Testing relativity with gravitational waves

Transcription

1 Testing relativity with gravitational waves Michał Bejger (CAMK PAN) ECT* workshop New perspectives on Neutron Star Interiors Trento, (DCC G )

2 Gravitation: Newton vs Einstein Absolute time and space, deterministic solutions, Eternal two body systems. Stable two body system does not exist, Constant evolution due to the existence of a third body : the spacetime.

3 Coalescence of binary neutron stars and black holes

4 First access to the strong-field dynamics of spacetime Before the direct detection of gravitational waves: Solar system tests: weak-field; dynamics of spacetime itself not being probed Binary neutron stars: relatively weak-field test of spacetime dynamics Cosmology: dark matter and dark energy may signal GR breakdown Direct detection of GW from binary black hole mergers: Genuinely strong-field dynamics (Presumed) pure spacetime events Yunes, Yagi, Pretorius, Phys. Rev. D 94, (2016)

5 Exploiting the phenomenology of inspiral, merger, ringdown Post-Newtonian description of inspiral Expansion of e.g. gravitational wave phase in powers of (v/c) Do the coefficients depend on masses, spins as predicted by GR? Tidal effects during inspiral Black hole mimickers : boson stars, dark matter stars, gravastars,... If less compact than neutron stars, can have large tidal effects Plunge and merger Most dynamical regime Consistency between inspiral and post-inspiral regimes Ringdown From the quasi-normal mode spectrum: (indirect) test of no-hair theorem Gravitational wave echoes Quantum-modified black holes, exotic objects: repeated bursts of GWs after ringdown Anomalous propagation of gravitational waves over large distances Massive graviton, violations of local Lorentz invariance

6 Gravitational waves: some estimates GWs correspond to accelerated movement of masses. Consider a binary system of m 1 and m 2, semiaxis a with total mass M = m 1 + m 2, reduced mass µ = m 1 m 2 /M, mass quadrupole moment Q Ma 2, Kepler s third law GM = a 3 ω 2. h(r) 1 r 2 (Ma 2 ) t 2 = G2 1 c 4 r Mµ a = G5/3 c 4 1 r M2/3 µω 2/3.

7 Binary system: chirp mass Waves are emitted at the expense of the orbital energy: E orb = Gm 1m 2, 2a de orb dt Resulting evolution of the orbital frequency ω: ω 3 = ( ) 96 3 ω 11 5 c 15 G5 µ 3 M 2 = Gm 1m 2 2a 2 ȧ = de GW. dt ( ) 96 3 ω 11 5 c 15 G5 M 5, where M = ( µ 3 M 2) 1/5 = (m1 m 2 ) 3/5 /(m 1 + m 2 ) 1/5 is the chirp mass. GWs frequency from a binary system is primarily twice the orbital frequency (2πf GW = 2ω). Hence M is a directly measured quantity: ( M = c3 5 3/5 G 96 π 8/3 f 11/3 GW ḟgw).

8 LIGO SENSITIVITY DURING FIRST OBSERVING RUN (O1) (b) A BNS 50 Mpc

9 Binary inspiral vs the sensitivity curve The so-called Newtonian signal at instantaneous frequency f GW is h = Q(angles) M 5/3 f 2/3 GW r 1 e iφ. where the signal s phase is Φ(t) = The relation between f GW and t The orbital velocity 2πf GW (t )dt. ( 5M πmf GW (t) = 256(t c t) v (πmf GW ) 1/3 ) 3/8

10 Binary inspiral vs the sensitivity curve Match filtering means that the signal is integrated as is sweeps through the range of frequencies. Sensitivity curves most often show the effective (match-filtered) h eff, and not the instantaneous h. Order-of-magnitude estimation of the frequency slope: h eff N cycles h f GW t h f GW f 8/3 GW f 2/3 GW f 1/6 GW.

11 Binary inspiral vs the sensitivity curve Actually used in estimating the SNR is the frequency-domain match-filtering signal model h(f) ( h eff, Fourier transform of h(t)), 5 h(f) π 2/3M5/6 = Q(angles) f 7/6 24 r GW e iψ(f), where the frequency domain phase Ψ is (in point-particle approximation): Ψ(f) Ψ PP (f) = 2πft c φ c π 4 + 3M 128µv 5/2 N α k v k/2. k=0

12 Binary system: source distance estimate At cosmological distances, the observed frequency f GW is redshifted by (1+z): f f/(1+z) There is no mass scale in vacuum GR, so redshifting of f GW cannot be distinguished from rescaling the masses because of the expansion in powers of v (πmf GW ) 1/3 = inferred masses are m = (1+z)m source Direct, independent luminosity distance measurement (but not z) from GW with f GW and the strain h: r = 5 c ḟ GW. 96π 2 h fgw 3

13 GW spectrum of material binaries (e.g., BNSs) Phase evolution for extended bodies: Ψ(f) = Ψ PP (f)+ψ tidal (f)

14 Anomalous tidal effects during inspiral Tidal field of one body causes quadrupole deformation in the other: where depends on internal structure (equation of state) Black holes: λ 0 Boson stars, dark matter stars: λ > 0 Gravastars: λ < 0 Enters inspiral phase at 5PN order, through O( ) for neutron stars Can be still larger for Dark matter stars Boson stars Detectable with Advanced LIGO/Virgo Giudice et al., JCAP 1610, 001 (2016) Cardoso et al., arxiv:

15 Cosmology from tidal interactions & microphysics (from B.S. Sathyaprakash slides)

16 Complementary information from different events Matched filter signal-to-noise (SNR) ρ : ρ 2 = 0 ( 2 h(f) ) 2 f d ln(f) Sn(f) GW (ρ 24): merger at the most sensitive detector frequencies, GW (ρ 13): long inspiral in sensitive frequency band, GW (ρ 13): twice as far away effects of distance on propagation

17 GW170814: network of three detectors observation SNR 15, three detectors network allow for first meaningful GW polarization studies (PRL in print, arxiv: ).

18 A zoo of alternative theories of gravity Lovelock s theorem: In four spacetime dimensions the only divergence-free symmetric rank-2 tensor constructed solely from the metric and its derivatives up to second order, and preserving diffeomorphism invariance, is the Einstein tensor plus a cosmological term which means If a local gravitational action contains only up to second derivatives of the four-dimensional spacetime metric, then the only possible equations of motion are the Einstein field equations.

19 A zoo of alternative theories of gravity

20 Residual data after subtraction of best-fitting waveform After subtraction of best-fitting waveform, is residual data consistent with noise? SNRres 2 = 1 FF 2 FF 2 SNRdet 2 In case of GW150914, FF 0.96; GR violations limited to 4%, at least for effects that can not be absorbed into redefinition of physical parameters.

21 Parameterized tests of the coalescence process Phenomenological frequency domain waveforms Parameters multiplying different functions of frequency in 3 regimes Introduce parameterized deformations of the waveform by replacing and letting vary freely (along with masses, spins, extrinsic parameters) Do this for each of the in turn Accurate model-independent tests Li et al., Phys. Rev. D 85, (2012)

22 Parameterized tests of the coalescence process inspiral LSC+Virgo, Phys. Rev. X 6, (2016)

23 Parameterized tests of the coalescence process intermediate LSC+Virgo, Phys. Rev. X 6, (2016)

24 Parameterized tests of the coalescence process merger/ringdown LSC+Virgo, Phys. Rev. X 6, (2016)

25 GW150914: short inspiral, but merger well visible intermediate, merger/ringdown LSC+Virgo, Phys. Rev. X 6, (2016)

26 GW151226: long inspiral, merger at higher frequency inspiral LSC+Virgo, Phys. Rev. X 6, (2016)

27 GW GW GW LSC+Virgo, Phys. Rev. Lett. 118, (2017)

28 Testing the post-newtonian description of inspiral First-ever bounds on post-newtonian coefficients (inspiral dynamics) beyond leading order Massive graviton LSC+Virgo, Phys. Rev. Lett. 116, (2016)

29 Testing the post-newtonian description of inspiral First-ever bounds on post-newtonian coefficients (inspiral dynamics) beyond leading order - Dynamical self-interaction - Spin-orbit interactions LSC+Virgo, Phys. Rev. Lett. 116, (2016)

30 Testing the post-newtonian description of inspiral First-ever bounds on post-newtonian coefficients (inspiral dynamics) beyond leading order Spin-spin interactions LSC+Virgo, Phys. Rev. Lett. 116, (2016)

31 Testing the post-newtonian description of inspiral Combined bounds from GW and GW151226: LSC+Virgo, Phys. Rev. X 6, (2016)

32 LSC+Virgo, Phys. Rev. Lett. 116, (2016) Do gravitational waves propagate as predicted? Dispersion of gravitational waves? New bound on graviton Compton wavelength and mass: λ g > km m g < ev/c 2 3 orders of magnitude better than only other existing dynamical bound Factor of a few better than (static) Solar system bound

33 Do gravitational waves propagate as predicted? Anomalous dispersion of gravitational waves (Violating local Lorentz invariance): Modified group velocity: Modification to the gravitational wave phase: LSC+Virgo, Phys. Rev. Lett. 118, (2017)

34 Do gravitational waves propagate as predicted? Anomalous dispersion of gravitational waves (Violating local Lorentz invariance): LSC+Virgo, Phys. Rev. Lett. 118, (2017)

35 LSC+Virgo, Phys. Rev. Lett. 116, (2016) Consistency between inspiral and post-inspiral General relativity predicts relationship between Masses and spins of component objects Mass and spin of final object Relationship can be extracted from numerical simulations Accurate analytical fits (Healy et al. 2014) Compare inferred values from inspiral and post-inspiral

36 LSC+Virgo, Phys. Rev. Lett. 116, (2016) Ringdown Ringdown regime: Kerr metric + linear perturbations Ringdown signal is a superposition of quasi-normal modes with characteristic frequencies ω lmn and damping times τ lmn Numerical relativity: linearized regime valid from ~10 M For GW150914: 10 M ~ 3.5 milliseconds Evidence for a least-damped quasi-normal mode from fitting damped sinusoid:

37 Searching for exotic compact objects Black hole mimickers : Boson stars Dark matter stars Gravastars Firewalls, fuzzballs... Giudice et al., JCAP 1610, 001 (2016) Find through: Anomalous tidal effects during inspiral Cardoso et al., arxiv: Anomalous ringdown spectrum Meidam et al., Phys. Rev. D 90, (2014) Gravitational wave echoes after ringdown Cardoso et al., Phys. Rev. D 94, (2016)

38 However, see also Ashton et al arxiv: Gravitational wave echoes after ringdown If instead of black hole horizon, structure with characteristic size l c echoes at time intervals Δt = n M log(m/l c ) n depends on nature of object (e.g. n = 8 for wormholes) For mass M similar to GW1509 l c the Planck length Δt = O(10) ms Amplitudes of first few echo may be visible with aligo Already claimed to have been det using publicly available data! Abedi et al., arxiv:

39 Alternative polarization states 6 different polarizations in a most general metric theory of gravity: For GW150914, comparing Bayes factors for GR polarizations against pure breathing mode: log B GR scalar = 0.2±0.5 Will, LRR 17, 4 (2014) For GW170814, first tests using three detectors: Bscalar GR 1000, Bvector GR 200 (mixed modes analysis in the making!)

40 Summary First tests of the genuinely strong-field dynamics of pure spacetime with GW150914, GW151226, GW and GW No evidence for violations of GR. Tests of coalescence dynamics Parameterized tests in inspiral and merger/ringdown regimes, Consistency of masses and spins between inspiral and post-inspiral. Tests of gravitational wave propagation: Bound on graviton mass, Bounds on violation of local Lorentz invariance. First tests of non-gr polarizations (Advanced LIGO+Advanced Virgo + future KAGRA, LIGO India). Incoming: Tests of the black hole nature of the component and remnant objects, Ringdown and no-hair theorem tests, GW echoes, GWs from material objects (EM-bright), Cosmology/cosmography with GWs.