Strong-Field Gravitational Wave Tests of General Relativity

Transcription

1 Strong-Field Gravitational Wave Tests of General Relativity Nico L. Sampson, N. Cornish Montana State University Yukawa Workshop, Kyoto 2013 arxiv: (submitted to PRD) arxiv: (accepted in PRD) arxiv: (PRD 86, 2012) arxiv: (PRD 84, 2011) arxiv: (PRD 80, 2009)

2 Standing on the Shoulders of... Clifford Will, Jim Gates, Stephon Alexander, Abhay Ashtekar, Sam Finn, Ben Owen, Pablo Laguna, Emanuele Berti, Uli Sperhake, Dimitrios Psaltis, Avi Loeb, Vitor Cardoso, Leonardo Gualtieri, Daniel Grumiller, David Spergel, Frans Pretorius, Neil Cornish, Scott Hughes, Carlos Sopuerta, Takahiro Tanaka, Jon Gair, An incomplete summary of what GWs will tell us about the gravitational interaction Paolo Pani, Antoine Klein, Kent Yagi, Laura Sampson, Leo Stein, Sarah Vigeland, Katerina Chatziioannou, Haris Apostolatos, Philippe Jetzer, Leor Barack, Curt Cutler, Kostas Glampedakis, Stanislav Babak, Ilya Mandel, Chao Li, Eliu Huerta, Chris Berry, Alberto Sesana, Carl Rodriguez, Georgios Lukes- Gerakopoulos, George Contopoulus, Chris van den Broeck, Walter del Pozzo, Jon Veitch, Nathan Collins, Deirdre Shoemaker, Sathyaprakash, etc.

3 Tests of General Relativity Curvature Strength Weak Field Tests ξ 1/2 =(M/r 3 ) 1/2 [km -1 ] LAGEOS Earth's Surface Lunar Laser Ranging Strong Field Tests Perihelion Precession of Mercury Double Binary Pulsar Sun's Surface LIGO NS-NS Merger LIGO BH-BH Merger IMRIs IMBH-SCO LISA IMBH-IMBH Merger EMRIs SMBH-SCO LISA SMBH-SMBH Merger Pulsar Timing Arrays ε=m/r with SNRs in the 10s with SNRs in the 1e3s Field Strength GWs can probe the non-linear, dynamical, strong-field regime Will, Liv. Rev., 2005, Psaltis, Liv. Rev., 2008, Siemens &, Liv. Rev

4 Gravitational Wave Information h (t) M D L cos (M!) 2/3 cos gravitational wave symmetric mass ratio distance to the source inclination angle total mass orbital freq. orbital phase 2 Gravitational Waves contain information 1 Inspiral Merger Ring down about the system that generates them. h + 0 Learn About Astrophysics, Black holes, Neutron stars. Test General Relativity and search for GR Deviations Post-Newtonian t/m Num. Rel. BH Pert. Theory

5 Road Map I. Gravitational Waves and Modified Theories II. Parametrized post-einsteinian: Theory III. Parametrized post-einsteinian: Implementation

6 Gravitational Waves: Detection

7 Detectors LHO GEO KAGRA LLO Virgo/AdV Ligo-India Bounce light off mirrors and look for interference pattern when the light recombines.

8 Data Analysis at work C. Hanna, LSC/PI Matched Filtering: Maximize the SNR over all template parameters signal-tonoise ratio (SNR) detector noise (spectral noise density) data 2 Z s(f) h(f, µ ) df S n (f) template param that characterize system template (projection of GW metric perturbation)

9 Gravitational Waves: Modified Theories

10 Straw Man Dynamical Chern-Simons Modifications to GR? [Alexander &, Phys. Repts 480, 2009] Action: Z S GR = Z S Kin = coupling constants d 4 x p gappler S CS = Z d 4 x p d 4 x p 4 g (@ a #)(@ a #) scalar field g#r abcd R abcd Field Equations: G ab +( /apple)c ab =1/(2apple)T ab # RR C ab cde(a r e R b) dr c # + R d(ab)c r c r d #

11 Gravitational Wave Construction (I) (concentrating on compact binary inspirals) I. Series expand field equations in weak-field, slow-motion (PN). Solve! Eg. Dynamical CS gravity: [ & Pretorius, PRD 79, 2009; Yagi,, Tanaka, PRD 86, 2012] # abuv h ad,gb h v [g,d] u # ijk r 2 (U,im V k,jm ) (Cannot always use point-particle approx; spinning CS BHs have scalar charge) II. Calculate effective GW stress-energy. Eg. Dynamical CS gravity: [Stein &, PRD 83, 2011] T GW ab h cd,(a h cd,b) swa

12 Gravitational Wave Construction (II) III. From the near-zone solution, construct the Hamiltonian. Eg. Dynamical CS gravity: [Yagi,, Tanaka, accepted to PRL] E = M 2 r 12 apple 1+1PN PN + O 2 S2 m 2 m 2 r 2 12 IV. From the far-zone solution, construct the RR force (fluxes). Eg. Dynamical CS gravity: [Yagi, Stein,, Tanaka, PRD 85, 2012] Ė = 32 5 apple m 5 1+1PN apple +1.5PN PN + O 5 M Ė = 32 5 r 12 r PN PN + O 2 S2 2 S2 m 2 m 2 r 2 12 m 2 m 2 r 2 12

13 Gravitational Wave Construction (III) V. From E and Edot, find the equations of motion with dissipation Eg. Dynamical CS gravity: [Yagi, f f apple1+1pn 11/3, Tanaka, apple1+1pn accepted to PRL] +1.5PN PN + O f f 11/ PN + O VI. Understand the propagation of metric perturbations. Eg. Dynamical CS gravity: [Sopuerta &, PRD 84, 2011] Eg 2 p 2 g 2 = gp 2 g 2 S2 m 2 f 4/3 2 S2 m 2 f 4/3 VII. Construct the response function and Fourier transform it. Eg. Dynamical CS gravity: [Yagi,, Tanaka, accepted n to PRL] f 7/6 e i ( Mf) 5/3h n 1+1PN+1.5PN PN+O 3 D L 128 ( Mf) 5/3h 1+1PN PN+O h A M5/6 h A M5/6 D L f 7/6 e i 2 S 2 2 S 2 m 2 f 4/3 io M 2 f 4/3 io

14 Gravitational Waves in Alternative Theories (i) Scalar-Tensor theories: [Will, PRD 50, Scharre & Will, PRD 65, Will &, CQG 21, Berti, et al. PRD 71, Alsing et al, 2011.] h = h GR e i BD 2/5 f 7/3 inversely related to the BD coupling parameter GW freq. because of dipolar energy emission (ii) Massive Graviton Theories: [Will, PRD 57, 1998, Will &, CQG 21, 2004 Stavridis & Will, PRD 80, Arun & Will, CQG 26, 2009.] (iii) Gravitational Parity Violation: [Alexander, Finn &, PRD 78, 2008., et al, PRD 82, Alexander and, Phys. Rept. 480, 2009] h = h GR e i MG 0 f 1 related to graviton Compton wavelength h = h GR 1+ PV 0 f 1 related to CS coupling (iv) G(t) theories: [, Pretorius, & Spergel, PRD 81, 2010.] h = h GR 1+ Ġ 3/5 f 8/3 e i Ġ 3/5 f 13/3 related to G variability

15 Gravitational Waves in Alternative Theories (v) Quadratic Gravity [ & Stein, PRD 83, 2011 Yagi, Stein, & Tanaka, accepted in PRD.] (vi) Lorentz-Violating GW Propagation: [Mirshekari, & Will, PRD 85, 2012] h = h GR e i QG 4/5 f 1/3 h = h GR e i LV 0 f 1 because it s a higher curvature correction related to theory couplings related to degree of Lorentz violation We have still not found any theories whose predicted gravitational wave cannot be mapped to such phase and amplitude corrections (assuming analyticity).

16 Parameterized post-einsteinian theory

17 Parameterized post-einsteinian Framework I. Parametrically deform the Hamiltonian. II. Parametrically deform the RR force. A = A GR + A A H,RR = H,RR vāh,rr III. Deform waveform generation. h = F + h + + F h + F s h s +... IV. Parametrically deform g propagation. E 2 g = p 2 gc 4 + p g Result: To leading PN order and leading GR deformation h = h GR (1 + f a ) e i f b h(f) = h GR (f)(1+ f a ) e i f b & Pretorius, PRD 2009 Mirshekari, & Will, PRD 2012 Chatziioannou, & Cornish, PRD 2012

18 Current Constraints -0.5PN 0PN 0.5PN GW Constraints -1PN 1PN -1.5PN 1.5PN -2PN -2.5PN h BD (f; ~ GR, EDGB BD) BD GR LV MG h LV (f; ~ GR, LV ) CS 2PN 2.5PN -3PN Gdot h D>4 (f; ~ GR, D>4) 3PN h ppe (f; ~ GR, ~ ppe) -3.5PN 3.5PN -4PN 0 4PN

19 Parameterized post-einsteinian Framework Templates/ Theories GR Not GR GR Business as usual Quantify fundamental bias introduced by filtering non-gr events with GR templates ppe Quantify the statistical significance that the detected event is within GR. Anomalies? Can we measure deviations from GR characterized by non-gr signals? Model Evidence. h = h GR (1 + f a ) e i f b h(f) = h GR (f)(1+ f a ) e i f b [ & Pretorius, PRD 2009, Mirshekari, & Will, PRD 2012, Chatziioannou, & Cornish, PRD 2012]

20 Parameterized post-einsteinian Implementation

21 Fundamental Bias Non-GR Signal/GR Templates, SNR = 20 Non GR injection, extracted with GR templates (blue) and ppe templates (red). GR template extraction is wrong by much more than the systematic (statistical) error. Fundamental Bias BF = 0.3 β = 1 BF = 5.6 β = 5 BF = 53 ppe GR injected value ln(m) ln(m) D L (Gpc) BF = 322 β = 10 BF = 3300 β = 20 BF = 1 ppe GR injected value ln(m) ln(m) D L (Gpc) Cornish, Sampson, & Pretorius, 2011

22 Ignoring Fundamental Bias... 1 injection = (not-ruled out) ppe template=gr Fitting Factor Fitting Factor Deteriorates PN, 2.0PN /100 Physical Parameters Completely Biased Chirpmass PN, 2.0PN /100 Sampson, 2013

23 Stealth Bias SNR needed for fundamental bias error to be larger than statistical error Fundamental Bias that we can t detect! SNR needed to detect a GR deviation Negligible Bias Stealth Bias Overt Bias Vallisneri &, 2013

24 Constraining GR deviations GR Signal/ppE Templates, 3-sigma constraints, SNR = 20 Newt 1PN Double Binary Pulsar bounds aligo projected bounds Weak Field Strong Field h(f) = h GR (f)(1+ f a ) e i f b & Hughes, 2010, Cornish, Sampson, & Pretorius, 2011 Sampson, Cornish, 2013.

25 Simple ppe Performance Bayes Factor between a 1-parameter ppe template and a GR template (red) and between a 2-parameter ppe template and a GR template (blue), given a non-gr injection with 3 phase deformations, as a function of the magnitude of the leadingorder phase deformation. Sampson, Cornish &, 2013

26 What does it all mean? GW Observations of compact binary inspirals will provide unparalleled information about the gravitational interaction in the dynamical, non-linear regime. Is the non-linear and dynamical sector of the Einstein equations correct at astrophysical black hole horizon scales? Does the point-particle approximation hold for BH and NS binaries? Doveryai, no proveryai Do GWs have only two massless polarizations? Gravitational waves will allow us to constrain deviations from General Relativity in the strong-field to unparalleled levels.