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
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
noise can be detected by cross-correlating the data with “banks” of theoretical templates.
source parameters signal template data SNR
⇢ ≡ maxλ h d ? ˆ h(λ) i
h(λ)
t t
Cross-correlation Signal template Data
d ? ˆ h(λ)
parameters can be estimated by Bayesian inference.
p(λ|d) ∝ p0(λ) L(d|λ)
prior distribution
posterior distribution
likelihood of d, given λ chirp mass (M⊙) symmetric mass ratio luminosity distance posterior probability HHLV network HLVA network
[Veitch et al (2012)]
1 2 3 4 100 100 200
signals from SGRBs can constrain the speed of GWs [Will 1998].
time space source detector
GWs with vg = c photons GWs with vg < c
D
signals from SGRBs can constrain the speed of GWs [Will 1998].
From the coincident GW+EM observation (Δt = 1sec) of one SGRB, powered by NSBH merger (located at the horizon distance).
1 5 10 15 10
16
10
17
10
18
10
19
m 2 (M⊙) Bounds on c/(c − vg)
− − − −
AdvLIGO LIGO−3 ET
m1 = 1.4 M
speed of GWs (vg= c in GR)
difference btwn the GW & EM signals distance to the source
graviton-mass [Will 1998].
From the coincident GW+EM observation (Δt = 1sec) of one SGRB, powered by NSBH merger (located at the horizon distance).
g/c2 = 1 − m2 g c4/E2 g,
speed of GWs (vg= c in GR)
Dispersion relation
energy of the graviton rest mass of the graviton (mg= 0 in GR)
15 1 5 10 15 10
−3
10
−2
10
−1
m 2 (M⊙) Bound on λ g ≡ h m gc (pc)
Solar system limit − AdvLIGO LIGO−3 ET
m1 = 1.4 M
−1000 −800 −600 −400 −200 −0.2 −0.1 0.1 0.2 0.3 t / M h(t) − − − − −
− − −
− − − − −
− − −
GR Massive graviton
mass of graviton without relying on an EM
g/c2 = 1 − m2 g c4/E2 g,
hfGW
Different frequency components travel with different speeds ➝ characteristic deformation in the observed signal!
mass of graviton without relying on an EM
32 pc 3.2 pc 0.3 pc 0.03 pc
solar system bound
[Keppel & Ajith (2010)]
Expected bounds on the Compton wavelength of the graviton from BBH observations by future detectors. (dL = 1 Gpc)
mass of graviton without relying on an EM
[Del Pozzo et al (2011)]
95% lower bound on the Compton wavelength of the graviton obtained from 100 simulated detections with 5 < SNR < 25.
p(λ|d) ∝ p0(λ) L(d|λ)
prior posterior distribution
likelihood of d, given λ
constrain the coupling parameter in known theories (e.g Brans-Dicke) & generic ST theories.
5 10 15 20 BH Mass (MO . ) 10
2
10
3
10
4
10
5
10
6
Bound on ωBD
Cassini bound AdvLIGO:(1.4+5) MO . at 300 Mpc ET
50 100 150 200 Mass of the binary (MO . ) 10
10
Bounds on dipole parameter α
AdvLIGO:α ET:α
50 100 150 200 Mass of the binary (MO . ) 10
10
10
10 Bounds on dipole parameter β
AdvLIGO: β ET: β
[Arun (2012)] [Arun & Pai (2013)]
coefficients of the GW phase by treating each coefficient as a free parameter
[Kramer & Wex (2009)] Analogous to the tests of GR using binary pulsars [Arun et al (2006)]
0.5 1 1.5 2 10
6(m1/MO)
. 0.5 1 1.5 2 10
6(m2/MO)
.
ψ4 ψ3 ψ6 ψ7 ψ6l ψ5l
coefficients of the GW phase by treating each coefficient as a free parameter
50 100 150
Total Mass (MO) .
10
10
10
10 10
1
10
2
Δψ3/ψ3
RWF FWF
m low L
50 100 150
Total Mass (MO) .
10
10
10
10 10
1
10
2
Δψ5l/ψ5l
RWF FWF
AdvLIGO; qm=0.1; Flow=20Hz; DL=300Mpc
Expected constraints on the deviations from the PN coefficients in Adv LIGO (source located at 300 Mpc)
[Mishra et al (2010)]
coefficients of the GW phase by treating each coefficient as a free parameter
j = P(Hi|d)
Odds ratio of two hypotheses
[Li et al (2012)]
GR modified gravity
Introduce deviations in the amplitude and phase
alternative theories. [Yunes & Pritorius]
[Sampson et al (2013)]
A(f) →
αiuai
Ψ(f) →
βiubi
Theory a α b β Brans-Dicke [9, 10, 14–16] –
β Parity-Violation [22, 34–37] 1 α – Variable G(t) [38]
α
β Massive Graviton [8–14] –
β Quadratic Curvature [23, 44] –
β Extra Dimensions [45] –
β Dynamical Chern-Simons [46] +3 α +4/3 β
0.001 0.01 0.1 1 10
β uncertainty b
no noise noise seed 1 noise seed 2 noise seed 3
0.001 0.01 0.1 1 10 100 1000 0.002 0.004 0.006 0.008 0.01 0.012 0.014
Bayes Factor β-3
0.58 0.60 0.62 0.64 Dimensionless BH spin 5.00 5.10 5.20 BH mass in 10
2 MO .
τ22 ω33 ω22
O .
mass and spin. If we treat frequencies as free parameters, they all should intersect at one point in the mass-spin plane.
[Gossan et al (2012)]
[Meidam et al (2014)]
mass and spin. If we treat frequencies as free parameters, they all should intersect at one point in the mass-spin plane.
energetic astrophysical processes after the Big Bang.
most of the energy is radiated
merger (time scale ~ 1000 M)
larger than the total luminosity of the
[Ongoing work with Abhirup Ghosh, Archisman Ghosh and Walter Del Pozzo]
most energetic astrophysical processes after the Big Bang.
ringdown signal with good enough SNR, the initial parameters of the binary can be measured from just the inspiral portion of the signal.
103 101 102 103
f [Hz]
10−3 10−2 10−1 100
E(f)
cumulative energy radiated (fractional)
inspiral merger ringdown time h(t)
most energetic astrophysical processes after the Big Bang.
ringdown signal with good enough SNR, the initial parameters of the binary can be measured from just the inspiral portion of the signal.
the BBH can be predicted using NR simulations.
numerical relativity simulations
most energetic astrophysical processes after the Big Bang.
ringdown signal with good enough SNR, the initial parameters of the binary can be measured from just the inspiral portion of the signal.
the BBH can be predicted using NR simulations.
hole can be measured independently from the ringdown part of the signal.
ringdown estimate inspiral estimate
[Pic. Abhirup Ghosh]
q FGR (v1)
[Pic. Abhirup Ghosh]
Inconsistency between these estimates point to unexplained loss of energy and angular momentum (extra dimensions?, dissipation?)
[PhD project of Abhirup Ghosh]
ringdown estimate inspiral estimate
constant(s) from GW observations. [K. G. Arun, PA,
[PA, A. Ghosh, ...]
best fit GR template from the data. Is the residual consistent with the noise?
have calibration uncertainty ~few percents in amplitude and few degrees in phase.
spins, precession, eccentricity, non-quadrupole modes, matter effects, etc.
calculations are known only up to limited order, numerical and gauge issues in NR simulations, ...
have calibration uncertainty ~few percents in amplitude and few degrees in phase.
spins, precession, eccentricity, non-quadrupole modes, matter effects, etc.
calculations are known only up to limited order, numerical and gauge issues in NR simulations, ...
GR simulations including effects of spins, tidal effects, calibration uncertainties non- GR simul ations
“Known unknowns”: Possible to model most of the errors and to account for them ...
−40 −20 20 40 60 80 100 120 140 ln OmodGR
GR
0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 P(ln OmodGR
GR
)
TaylorT4 + all (70 catalogs) δχ3 = −0.1 (30 catalogs)
[Agathos et al (2014)] [PhD projects of M. Saleem, Anuradha S]
[Quoted from Berti et al (2015)]
The conceptual foundations of GR are so elegant and solid that when asked what he would do if Eddington’s expedition to the island of Principe failed to match his theory, Einstein famously replied: “I would feel sorry for the good Lord. The theory is correct.” Chandrasekhar made a similar private remark to Clifford Will when Will was a postdoc in Chicago: “Why do you spend so much time and energy testing GR? We know that the theory is right.” Giving up the fundamental, well tested principles underlying Einstein’s theory has dramatic consequences, often spoiling the beauty