Effective Field Theory
                             Approach to Testing GR

                                      AIMS, Ca...
Outline
                      I. Brief introduction to GWs
                      II. Motivation : probe non-linearities of...
Results

                     •       Measurement of radiation loss from the Hulse-
                             Taylor Bi...
I. Introduction to GW
                             •   Gravitational waves are oscillations of the
                       ...
Wave equation

                    hT T = 0
                      µν
                                       speed of light...
Binary Pulsar : important test




              A pulsar is a highly magnetized, rotating neutron star that emits EM radi...
Hulse-Taylor Binary (1974)




                        The pulsar rotates on its axis17 times per second, pulse period is ...
Inferred detection.
  Orbital decay due to energy loss via gravitational radiation.




                  The data points ...
Quest for direct detection




        Network of GW detectors
         (LIGO,Virgo, LISA,etc)


Friday, September 17, 2010
A closer look

                   Animation:    h ∼ 0.5
                                 f ∼ 2 seconds


                 ...
Estimates at interferometers
                   Physical effect of a passing GW, perturb relative positions of freely-fall...
Sources  Sensitivity Curves




                                                                                        SB...
Example: NS-NS coalescence                                   3.1   Inspiral of binary stars 137




                      ...
Example: NS-NS coalescence                                   3.1   Inspiral of binary stars 137




                      ...
II. Motivation
                     •       GR is non-linear

                     •       Two labs where non-linearities ...
Post-Newtonian Expansion

                 •       What is it? Post-Newtonian terms in GR are
                         cor...
EFT method
                     •       UV divergences due to field theory coupled to
                             point-pa...
III. Tools: NRGR Tutorial

                     •       “Non relativistic General Relativity”

                     •     ...
Main Ingredients of NRGR
                     •       Identify relevant dof at the scale of interest.
                    ...
Relevant Scales of a Binary System




                                      We want two EFTs,
                           ...
Starting point
                 Theory of relativistic point particles coupled to gravity:

                              ...
Potential  radiation gravitons




Friday, September 17, 2010
H and h scale differently




                                     k µ ∼ (v/r, 1/r)
                                     k...
So?




Friday, September 17, 2010
Feynman Building Blocks:
                                Graviton Vertices
                                               ...
Feynman Building Blocks:
                                 Matter Vertices
                                                ...
Which diagrams are allowed?




Friday, September 17, 2010
Orbital Scale EFT
                             Newton’s Potential (0 PN)




Friday, September 17, 2010
Orbital Scale EFT
                             EIH Lagrangian (1 PN)




Friday, September 17, 2010
Tools
        Basic Results in NRGR


The EIH Lagrangian
                     The potential Lagrangian (orbital scale)
   ...
The 2PN Radiation Lagrangian

       The 1PN radiation Lagrangian is identically zero in the CM. The
                     ...
Tools
                      Basic Results in NRGR


               Quadrupole Radiation Forumla
                          ...
v2



                             The radiation Lagrangian (2.5PN)

                                     h00            1...
Extracting the Three-Graviton and Four-Graviton Vertices from Binary Pulsars and Coalescing Binaries
                     ...
Extracting the Three-Graviton and Four-Graviton Vertices from Binary Pulsars and Coalescing Binaries
                 Resu...
Extracting the Three-Graviton and Four-Graviton Vertices from Binary Pulsars and Coalescing Binaries
                     ...
N
                 possible vertices, and we must Qij Qij the framework of multiscalar-tensor theories, the e
   (17)
ctio...
Extracting the Three-Graviton and Four-Graviton Vertices from Binary Pulsars and Coalescing Binaries
                Resul...
Extracting the Three-Graviton and Four-Graviton Vertices from Binary Pu
acting the Three-Graviton and Four-Graviton Vertic...
Interpretation


                     •       Radiation from Hulse-Taylor binary pulsar provides
                         ...
Not the end of the story...




                     • If GR is not the correct low-energy EFT,
                          ...
Friday, September 17, 2010
Upcoming SlideShare
Loading in...5
×

Hillary Sanctuary's Cosmology Seminar

656

Published on

Published in: Education
0 Comments
0 Likes
Statistics
Notes
  • Be the first to comment

  • Be the first to like this

No Downloads
Views
Total Views
656
On Slideshare
0
From Embeds
0
Number of Embeds
1
Actions
Shares
0
Downloads
0
Comments
0
Likes
0
Embeds 0
No embeds

No notes for slide

Hillary Sanctuary's Cosmology Seminar

  1. 1. Effective Field Theory Approach to Testing GR AIMS, Cape Town September 1st 2010 Hillary Sanctuary Friday, September 17, 2010
  2. 2. Outline I. Brief introduction to GWs II. Motivation : probe non-linearities of GR III. Tools : Effective Field Theory Method (NRGR) IV. Measuring deviations from GR. Physics beyond GR? Friday, September 17, 2010
  3. 3. Results • Measurement of radiation loss from the Hulse- Taylor Binary provides an important confirmation of the gauge structure of GR to 0.1%. • Careful: provides experimental bounds unknown physics IF General Relativity is the correct low- energy theory of gravity. Friday, September 17, 2010
  4. 4. I. Introduction to GW • Gravitational waves are oscillations of the “fabric” of spacetime. • To see this (weak field limit) of Einstein’s eqns: gµν ηµν hµν |hµν | Friday, September 17, 2010
  5. 5. Wave equation hT T = 0 µν speed of light c h+ ikσ xσ TT hµν = Cµν e   0 0 0 0 h×  0 h+ h× 0  Cµν =  0  h× h+ 0  0 0 0 0 Spin=2 Friday, September 17, 2010
  6. 6. Binary Pulsar : important test A pulsar is a highly magnetized, rotating neutron star that emits EM radiation. A binary pulsar is a pulsar + companion. Friday, September 17, 2010
  7. 7. Hulse-Taylor Binary (1974) The pulsar rotates on its axis17 times per second, pulse period is 59ms. The orbital period is 7.75 hours. Separation at periastron: 1,000,000 km. Inspiral for 300,000,000 years. Gravitational waves? Friday, September 17, 2010
  8. 8. Inferred detection. Orbital decay due to energy loss via gravitational radiation. The data points indicate the observed change in the epoch of periastron with date while the parabola illustrates the theoretically expected change in epoch according to GR. astro-ph/0407149 Friday, September 17, 2010
  9. 9. Quest for direct detection Network of GW detectors (LIGO,Virgo, LISA,etc) Friday, September 17, 2010
  10. 10. A closer look Animation: h ∼ 0.5 f ∼ 2 seconds BH coalescence: (10M⊙ , r = 10RS , R = 100 Mpc) h ∼ 10−21 f ∼ 100 seconds−1 Friday, September 17, 2010
  11. 11. Estimates at interferometers Physical effect of a passing GW, perturb relative positions of freely-falling masses: δL ∼h L h L δL ∼ 10 −16 cm 10 −21 km Bohr radius (atom): a0 ∼ 5 × 10−9 cm Nucleus: 1 f m = 10−13 cm Need to measure miniscule perturbations. Friday, September 17, 2010
  12. 12. Sources Sensitivity Curves SB SB h th ed SB rs nc h Fi Best candidates for ed ha nc En 25BH/25BH va 10-20 Inspiral @ 150Mpc Rin earth-based detectors: Ad Collision gd SN hang own NS/NS @ up @ 10 30Mpc o 0km, 15M r 10BH/1 BH and NS 0BH @ 1 pc hc = h!n 50Mpc gup c han 15Mp 10-21 @2 SN km , 0 coalescences. Rin Inspiral gdo Collision NS/NS @ 300Mpc wn or 10BH /10BH @ 150 30B 0Mpc SN Boiling @ z H/30B 10-22 at 20 kpc =1 H 10 100 1000 10000 frequency, Hz igure 3: LIGO’s projected broad-band noise sensitivity to bursts hSB (Refs. [12, 15]) compared ith the characteristic amplitudes hc of the waves from several hypothesized sources. The signal √ o noise ratios are 2 higher than in Ref. [12] because of a factor 2 error in Eq. (29) of Ref. [11]. Friday, September 17, 2010
  13. 13. Example: NS-NS coalescence 3.1 Inspiral of binary stars 137 ! Fig. 3.2 The time evolution of the GW amplitude in the inspiral phase of a binary system. 1.45M⊙ Using the explicit expression (3.16) we find (recall that ∂/∂τ = −∂/∂t) Φ(τ ) = −2 45 kmτ 5GM c3 c −5/8 5/8 + Φ0 , (3.29) where Φ0 = Φ(τ = 0) is an arXiv:0804.0594 integration constant, equal to the value of Φ at coalescence. Since both fgw , given in eq. (3.16) and Φ in eq. (3.29) depend only on the combination τ , the GW amplitude can be expressed directly in terms of the time t of the observer, and the time of coalescence of the observer, tcoal , 5/4 1/4 1 GMc 5 1 + cos2 ι h+ (t) = cos [Φ(τ )] , r c2 cτ 2 5/4 1/4 1 GMc 5 h× (t) = cos ι sin [Φ(τ )] , (3.30) r c2 cτ where Friday, September 17, 2010
  14. 14. Example: NS-NS coalescence 3.1 Inspiral of binary stars 137 ! Fig. 3.2 The time evolution of the GW amplitude in the inspiral phase of a binary system. 1.45M⊙ Using the explicit expression (3.16) we find (recall that ∂/∂τ = −∂/∂t) Φ(τ ) = −2 45 kmτ 5GM c3 c −5/8 5/8 + Φ0 , (3.29) where Φ0 = Φ(τ = 0) is an arXiv:0804.0594 integration constant, equal to the value of Φ at coalescence. Since both fgw , given in eq. (3.16) and Φ in eq. (3.29) depend only on the combination τ , the GW amplitude can be expressed directly in terms of the time t of the observer, and the time of coalescence of the observer, tcoal , 5/4 1/4 1 GMc 5 1 + cos2 ι h+ (t) = cos [Φ(τ )] , r c2 cτ 2 5/4 1/4 1 GMc 5 h× (t) = cos ι sin [Φ(τ )] , (3.30) r c2 cτ where Friday, September 17, 2010
  15. 15. II. Motivation • GR is non-linear • Two labs where non-linearities are at work (binary pulsars, coalescences) • Non-linearities (non-abelian vertices): • Can we measure these vertices? YES (Tevatron, LEP for SM, deviations from GR?) Friday, September 17, 2010
  16. 16. Post-Newtonian Expansion • What is it? Post-Newtonian terms in GR are corrections to Newtonian Gravity in powers of v/c 1 (c = 1) • Why? GW experiments such as VIRGO/LIGO need high order corrections for detection (phase). • Several techniques available to calculate PN corrections, UV divergences. Friday, September 17, 2010
  17. 17. EFT method • UV divergences due to field theory coupled to point-particles. • Reformulation of PN corrections in terms of Feynman diagrams hep-th/0409156 • NRGR : binary inspiral as at EFT calculation Track this contribution in observables. Friday, September 17, 2010
  18. 18. III. Tools: NRGR Tutorial • “Non relativistic General Relativity” • Translates PN corrections of N-body (binary) systems into Feynman diagrams. • Powerful toolbox of EFT techniques (UV divergences), manifest power-counting. Friday, September 17, 2010
  19. 19. Main Ingredients of NRGR • Identify relevant dof at the scale of interest. gµν , x (λ) µ • Construct effective Lagrangian allowed by µ symmetries. GCI :x → x (x) µ Worldline RPI :λ → λ (λ) • Separate into conservative gravitons H and radiative gravitons h • Identify how terms scale in powers of v • Collect Feynman diagrams to desired powers in v Friday, September 17, 2010
  20. 20. Relevant Scales of a Binary System We want two EFTs, one at the orbital scale of the binary, the other at the scale of radiation. Friday, September 17, 2010
  21. 21. Starting point Theory of relativistic point particles coupled to gravity: S = SEH + Spp √ SEH =−2m2 l P 4 d x gR(x) Spp =− ma dτa + ... O(v 10 ) Finite size effect Neglect spin a dτ 2 = gµν dxµ dxν Friday, September 17, 2010
  22. 22. Potential radiation gravitons Friday, September 17, 2010
  23. 23. H and h scale differently k µ ∼ (v/r, 1/r) k µ ∼ (v/r, v/r) Friday, September 17, 2010
  24. 24. So? Friday, September 17, 2010
  25. 25. Feynman Building Blocks: Graviton Vertices 1 ¯ gµν = ηµν + (Hµν + hµν ) MP l Friday, September 17, 2010
  26. 26. Feynman Building Blocks: Matter Vertices 1 ¯ gµν = ηµν + (Hµν + hµν ) MP l Friday, September 17, 2010
  27. 27. Which diagrams are allowed? Friday, September 17, 2010
  28. 28. Orbital Scale EFT Newton’s Potential (0 PN) Friday, September 17, 2010
  29. 29. Orbital Scale EFT EIH Lagrangian (1 PN) Friday, September 17, 2010
  30. 30. Tools Basic Results in NRGR The EIH Lagrangian The potential Lagrangian (orbital scale) 1 L = L0 + L2 c2 1 2 1 2 Gm1 m2 L0 = m1 v1 + m2 v2 + 2 2 r 1 2 1 4 Gm1 m2 L2 = m1 v2 + m2 v2 + 8 8 2r 2 2 G(m1 + m2 ) × 3(v1 + v2 ) − 7v1 · v2 − (ˆ · v1 )(ˆ · v2 ) − r r r The effective Lagrangian (conservative dynamics) valid to 1PN. Friday, September 17, 2010
  31. 31. The 2PN Radiation Lagrangian The 1PN radiation Lagrangian is identically zero in the CM. The Radiation Scale EFT 2PN radiation Lagrangian is the next-to-leading correction : v2 h00 1 2 Gm1 m2 Lrad = − ma va − 2MP l 2 a r 1 1 O(v 5/2 ) − ijk Lk ∂j hi0 + ma rai raj R0i0j 2MP l 2MP l a Friday, September 17, 2010
  32. 32. Tools Basic Results in NRGR Quadrupole Radiation Forumla Extracting the Three-Graviton and Four-Graviton Vertices from Binary Pulsars and Coalescing Binaries Tools Quadrupole Radiation (2.5PN) Basic Results in NRGR Quadrupole Radiation Forumla 2 1 1 1 Im −i 2MP l a,b dt1 dt2 Qij (t1 )Qkl (t2 ) R0i0j (t1 , Xcm )R0k0l (t2 , Xcm ) 2 1 1 1 Im −i 2MP l a,b dt1 dt2 Qij (t1 )Qkl (t2 ) R0i0j (t1 , Xcm )R0k0l (t2 , Xcm ) GN ... ... P = Q... Q G5 ... ij ij N P = Qij Qij 5 where the quadrupole moment is defined by: where the quadrupole moment is defined by: 1 12 2 Qij ij = Q= ma rraiajaj −δij rδij ra ma ai r r − 3 3a aa Friday, September 17, 2010
  33. 33. v2 The radiation Lagrangian (2.5PN) h00 1 2 Gm1 m2 Lrad = − ma va − 2MP l 2 a r 1 1 − ijk Lk ∂j hi0 + ma rai raj R0i0j 2MP l 2MP l a The effective Lagrangian responsible for radiation to leading order. Friday, September 17, 2010
  34. 34. Extracting the Three-Graviton and Four-Graviton Vertices from Binary Pulsars and Coalescing Binaries Tools Basic Results in NRGR NRGR in a nutshell NRGR Summary We saw: The different length scales at hand (rs , r ∼ H, h) How to build the NRGR EFT How to get Lconservative with PN corrections (Newton + EIH + ...) How to get Lradiation with PN corrections. More importantly, we have seen exactly how the 3- and 4- graviton More importantly, wePN corrections. how the vertices contribute to these have seen three graviton vertex contributes to the -1PN correction (EIH) - quadrupole radiation Friday, September 17, 2010
  35. 35. Extracting the Three-Graviton and Four-Graviton Vertices from Binary Pulsars and Coalescing Binaries Results Modification of the 3-graviton vertex IV. Measuring deviations (GR) Modifying the 3g Vertex arxiv:0907.2186v2 → (1 + β3 )× This factor will affect in particular the following diagrams HHH and HHh: (1 + β3 ) (1 + β3 ) Friday, September 17, 2010
  36. 36. Extracting the Three-Graviton and Four-Graviton Vertices from Binary Pulsars and Coalescing Binaries Results Comparing with Classical Tests of GR Estimating β3 :Estimating β3 Classical Tests (orbit) By modifying the three-graviton vertex, we have modified the conservative part of the Lagrangian: Modification to the 1PN Lagrangian G2 m1 m2 (m1 +m2 ) ∆Lcons = −β3 N r2 In terms of PPN parameters, we can identify β = 1 + β3 and γ = 1. Perihelion of Mercury |β − 1| 3 · 10−3 −→ |β3 | 3 · 10−3 Lunar Laser Ranging |4β − γ − 3| 9 · 10−4 −→ |β3 | 2 · 10−4 Friday, September 17, 2010
  37. 37. N possible vertices, and we must Qij Qij the framework of multiscalar-tensor theories, the e (17) ction of PQQ = G compute, the the PPN formalism introduced in Ref [11] a in imaginary(22) part of PQQ = 5 N Q Q , of tension ··· ··· (22) ij lows for a consistent treatment of both the conservati ij (18) 5 ith our as already found in [34]. Computingdynamics (including the effects. strongly self-gravitatin 4 the otherradiative case of contribu- −i bodies)band of (18) a b a tions 2 find thatdt2 I[34]. )Ikl (t2 ) Sij (t1 Pqq (t2 ) interesting to see what bounds on β3 ca as already found in ijterms PQq andIt)Skl vanish(21) we dt1 the (t1 Computing the other contribu- is clearly , identi- 8MPl Estimating β (radiation) cally. In fact, the Qq and qQ graphs vanish becauseidenti- probe the radiati tions we find that the terms PQq and Pqq vanishtheQij thatbinary pulsars or th be obtained from experiments (19) a,b=1 j h(19) 3 sector of because δij δkl of of GR, such as cally. In fact, the qδ , and δqQβgraphs vanish on the Q Qq β V , Z )observation because timing is traceless, while the qq graph vanishes of the coalescence ij compact binaries at i ij )] , a where Iij = (Qij , ij 3 ij 3 ij terferometers. The effective Lagrangian describing th depends is the gives zero when contracted δik δjl + vanishes2 δijh kl , on δij δkl is traceless, while S a = graph δil δ , δ− 3 of, δij ) which matter variables andthe qq (R0i0j , R0i0jjk ij h002 the binary system with radiation gravito because (16) interaction is the tensor thatfield. ijWhenδboth the il δjk −bythefunctionthree graphs in Fig. 2 (co the gravitational contracted from +is obtained 3 δij δdia-which gives zero when comes out ik δmore complicated. δ two-point kl , 0i0i ,and is is rce the The R0k0l . The formula and V Z graphs Fig. 6 of ref.for and the introduction R the radiation QV , qZ is responding to vanish [34]), jl vertices of computing the 0i0i ,= β3 is gram in Fig. 3that proportionalfrom the two-pointone in Fig. 2c. is 0i0j tensor are comes out to the 3quadrupole, vertex β affects the HHh function similar R0k0l . The QV , qZ and V contributions come in ref. [34], but with o obtains reasons, so the only relevant Z graphs vanish as R0i0j the usual GR result Computing these graphs for r orbit β3 = reorbit the (17) from thereasons, so the G ···and we find three-graviton vertex, we find similar QZ and qV graphs, relevant contributions come only ··· modified N cation re the from the QZ andQQ =graphs, and ,we find1 [Qij R0i0j + qR0i0i + β3 (3V h00 + Z ij hij )] P qV 5 Qij Qij ··· Lrad = ˙ (22) PQZ = −2β3 GN Qij Zij , 2MPl (23) cation(18) in ··· ˙ as already found P [34]. ComputingQ where Qij is the quadrupole moment of the source an theZ , contribu- (23) other (1 upled and QZ = −2β3 GN ij ij tions we find that the terms PQq and weqq vanish identi- P define upled oupled cally. In fact, the Qq and qQ graphs vanish because Qij 1 (19) and ··· ˙ PqV = −6β3 Gvanishes. because δ q = 3 ma x2 , terms oupled is traceless, while the qq graph N qV (24) (1 ij δkl a a ··· ˙ 2 δ δ , which )terms is the e can As for thewhen and ZZ= −6β3+they V 3 ij contributionm1 m2 , gives zero V V contracted δik δjl Gδil δq give a kl V (r) = GN r PqV graphs, N jk − . (24) (1 R0i0i , is is the tensor that comes out from the two-point function that, from theVpoint of view of the multipole expansion,m1 m2 ri rj As0i0j R0k0l . The QV , qZ and V Z graphs vanish(r) = GN 3 R for the V and ZZ graphs, they give a contribution no same order . ation or β3 = ce can Z ij for , (1 Note:thedipole radiationas the quadrupole radiation but pro- r is of from the so the only relevant contributions expansion, e orbit similar reasons, point of view of the multipole come that, uation (20) 2 portional QZ β3 , and graphs, and we find r = x1 − x2 . The term Qij R0i0j in eq. (16) is th to and qV can be neglected. where from the same order as the quadrupole radiation but pro- are the is of the We can now use these results to perform the compari-The second term, qR0i0i , 2 usual quadrupole interaction. fication (20) portional to β3 , and can be neglected. ··· ˙ ijnon-radiating when β3 =radiated powersee thatthe orb 0, but we will for β3 he or- son with binary QZ = −2β3 GN Qij Z 0 it contributes to(23) P pulsars and with interferometers. the , when We can now use these results to isperform the compari- in eq. (16) are th non-circular. The last two terms on for coupled 17,and Friday, September 2010 explicit β3 -dependent terms induced by the modificatio
  38. 38. Extracting the Three-Graviton and Four-Graviton Vertices from Binary Pulsars and Coalescing Binaries Results Comparing with the Hulse-Taylor Binary The Hulse-Taylor Binary Pulsar Estimating inβ3 Extracting the Three-Graviton and Four-Graviton Vertices from Binary Pulsars and Coalescing Binaries The Hulse-Binary Pulsar was first detected 1974. Results Modification of the 3-graviton vertex The classical GR results for the period slow-down is: Calculating the Power Period Slow-Down Plugging in the Newtonian equations of motion for elliptic orbits, ˙ P GR GR −8/3 Pb 96 5/3 we have: 5/3 b GR Pb = − 5 GN ν M 2π [f (e)] 32G4 µ2 M 3 1 73 37 PQQ = N 1 + e2 + e4 , 5a5 (1 − e2 )7/2 24 96 32G4 µ2 M 3 1 5 175 85 PQZ = β3period5 as calculated with the2 modified, The slow-down N + e + e4 5a (1 − e2 )7/2 2 24 96 three-graviton vertex:4 µ2 M 3 32GN 1 5 2 5 ˙β PqV = −β3 β β3−8/3 2 7/2 e + e4 . Pb 96 5/3 5a5 Pb 5/3 (1 − e ) 16 64 β =− 5 GN ν M 2π [f (e) + β3 g(e)] Pb What M =can + m2extract m1 m2 /M 2 information m1 we ν = from this? M1 M2 ˙β ˙ ν= 0≤e Pb = 0 P GR . Compare≤ 1, ewithfor bcicular orbits. M M = M1 + M2 Friday, September 17, 2010
  39. 39. Extracting the Three-Graviton and Four-Graviton Vertices from Binary Pu acting the Three-Graviton and Four-Graviton Vertices from Binary Pulsars and Coalescing Binaries esults Results Extracting the Three-Graviton and Four-Graviton Vertices from Binary Pulsars and Coalescing Binaries Comparing with the Hulse-Taylor Binary Comparing with the Hulse-Taylor Binary Results Comparing with the Hulse-Taylor Binary stimating β3 Estimating β33 Estimating β Estimating β3 The total mass M (Tentative(Tentative are andcalculations.) Replacing M → Mβ and ν M ν→ the ratio ν calculations.) Replacing → β determined by the ˙1β / β GR ˙˜ PbβωP GR = Pb + P3 g (e) = 1 + periastron shift˙ /˙ and the Einstein where g (e) 2.70gfor the Hulse-Binary Pulsar. ˜ where ˜(e) time delay γ. The 2.70 for the Hulse-Binary Compared to experiment: ωβ3 = (1 point is that these experiment:− β3 /3) ωGR Compared to ng the Three-Graviton and Four-Graviton Vertices from Binary Pulsars and Coalescing Binaries ˙ Pbobs /PbGR γβ3 = 1 two parameters = 1.0013(21) γGR + 2.70β3 ˙ ts ˙ ˙ obs M 3 = = 1.0013(21) are in principle Pb /PβGR (1 + β3 /2) MGR mparing with the Hulse-Taylor Binary b we get: modified by β3 . νβ3 = (1 + Cβ3 )νGR mating β3 we get: Hulse-Taylor → β3 (Tentative calculations.) Replacing M → Mβ and ν → νβ Hulse-Taylor we get, → β3 Pbβ /P GR = 1 + β3 g (e) ˙ ˙ ˜ β3 = (4.0 ± 6.4) · 10−4 where g (e) 2.70 for the Hulse-Binary Pulsar. ˜ Compared to experiment: β3 = (4.0 ± 6.4) · 10 ˙ ˙ Pbobs /PbGR = 1.0013(21) 1 + 2.70β3 we get: Friday, September 17, 2010
  40. 40. Interpretation • Radiation from Hulse-Taylor binary pulsar provides measurement of the gauge structure of GR (0.1%). • Assumes that GR is the low-energy limit of a high- energy theory gravity, then experimental accuracy provides bounds on possible deviations generated by new physics. Friday, September 17, 2010
  41. 41. Not the end of the story... • If GR is not the correct low-energy EFT, could have different bounds. Friday, September 17, 2010
  42. 42. Friday, September 17, 2010

×