuration optimization Optimize period Optimize radius (semi-major axis) iteratively Dark 2012 Dark Energy via GW Measurements W-T Ni 37

ASTROD-GW inclined orbit configuration-- with nondegenerate angular resolution in the whole sky In the original proposal, the ASTROD-GW orbits are chosen in the ecliptic plane. The angular resolution in the sky has antipodal ambiguity and, near ecliptic poles, the resolution is poor, although over most of sky the resolution is good. Revising the orbits of ASTROD-GW spacecraft to have small inclinations of 1-3 degrees to resolve these issues while keeping the variation of the arm lengths in the tolerable range Dark 2012 Dark Energy via GW Measurements W-T Ni 38

Summary Dark 2012 Dark Energy via GW Measurements W-T Ni 39 Introduction -- dark energy talks Luminosity distance vs redshift to test and to determine the dark energy models Determining the source parameters with GW observations Classification of GWs and methods of detection Gravitational-wave missions – NGO/eLISA, ASTROD-GW, DECIGO Distinguishing dark energy models and the lensing effects Discussion and Outlook

Thank you! Dark 2012 Dark Energy via GW Measurements W-T Ni 40

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The fractional arm length variation is within (1/2) sin2 λ which is about 10^-4 for λ about 1° and about 10^-3 for λ about 3° Armlength Dark 2012 Dark Energy via GW Measurements W-T Ni 43

Sensitivities of Ground and Space Interferometers Dark 2012 Dark Energy via GW Measurements W-T Ni 44 AI