Testing GR with GW polarizations

Transcription

1 Testing GR with GW polarizations using LIGO and Virgo Maximiliano Isi July 12, Amaldi12 LIGO Laboratory, California Institute of Technology

2 Testing GR with GWs we have already learned a lot from transients: dispersion agreement with NR self-consistency not about polarizations! there are currently no model-independent measurements of GW polarizations 2

3 [tl;dr] it is important to probe GW polarizations we can do so with current detectors using long-lived signals [too long ; didn t read] 3

4 plus y vector x x breathing y x z x y y y x z z cross vector y longitudinal 4

5 Theory + x x y b l General Relativity GR in noncompactified 4/6D Minkowski Einstein-Æther 5D Kaluza-Klein Randall-Sundrum braneworld Dvali-Gabadadze-Porrati braneworld Brans-Dicke f(r) gravity Bimetric theory Four-Vector Gravity Nishizawa et al., Phys. Rev. D 79, (2009) [except G4v & Einstein-Æther]. allowed / depends / forbidden 5

6 motivation GR makes unequivocal prediction that only + & x should propagate polarizations are go/no-go test, so let s check! 6

7 vector x breathing plus vector y longitudinal cross 7

8 * source detector antenna pattern for cross polarization 8

9 persistent signals antenna patterns leave imprint in persistent signals characteristic of each polarization continuous-waves stochastic background 9

10 new bayesian analyses detect long GWs of any polarization (from known pulsars, or a stochastic background) distinguish between GR and non-gr }model selection limit amplitude of scalar/vector modes Isi et al. (2017) [arxiv: ] Callister et al. (2017) [arxiv: ] parameter estimation 10

11 continuous waves CW [arxiv: ] NASA / CXC / SAO crab pulsar one of ~200 known pulsars potentially in LIGO s band 11

12 continuous waves CW [arxiv: ] coherent, monochromatic, well-localized simple form, in general relativity: h(t) =h cos2 F + (t) cos (t)+h 0 cos F (t)sin (t) (t) 2 (2f rot ) + doppler and other timing corrections in a generic metric theory of gravity: h(t) = X p F p (t)a p cos( (t)+ p ) phase offset polarization amplitude p 2 {+,, x, y, s} h 0, overall strength;, inclination; F (t), antenna pattern; f rot, rotational frequency 12

13 polarization antenna pattern tensor Crab pulsar LIGO H1 CW [arxiv: ] amplitude modulation over a sidereal day vector Crab pulsar LIGO H1 time (h) scalar Crab pulsar LIGO H1 antenna response time (h) time (h) 13

14 signal vs noise CW [arxiv: ] tensor injections Crab H1L1V1 1yr advanced design 10 4 Any GR odds (detection statistic) ln O m N h GR 14

15 signal vs noise CW [arxiv: ] vector injections Crab H1L1V1 1yr advanced design 10 4 Any GR odds (detection statistic) ln O m N h G4V vector 15

16 gr signal vs noise CW [arxiv: ] Crab H1L1V1 1yr advanced design scalar-tensor injections 10 5 signal scalar amplitude hb ln B N GR h GR 0 noise 16

17 any signal vs noise CW [arxiv: ] Crab H1L1V1 1yr advanced design scalar-tensor injections 10 5 signal scalar amplitude hb ln O S N h GR 0 noise 17

18 non-gr vs gr CW [arxiv: ] Crab H1L1V1 1yr advanced design scalar-tensor injections not GR scalar amplitude hb ln O GR ngr h GR GR 18

19 scalar upper limits CW [arxiv: ] Results ASD sensitivity projections for h 95% b design aligo + Virgo p S n (1/ p Hz) f GW (Hz) (each point represents one pulsar) 19

20 vector upper limits CW [arxiv: ] Results ASD sensitivity projections for h 95% v design aligo + Virgo p S n (1/ p Hz) f GW (Hz) (each point represents one pulsar) h v h 2 x + h 2 y 1/2 20

21 stochastic background SB [arxiv: ] incoherent superposition of myriad unresolvable sources see Andrew Mata s overview talk on Friday! SNR (top) and 90%-confidence upper-limits (bottom) from radiometer stochastic background search [Abbott et al., PRL 118, (2017)] 21

22 stochastic background SB [arxiv: ] incoherent, broadband, all-sky measure correlated strain power in two detectors D h 1 (f) h 2(f 0 )E = 3H (f f 0 ) f 3 (f) (f) overlap-reduction function with the canonical GW energy density usually parametrized by (f) = 0 (f/f 0 ) in a generic metric theory of gravity: spectral index ( slope ) D h 1 (f) h 2(f 0 )E = 3H (f f 0 ) f 3 X p p 0 f f 0 p p(f) p 2 {+,, x, y, s} polarization amplitude 22

23 stochastic background SB [arxiv: ] overlap reduction functions encode effect of time-of-flight and differences between polarizations 0.6 Hanford-Livingston 0.20 Livingston-Virgo (f) Tensor Vector Scalar (f) Tensor Vector Scalar f (Hz) (f) = 5 8 X p Z sky sky location i2 f ˆn dˆn e ~x/c f (Hz) F p 1 (ˆn)F p 2 (ˆn) detector separation 23

24 signal vs noise SB [arxiv: ] 100 tensor injections H1L1 3yr advanced design 80 odds (detection statistic) ln O n sig (spec. index 2/3) Tensor 0 24

25 signal vs noise SB [arxiv: ] 100 vector injections H1L1 3yr advanced design 80 odds (detection statistic) ln O n sig (spec. index 2/3) Vector 0 25

26 signal vs noise SB [arxiv: ] 100 scalar injections H1L1 3yr advanced design 80 odds (detection statistic) ln O n sig (spec. index 2/3) Scalar 0 26

27 non-gr vs gr SB [arxiv: ] H1L1V1 3yr advanced design scalar-tensor injections signal scalar amplitude Scalar log S ln O n sig (spec. index 2/3) Tensor log T 0 3 noise 27

28 non-gr vs gr SB [arxiv: ] H1L1V1 3yr advanced design scalar-tensor injections not GR scalar amplitude Scalar log S ln O gr ngr (spec. index 2/3) Tensor log T 0 3 GR 28

29 parameter estimation SB [arxiv: ] 3yr sensitivity projections for design aligo + Virgo log T 0 = log V 0 = log S 0 = T = V = S = log T log V log S T V S tensor vector scalar amplitudes tensor vector scalar slopes gray histograms are LIGO-only results, dashed lines mark priors projected 95%-credible amplitude upper limits log T 0 < 10.1 log V 0 < 9.9 log S 0 <

30 parameter estimation SB [arxiv: ] 3yr scalar-tensor signal with design aligo + Virgo log T 0 = log V 0 = log S 0 = T = V = S = log T log V log S T V S tensor vector scalar amplitudes tensor vector scalar slopes gray histograms are LIGO-only results, dashed lines mark priors Virgo does not increase sensitivity but helps break degeneracy between scalar and vector 30

31 conclusion we are now able to detect persistent signals of any polarization content in a model-independent way we can directly measure polarization content and quantify agreement with GR this will allow us to explore a new side of gravity! [arxiv: ] [arxiv: ] thank you! 31