T A T A I N S T I T U T E O F F U N D A M E N T A L R E S E - PowerPoint PPT Presentation

 T A T A I N S T I T U T E O F F U N D A M E N T A L R E S E A R C H ����������������������������������������������� Testing theories of gravity using upcoming gravitational- wave observations Parameswaran Ajith International Center for Theoretical Sciences, Tata Institute of Fundamental Research, Bangalore CMI Silver Jubilee Workshop: Astronomy, Cosmology & Fundamental Physics with GWs Chennai 4 March 2015

Extracting information from GW observations • For sources such as CBCs, expected signals are well-modelled in GR. Weak signals buried in the noise can be detected by cross-correlating the data with “banks” of theoretical templates. h i d ? ˆ ⇢ ≡ max λ h ( λ ) source data parameters signal SNR template Signal template Data Cross-correlation h ( λ ) d ? ˆ h ( λ ) d 2 τ t t

Extracting information from GW observations • Posterior distribution of the source prior distribution parameters can be estimated by of parameter λ Bayesian inference. p ( λ | d ) ∝ p 0 ( λ ) L ( d | λ ) likelihood of d, posterior distribution given λ of λ , given data d posterior probability HHLV network HLVA network symmetric mass ratio luminosity distance chirp mass ( M ⊙ ) [Veitch et al (2012)] 3

Speed of GWs from joint GW-EM measurements • Time-delay between GW and EM ( γ -ray) signals from SGRBs can constrain the speed of GWs [Will 1998] . detector GWs with v g = c GWs with v g < c 0 0 4 photons 200 D 0 100 0 3 space 0 0 2 100 0 0 1 source time 4

Tests of GR using GW observations • Time-delay between GW and EM ( γ -ray) 19 − 10 signals from SGRBs can constrain the AdvLIGO speed of GWs [Will 1998] . Bounds on c/ ( c − v g ) LIGO − 3 ET 18 − 10 distance to the source c D 17 − 10 = c ∆ t ; c − v g m 1 = 1 . 4 M � time-delay between the 16 − speed of GWs 10 observed time- 1 5 10 15 (v g = c in GR) difference btwn the m 2 ( M ⊙ ) GW & EM signals From the coincident GW+EM observation ( Δ t = 1sec) of one SGRB, powered by NSBH merger (located at the horizon distance). 5

Mass of the graviton from joint GW-EM measurements • A bound on v g implies a bound on the − 1 10 graviton-mass [Will 1998] . m g c (pc) Solar system limit − AdvLIGO LIGO − 3 h ET Bound on λ g ≡ − 2 10 Dispersion relation g / c 2 = 1 − m 2 v 2 g c 4 / E 2 g , frequency f , h being m 1 = 1 . 4 M � rest mass of − 3 speed of GWs energy of 10 the graviton 15 (v g = c in GR) 1 5 10 15 the graviton (m g = 0 in GR) m 2 ( M ⊙ ) From the coincident GW+EM observation ( Δ t = 1sec) of one SGRB, powered by NSBH merger (located at the horizon distance). 6

Parametrized deviations from GR: Mass of the graviton • GW observations of CBCs can constrain the mass of graviton without relying on an EM counterpart. [Will 1998] . 0.3 GR Massive graviton 0.2 hf GW 0.1 g / c 2 = 1 − m 2 v 2 g c 4 / E 2 h(t) g , 0 frequency f , h being − 0.1 Different frequency components travel − 0.2 with different speeds ➝ characteristic deformation in the observed signal! − 1000 − 800 − 600 − 400 − 200 0 t / M 7 − − − − − − − − − − − − − − − −

Parametrized deviations from GR: Mass of the graviton • GW observations of CBCs can constrain the [Keppel & Ajith (2010)] mass of graviton without relying on an EM 32 pc counterpart. [Will 1998] . 3.2 pc 0.3 pc solar system bound 0.03 pc Expected bounds on the Compton wavelength of the graviton from BBH observations by future detectors. ( d L = 1 Gpc) 8

Parametrized deviations from GR: Mass of the graviton • GW observations of CBCs can constrain the [Del Pozzo et al (2011)] mass of graviton without relying on an EM counterpart. [Will 1998] . prior p ( λ | d ) ∝ p 0 ( λ ) L ( d | λ ) posterior distribution likelihood of d, of λ , given data d given λ 95% lower bound on the Compton wavelength of the graviton obtained from 100 simulated detections with 5 < SNR < 25. 9

Parametrized deviations from GR: Scalar-tensor theories 6 10 • Leading order radiation is dipolar. Possible to ET constrain the coupling parameter in known 5 10 theories (e.g Brans-Dicke) & generic ST theories. Cassini bound Bound on ω BD 4 10 3 10 AdvLIGO:(1.4+5) M O . at 300 Mpc 2 10 5 10 15 20 BH Mass (M O . ) [Arun (2012)] [Arun & Pai (2013)] 0 10 Bounds on dipole parameter α Bounds on dipole parameter β -2 10 -2 10 -4 10 AdvLIGO: α AdvLIGO: β ET: α ET: β -6 10 -4 10 10 0 50 100 150 200 0 50 100 150 200 Mass of the binary (M O . ) Mass of the binary (M O . )

Parametrized (generic) deviations from GR • Measure the deviations from the known PN Analogous to the tests of coefficients of the GW phase by treating each GR using binary pulsars coefficient as a free parameter [Kramer & Wex (2009)] 2 [Arun et al (2006)] ψ 3 ψ 4 ψ 5 l 1.5 6 (m 2 /M O ) . ψ 6 1 10 0.5 ψ 6 l ψ 7 0 0 0.5 1 1.5 2 6 (m 1 /M O ) 11 10 .

Parametrized (generic) deviations from GR [Mishra et al (2010)] • Measure the deviations from the known PN coefficients of the GW phase by treating each coefficient as a free parameter AdvLIGO; q m =0.1; F low =20Hz; D L =300Mpc m low L 2 2 10 10 RWF RWF FWF FWF 1 1 10 10 0 0 10 10 Δψ 5 l / ψ 5 l Δψ 3 / ψ 3 -1 -1 10 10 -2 -2 10 10 -3 -3 10 10 0 50 100 150 0 50 100 150 Total Mass (M O ) Total Mass (M O ) . . Expected constraints on the deviations from the PN coefficients in 12 Adv LIGO (source located at 300 Mpc)

Parametrized (generic) deviations from GR • Measure the deviations from the known PN [Li et al (2012)] coefficients of the GW phase by treating each coefficient as a free parameter Odds ratio of two hypotheses modified gravity j = P ( H i | d ) O i P ( H j | d ) GR 13

Parametrized (more generic!) deviations from GR [Sampson et al (2013)] 10 • Parameterized Post-Einstein framework no noise noise seed 1 noise seed 2 noise seed 3 Introduce deviations in the amplitude and phase 1 of the GR signal, which are motivated by β uncertainty alternative theories. [Yunes & Pritorius] 0.1 � � � α i u a i 0.01 A ( f ) → 1 + A GR ( f ) , i � � 0.001 � -4 -3.5 -3 -2.5 -2 -1.5 -1 β i u b i Ψ ( f ) → Ψ GR ( f ) + , b 1000 i 100 Theory a α b β 10 Bayes Factor Brans-Dicke [9, 10, 14–16] – 0 -7/3 β Parity-Violation [22, 34–37] 1 α 0 – 1 Variable G ( t ) [38] -8/3 α -13/3 β Massive Graviton [8–14] – 0 -1 β 0.1 Quadratic Curvature [23, 44] – 0 -1/3 β Extra Dimensions [45] – 0 -13/3 β 0.01 Dynamical Chern-Simons [46] +3 α +4/3 β 0.001 14 0.002 0.004 0.006 0.008 0.01 0.012 0.014 β -3

Tests of no-hair theorem from black-hole ring downs [Gossan et al (2012)] • All QNM frequencies of a Kerr BH are unique functions of mass and spin. If we treat frequencies as free parameters, they all should intersect at one point in the mass-spin plane. . O 5.20 τ 22 2 M O . ω 33 ω 22 5.10 BH mass in 10 5.00 0.58 0.60 0.62 0.64 Dimensionless BH spin 15

Tests of no-hair theorem from black-hole ring downs • All QNM frequencies of a Kerr BH are unique functions of mass and spin. If we treat frequencies as free parameters, they all should intersect at one point in the mass-spin plane. [Meidam et al (2014)] 16

Measuring the energy and ang momentum loss from BBHs [Ongoing work with Abhirup • Binary black-hole coalescences are the most Ghosh, Archisman Ghosh and energetic astrophysical processes after the Big Walter Del Pozzo] Bang. 0 . 1 Mc 2 1000 GM/c 3 ∼ 10 22 L � L GW ∼ larger than the total most of the energy is radiated luminosity of the over the late-inspiral & observable EM universe! merger (time scale ~ 1000 M) 17

Measuring the energy and ang momentum loss from BBHs 10 0 • Binary black-hole coalescences are the cumulative energy radiated (fractional) most energetic astrophysical processes after the Big Bang. 10 − 1 • If we observe an inspiral-merger- E ( f ) ringdown signal with good enough SNR, the initial parameters of the binary can be measured from just the inspiral portion of 10 − 2 the signal. 10 − 3 10 3 10 1 10 2 10 3 f [Hz] inspiral merger ringdown h ( t ) 18 time

Measuring the energy and ang momentum loss from BBHs • Binary black-hole coalescences are the most energetic astrophysical processes after the Big Bang. numerical relativity • If we observe an inspiral-merger- simulations ringdown signal with good enough SNR, ( m 1 , m 2 , S 1 , S 2 ) → ( M f , S f ) the initial parameters of the binary can be measured from just the inspiral portion of the signal. • From these estimates, the final state of the BBH can be predicted using NR simulations. 19