Putting Einstein to the test with Gravitational Wave Observations Neil J. Cornish Outline • Theoretical Landscape • Observational landscape • First look at dynamical strong field gravity • Polarization • Future prospects Theoretical Landscape Lovelock theorem: GR is the only Don’t mess with WEP! “nice” purely metric theory in 4D. In 4D, the only divergence free symmetric rank-2 tensor constructed only by the metric and its derivatives up to 2nd order and preserving diffeomorphism invariance is the Einstein tensor plus a constant. [Berti et al, arXiv:1501.07274] Rouges Gallery of Alternative Theories [Berti et al, arXiv:1501.07274] Popular Examples Ultraviolet Modifications (e.g. EdGB, dCS) 1 S = p gd4x R 2 φ µφ V (φ)+S [ ,γ(φ)g ] 16⇡ − − rµ r − mat µ⌫ Z 2 h µ⌫ µ⌫⇢ + f1(φ)R + f2(φ)Rµ⌫ R + f3(φ)Rµ⌫⇢R + f4(φ)⇤RR i Infrared (screened) Modifications (e.g. Horndeski) S = d4xp g K(φ,X) G (φ,X) φ − − 3 ⇤ Z n + G (φ,X)R + G (φ,X) ( φ)2 ( φ)( µ ⌫ φ) 4 4,X ⇤ − rµr⌫ r r G (φ,X) + G (φ,X)G µ ⌫ φ ⇥5,X ( φ)3 3 φ( ⇤ φ)( µ ⌫ φ) 5 µ⌫ r r − 6 ⇤ − ⇤ rµr⌫ r r + 2( φ)( µ φ)( ⌫ σφ) ⇥ rµr⌫ r rσ r r ⇤o Observational Landscape [Yunes,Yagi, Pretorius, arXiv:1603.08955] Dark energy alternatives, screening mechanisms required [Baker, Psaltis, Skordis, arXiv:1412.3455] Null Tests, Generic Tests • Lacking compelling alternatives, prefer generic null tests • Do GR models leave behind a residual signal? • Parameterize possible departures from GR waveforms • Search for additional polarization states • Ringdown - GR predicts unique relationship between harmonics Morphology-independent signal reconstruction 10 5 0 h(t) -5 -10 6.7 6.75 6.8 6.85 6.9 6.95 7 7.05 7.1 10 injected 5 0 h(t) -5 recovered -10 6.7 6.75 6.8 6.85 6.9 6.95 7 7.05 7.1 t (s) [Cornish & Littenberg, arXiv:1410.3835] Extracting signals without templates } Inferred Signal Predicted Signal 94% match with GR waveform (discrepancy consistent with what we expect from noise) [LVC, PRL116, 061102 (2016); PRL 116 221101, (2016)] Search for Residual Signals data - signal = noise SNR2 = 1 res > 0.96 F s − SNR2 Deviations from GR < 4% SNRres < 7.3 Gravitational Wave Observations • Do gravitational waves travel at the speed of light? • Is the emission of energy and angular momentum as predicted by GR? • Is the graviton massless? • Are gravitational waves transverse? • Additional polarization states? • Did anyone hear an echo? 16 +7 10− Gravitational Waves Travel at the Speed of Light cgw =1 3⇥10 15 − ⇥ − [LIGO/Virgo/Fermi, ApJ Lett 848 (2017)] Bad news for many dark energy alternatives e.g. Horndeski S = d4xp g K(φ,X) G (φ,X) φ − − 3 ⇤ Z n + G (φ,X)R + G (φ,X) ( φ)2 ( φ)( µ ⌫ φ) 4 4,X ⇤ − rµr⌫ r r G (φ,X) + G (φ,X)G µ ⌫ φ ⇥5,X ( φ)3 3 φ( ⇤ φ)( µ ⌫ φ) 5 µ⌫ r r − 6 ⇤ − ⇤ rµr⌫ r r + 2( φ)( µ φ)( ⌫ σφ) ⇥ rµr⌫ r rσ r r [Creminelli, Vernizzi, arXiv:1710.05877, Sakstein, Jain, arXiv:1710.05893,⇤o Baker et al, arXiv:1710.06394] Many models that could potentially explain the accelerated expansion yet evade solar system constraints via screening have been ruled out One way out might be to build models that change behavior with length scale rather than density since λ R ,D R gw ⌧ H L ⌧ H [Battye, Pace, Trinh, arXiv:1802.09447] Gravitational Wave Observations • Do gravitational waves travel at the speed of light? • Is the emission of energy and angular momentum as predicted by GR? • Is the graviton massless? • Are gravitational waves transverse? • Additional polarization states? • Did anyone hear an echo? Is the emission of energy and angular momentum as predicted by GR? h(f)= (f) eiΨ(f) A Post-Newtonian Inspiral 5/6 5 7/6 ⇡ k (f)= M f − =2⇡ft +Φ + + u AGR 96 D π2/3 GR c c 4 k k= 5 X− u =(⇡ f)1/3 v M ⇠ Modified Waveforms 5/6 5 7/6 5 8 743 11 2/5 2 (f)= M f − 1 G˙ u− + + η η− u + ... A 96 D π2/3 −512 M 672 8 Variable G Scalar Field 2 π 3 5 25 8 5 S 3/5 2 Ψ(f)=2πftc Φc + u− 1 G˙ u− η u− − − 4 128 −1536 M −84 ωBD 2 3715 55 2/5 2 3/5 3 128 π D 2 + + η η− u 16πη− u 2 M u + ... 756 9 − − 3 λg(1 + z) Massive Graviton h(f)=(1+δ (f)) eiδ (f) h (f) A GR Parametrized Post-Einsteinian [Yunes, Pretorius, arXiv:0909.3328] [Arun, Iyer, Qusailah, Sathyaprakash, arXiv:gr-qc/0604018] No deviations seen from GR phasing Caveat emptor: These bounds are term-by-term (not jointly allowed to vary) k k Bounds would be weaker if all terms allowed to vary together [Sampson, Cornish, Yunes, arXiv:1303.1185] Inspiral Merger-ringdown [LVC, arXiv:1602.03841, arXiv:1606.04856] Gravitational Wave Observations • Do gravitational waves travel at the speed of light? • Is the emission of energy and angular momentum as predicted by GR? • Is the graviton massless? • Are gravitational waves transverse? • Additional polarization states? • Did anyone hear an echo? Is the graviton massless? 2 2 2 mg “Chirp Squeezing” - higher frequency signal from near the merger travels faster and arrive earlier cgw = cgw,0 1 2 − E ! 2 π 3 5 3715 55 2/5 2 3/5 3 128 π D 2 Ψ(f)=2πftc Φc + u− 1 + + η η− u 16πη− u 2 M u + ... − − 4 128 756 9 − − 3 λg(1 + z) Partially degenerate with changing the total mass Degeneracy mostly broken by higher PN terms and merger 22 m < 1.2 10− eV g ⇥ [LVC, arXiv:1602.03841, arXiv:1606.04856] Gravitational Wave Observations • Do gravitational waves travel at the speed of light? • Is the emission of energy and angular momentum as predicted by GR? 22 • Is the graviton massless? mg < 1.2 10− eV ⇥ • Are gravitational waves transverse? • Additional polarization states? • Did anyone hear an echo? Alternative Theories Predict additional Polarization States TT e+ = u u v v TT ⌦ − ⌦ uˆ e⇥ = u v + v u TT ⌦ ⌦ ST SL e = u u + v v kˆ ST ⌦ ⌦ vˆ e = k k SL ⌦ eu = u k + k u VL VL ⌦ ⌦ ev = v k + k v VL ⌦ ⌦ Antenna Patterns Interferometers Pulsar Timing TT TT ST VL ST SL VL SL [Yunes & Siemens, Living Rev.Rel. 16, 9 (2013)] Binary Black Hole Merger GW170814 - First Constraints on Polarization [LIGO/Virgo PRL 119, 141101 (2017)] Binary Black Hole Merger GW170814 - First Constraints on Polarization H1 [LIGO/Virgo PRL 119, 141101 (2017)] Tensor favored over Vector by 200:1 Tensor favored over Scalar by 1000:1 L1 Virgo [Isi & Weinstein, arXiv:1710.03794 (2017)] Binary Black Hole Merger GW170814 - BayesWave Constraints on Polarization Bayes Factors between models similar to those form template based analysis Binary Black Hole Merger GW170814 - First Constraints on Polarization Tensor Vector Scalar LIGO/Virgo Antenna Patterns First search for nontensorial gravitational waves from known pulsars Scalar T S V SV ST VT SVT Vector No detections so far, so bounds are weak Tensor Note: The analysis assumed that f gw =2 f orb , which is not always the case for dipole emission [LIGO/Virgo PRL 120, 031104 (2018)] A Search for Tensor, Vector, and Scalar Polarizations in the Stochastic Gravitational-Wave Background [LIGO/Virgo arXiv:1802.10194 (2018)] A Search for Tensor, Vector, and Scalar Polarizations in the Stochastic Gravitational-Wave Background LIGO O1 Limits: (Marginalized over spectral slope) f0 = 25Hz T 7 V 7 S 7 ⌦ < 2.0 10− ⌦ < 2.5 10− ⌦ < 8.4 10− 0 ⇥ 0 ⇥ 0 ⇥ [LIGO/Virgo arXiv:1802.10194 (2018)] Pulsar Timing PTA Two-Point Correlations 0.7 0.7 0.6 ΓTT 0.65 ΓST 0.5 TT 0.6 0.4 0.3 0.55 0.2 0.5 0.1 0.45 0 0.4 -0.1 -0.2 0.35 ST SL -0.3 0.3 0 0 20 40 60 80 20 40 60 80 100 120 140 160 180 100 120 140 160 180 12 500 450 10 ln(fL) ΓVL 400 (fL) ΓSL 8 ⇠ 350 ⇠ 6 300 250 4 200 2 150 100 0 VL 50 -2 0 0 0 20 40 60 80 20 40 60 80 100 120 140 160 180 100 120 140 160 180 ⇠ ⇠ EESL [Chamberlin & Siemens Phys.Rev. D85, 082001 (2012)] EEVL [Lee, Jenet & Price, Ap.J. 685, 1304 (2008)] Upper Limit using NANOGrav 9-year results TT 2 4/3 ST 2 VL 2 SL 2 2 Γ (f/f )− +(Γ +Γ +Γ )(f/f )− ab AQ y ab AST ab AVL ab ASL y Sab(f)= 2 2/3 (1 + (f/fy)− ) 15 < 3 10− ATT ⇥ 15 < 2 10− AST ⇥ 16 < 4 10− AVL ⇥ 17 < 4 10− ASL ⇥ [Cornish, O’Beirne, Taylor, Yunes, PRL (2018)] Gravitational Wave Observations • Do gravitational waves travel at the speed of light? • Is the emission of energy and angular momentum as predicted by GR? 22 • Is the graviton massless? mg < 1.2 10− eV ⇥ • Are gravitational waves transverse? no evidence to contrary • Additional polarization states? • Did anyone hear an echo? Echoes from the abyss? BH perturbation theory - structure of QN modes depends on inner boundary conditions. Any reflections from inside the light ring produce echoes [Cardoso, Hopper, Macedo, Palenzuela, Pani, arXiv:1608.08637] Echoes from the abyss? 2.5 σ hint of detection claimed using LIGO O1 detections [Abedi, Dykaar, Afshordi, arXiv:1612.00266] More careful reanalysis by some LIGO researchers found nothing [Westerweck et al, arXiv:1712.09966] 4.2 σ claim of detection using BNS GW170817 data [Abedi, Afshordi, arXiv:1803.10454] Detection of echoes also claimed for GW151226, GW170104, GW170606, GW170814, GW170817 [Conklin, Holdom, Ren, arXiv:1712.06517] I’m waiting for the analysis to be re-done using the specialized BayesWave search [Tsang et al, arXiv:1804.04877] Gravitational Wave Observations • Do gravitational waves travel at the speed of light? • Is the emission of energy and angular momentum as predicted by GR? 22 • Is the graviton massless? mg < 1.2 10− eV ⇥ • Are gravitational waves transverse? no evidence to contrary • Additional polarization states? • Did anyone hear an echo? Future Prospects Next steps - a worldwide network H H V K L I L V I K 3rd and 4th generation ground-based instruments A+: aLIGO upgrade, freq.