Parameterizing and constraining scalar corrections to GR

Parameterizing and constraining scalar corrections to GR Leo C. Stein Einstein Fellow Cornell University Texas XXVII 2013 Dec. 12

The takeaway Expect GR needs correction Look to compact binaries for corrections Pulsar timing Gravitational wave measurements Connect to observables by parameterizing theory space Hope that nature is kind Leo C. Stein Scalar corrections to GR Texas XXVII 2013 Dec. 12 2

Why test GR? 1. Ask nature So far, only weak-field tests Lots of theories GR Need to explore strong-field Strong curvature non-linear dynamical 2. Theory What does this mean? G ab = 8πG T ab Expect GR to be effective theory Leo C. Stein Scalar corrections to GR Texas XXVII 2013 Dec. 12 3

1 Ξ Gmr 3 12 km 1 inv. curvature radius 0.001 10 6 10 9 10 12 LLR Earth's surface LAGEOS Mercury precession Sun's surface J0737 3039 NS NS merger BH merger SMBH merger 10 12 10 10 10 8 10 6 10 4 0.01 1 ε

1 Ξ Gmr 3 12 km 1 inv. curvature radius 0.001 10 6 10 9 10 12 LLR Earth's surface LAGEOS Sun's surface Mercury precession Stronger J0737 3039 NS NS merger BH merger SMBH merger 10 12 10 10 10 8 10 6 10 4 0.01 1 ε Gmr compactness

The strong field Potential (Gm/r): Highly compact Curvature (Gm/r 3 ): Short length = low mass Dynamics ( t x ): High velocity Known pulsar binaries v 10 4 Compact binary merger v 0.1 Leo C. Stein Scalar corrections to GR Texas XXVII 2013 Dec. 12 5

Theories Fundamental approach: String theory Loop quantum gravity TeVeS Einstein-Æther Hǒrava Massive gravity drgt bi-metric... Pedestrian approach: effective field theory Learned from cond-mat, then nuclear and hep-th Theory with separation of scales Integrate out, effective theory for long (or short) wavelengths Works backwards! General relativity v/c 0 G 0 post-newtonian Special relativity Leo C. Stein Scalar corrections to GR Texas XXVII 2013 Dec. 12 7

EFT works Worked for describing superconductivity, predicting W, higgs, etc. Try to build EFT for gravity Metric, general covariance, Lorentz invariance Lowest order dynamical theory is Λ+GR! Beyond GR: add new l want to constrain this Leo C. Stein Scalar corrections to GR Texas XXVII 2013 Dec. 12 8

Past few years Program to study specific EFTs: EDGB and dcs EDGB: L m pl l 2 θ(riem 2 4Ric 2 + R 2 ) dcs: L m pl l 2 θ R abcd R abcd Studies: GW energy (PRD 83, 064038) BH structure (PRD 79, 084043; PRD 83, 104002) (Quasicircular BH) Binary inspirals (PRD 85, 064022) GWs from (PRL 109, 251105) NS structure, (eccentric) binary inspirals, GWs (PRD 87, 084058)...? Leo C. Stein Scalar corrections to GR Texas XXVII 2013 Dec. 12 9

Ξ Gmr 3 12 km 1 inv. curvature radius 1 0.001 10 6 10 9 10 12 LLR 700 km d 0,r 3 Earth's surface LAGEOS 10 8 km dcs Mercury precession Sun's surface 400 km J0737 3039 30 km 2 km EDGB NS NS merger BH merger SMBH merger 10 12 10 10 10 8 10 6 10 4 0.01 1 ε

Summary of phenomena Isolated bodies Scalar hair Shift in ω(r), ISCO, EH M R relation Binaries Scalar interaction changes orbit Pericenter precession Scalar radiation Orbital decay Gravitational waves Modified propagation New modes available Energy content Correction to waveforms... Leo C. Stein Scalar corrections to GR Texas XXVII 2013 Dec. 12 11

Scalar hair Scalar sourced by gravity, e.g. θ l 2 R abcd R abcd Compact objects acquire long-ranged scalar multipolar hair Requires strong-field matching calculation Examples dcs: θ BH µ iˆn i /r 2 (dipole l 2 S i /M 2 ; NS also dipole l 2 Ŝ i ) EDGB: θ BH q/r (monopole l 2 /M; NS maybe quadrupole?) Leo C. Stein Scalar corrections to GR Texas XXVII 2013 Dec. 12 12

Scalar hair Implications: No-hair theorems violated Effacement principle lost Scalar multipole-multipole interaction in binary ω dcs = ω [ GR 1 + ζf(m, χ, e, EOS)v 2 +... ] Scalar radiation from binary Ψ dcs (f) = Ψ GR (f) + ζf(m, χ, e, EOS)(πGMf) 1/3 +... Leo C. Stein Scalar corrections to GR Texas XXVII 2013 Dec. 12 13

Pause Common theme among theories: scalar hair Don t want to study each theory one by one Can we say anything generally? Yes! Parameterize Leo C. Stein Scalar corrections to GR Texas XXVII 2013 Dec. 12 14

Parameterize L int (m pl l)l θ T [ɛ 0,1, g, d, R r ] Specify ( ɛ, d, r), multipole numbers l BH, l NS Theory ɛ d r l BH l NS Scalar-Tensor 0 0 1-1 0 EDGB 0 0 2 1 0 2? dcs 1 0 2 1 1 1 Leo C. Stein Scalar corrections to GR Texas XXVII 2013 Dec. 12 15

Intimidation slide Many calculations ensue... estimate observables ω ( ) t l 2 ( ) l 2 (2s + 2t + 1)!! (C 1 C 2 ) r ω GR (Gm)(Gµ) R 1 R 2 ( ) s ( ) t R1 R2 f 2 (e)v 2(s+t 1) Gm Gm Ψ ppe (f) = Ψ GR (f) + β ppe (πgmf) b ppe b ppe = (6s 7)/3 ( ) 1 l 2+2 ( ) δm 2 β ppe η (12+6 )/5 (s = 1) Gm m ( ) 1 l 2+2 ( ) δm 2 β ppe η (8+6 )/5 (s = 0) Gm m Convert to estimated bounds Leo C. Stein Scalar corrections to GR Texas XXVII 2013 Dec. 12 16

Ξ Gmr 3 12 km 1 inv. curvature radius 0.001 10 6 10 9 10 12 1 10 0 LLR Earth's surface LAGEOS Mercury precession dcs EDGB Sun's surface Ω timing J0737 3039 NS NS merger BH merger SMBH merger 10 12 10 10 10 8 10 6 10 4 0.01 1 ε Gm r compactness 10 2 10 4 10 6 10 8 10 10 km

10 EDGB Ξ Gmr 3 12 km 1 inv. curvature radius 1 0.1 0.01 0.001 BHBH inspiral dcs NS merger BH merger EMRI NS 10 0 10 1 10 2 10 3 km 10 4 0.005 0.01 0.02 0.03 0.05 0.1 0.2 ε Gm r compactness 10 4

The takeaway Expect GR needs correction Look to compact binaries for corrections Pulsar timing Gravitational wave measurements Connect to observables by parameterizing theory space Hope that nature is kind arxiv:1310.6743 Leo C. Stein Scalar corrections to GR Texas XXVII 2013 Dec. 12 18