Gravitational Waves as Probes of Extreme Gravity€¦ · Jon Veitch, Nathan Collins, Deirdre...

Nicolas Yunes Montana State University

Testing Gravity 2015, January 15th, 2015 Yunes & Siemens, Living Reviews in Relativity 2014,

http://arxiv.org/abs/1304.3473

Gravitational Waves as Probes of Extreme Gravity

http://arxiv.org/abs/1304.3473

GW Probes of Extreme Gravity Yunes

An incomplete summary of what GWs will tell us about gravity

Clifford Will, Jim Gates, Stephon Alexander, Abhay Ashtekar, Sam Finn, Ben Owen, Pablo Laguna, Emanuele Berti, Uli Sperhake, Dimitrios Psaltis, Avi Loeb, Vitor Cardoso, Leonardo Gualtieri, Daniel Grumiller, David Spergel,

Frans Pretorius, Neil Cornish, Scott Hughes, Carlos Sopuerta, Takahiro Tanaka, Jon Gair, Paolo Pani, Antoine Klein, Kent Yagi, Laura Sampson, Luis

Lehner, Masaru Shibata, Curt Cutler, Haris Apostolatos,

2

Leo Stein, Sarah Vigeland, Katerina Chatziioannou, Philippe Jetzer, Leor Barack, Kostas Glampedakis, Stanislav Babak, Ilya Mandel, Chao Li, Eliu

Huerta, Chris Berry, Alberto Sesana, Carl Rodriguez, Georgios Lukes-Gerakopoulos, George Contopoulus, Chris van den Broeck, Walter del Pozzo,

Jon Veitch, Nathan Collins, Deirdre Shoemaker, Sathyaprakash, Devin Hansen, Enrico Barausse, Carlos Palenzuela, Marcelo Ponce, etc.

Standing on the Shoulders of...

YunesGW Probes of Extreme Gravity

Roadmap

3

What will we learn from GW tests of GR?

How do we use GWs to test GR?

How do GW tests differ from other

tests?

YunesGW Probes of Extreme Gravity 4

10-12 10-11 10-10 10-9 10-8 10-7 10-6 10-5 10-4 10-3 10-2 10-1 100

ε=M/r10-1310-1210-1110-1010-910-810-710-610-510-410-310-210-1

ξ1/2 =(

M/r3 )1/

2 [km

-1]

Double Binary Pulsar

Lunar Laser Ranging

LIGO BH-BH Merger

Sun's SurfaceEarth's Surface

LISA IMBH-IMBH Merger

Perihelion Precession of Mercury

LIGO NS-NS Merger

IMRIs IMBH-SCO

LAGEOSLISA SMBH-SMBH Merger

EMRIs SMBH-SCO

Pulsar Timing Arrays

1. Extreme Gravity:

[Baker, et al, Psaltis LRR]

How do GW tests Differ from Other Tests?

Sources: Compact Object Coalescence Supernova, deformed NSs, etc. (excluding pulsar timing in this talk)

Phases: Late Inspiral, Merger, Ringdown.

2. Clean:

Processes: Generation and Propagation of metric perturbation.

Absorption is negligible, lensing unimportant at low z, accretion disk and magnetic fields unimportant during inspiral.


4. Constraint Maps:

How do GW tests Differ from Other Tests?

If large # of sources detected. eg. preferred position tests.

5. Very Local Universe: z < 0.07 or D < 300 Mpc for NS/NS inspiral.

3. Localized: Distinct point sources in spacetime (not a background)

GW Probes of Extreme Gravity Yunes 6

[C. Hanna, PSU]

signal-to-noise ratio

(SNR)

detector noise (spectral noise

density)

data

template (projection of GW metric perturbation)

template param that characterize system

Matched Filtering:

⇢2 ⇠Z

s(f)h(f,�µ)

Sn(f)df

How do use GWs to test GR? Matched Filtering

• Create template “filters”

• Cross-correlate filters & data

• Find filter that maximizes the cross-correlation.

GW Probes of Extreme Gravity Yunes 7

80 100 120 140 160 180 200 220 240 260 280 300t/M

-2

-1

0

1

2

h+

InspiralMerger Ring down

Post-Newtonian

Num. Rel.BH Pert. Theory

gravitational wave

symmetric mass ratio distance to

the sourceinclination

angletotal mass

orbital freq.

orbital phase

h⇥(t) ⇠⌘M

DLcos ◆ (M!)2/3 cos 2�+ . . .

How do use GWs to test GR? Source Modeling

Inspiral: thousands of cycles, most SNR at low masses.

Approximations: PN + PM

Accuracy: 3.5 PN (“3 loop” order)

Template:


How do use GWs to test GR?

Top-Down (test specific theory) vs. Bottom-Up (search for deviations).

hBD(f ;~�GR,�BD)

”◆0”

hD>4(f ;~�GR,�D>4)

hLV (f ;~�GR,�LV )

hppE(f ;~�GR,~�ppE)

1PN

2PN

3PN

4PN

-1PN

-2PN

-3PN

-4PN

0.5PN

1.5PN

2.5PN

3.5PN

-0.5PN

-1.5PN

-2.5PN

-3.5PN

0PNCurrent

ConstraintsGW

Constraints

GRBD MG

EDGB

CS

Gdot

LV

[Yunes & Pretorius, PRD 2009, Mirshekari, Yunes & Will, PRD 2012, Chatziioannou, Yunes & Cornish, PRD 2012]


Templates/Theories GR ppE

GR Business as usualQuantify the statistical significance that

the detected event is within GR. Anomalies?

Not GRQuantify fundamental bias

introduced by filtering non-GR events with GR templates

Can we measure deviations from GR characterized by non-GR signals?

Model Evidence.

[Yunes & Pretorius, PRD 2009, Chatziioannou, Yunes & Cornish, PRD 2012]


Search for Generic Deviations: Parameterize post-Einsteinian (ppE)



1. Gravitational Lorentz Violation: Primarily from propagation speed w/coincident EM

2. Graviton Mass: Primarily from modification of dispersion relation.

3. Dipolar Emission: From activation of scalar or vectorial modes.

[Nishizawa & Nakamura, 2014, Jacobson, 2004, Yagi, Blas, Barausse, Yunes, PRD 2013, Hansen, Yunes, Yagi, 2014]

[Will, PRD 1994, Yagi, et al PRL 2013, Hansen, Yunes, Yagi 2014]

[Finn & Sutton PRD 2002, Baskaran, et al, PRD 2008, Will, PRD 1998, Will & Yunes, CQG 2004, Berti, Buonanno & Will, CQG 2005]



4. Higher Curvature Action: Effective theories (EDGB, CS)

5. Screening Strong-Field Mechanism: Scalarization

6. No-Hair Theorem: From binary black hole ringdown. (more difficult, requires high SNR)

[Damour & Esposito-Farese, CQG, 1992, Freire et al, MNRAS 2012, Sampson et al, PRD 2014]

[Alexander & Yunes, Phys. Rept, 2009 Yagi, PRD 2012, Yagi, et al, PRD 2012]

[Dreyer, et al, CQG, 2004, Berti et al, PRD 2006, Gossan et al, PRD 2012]


GW tests will constrain a variety of phenomena: Lorentz violation, graviton mass, dipole emission, higher curvature

action, screening mechanisms, no-hair theorem.

GW tests of GR differ from other tests in a variety of ways: probe extreme gravity, clean, localized, constraint maps, present day.

Doveryai, no proveryai

What does it all mean?



14

Nico’s (GW-Biased) GW Modified Theory Classification:

Nico’s (GW-Biased) Cosmological Modified Theory Classification:

Screened Unscreened

Late-time expansion, DEEg, chameleon, Vainshtein, etc.

Early-time cosmology, inflationEg, Chern-Simons, Gauss-Bonnet, etc.

“Weak Field” Strong-Field

Well-constrained by binary pulsars, so need screeningEg, Scalar-Tensor theories

Constrainable with GW observations, natural suppression without screening Eg, Chern-Simons, Gauss-Bonnet, etc.


Screening in Cosmology ≉ Screening in GWs

15

Weak Field, Low Energy

In Cosmology

Strong Field, High Energy

Solar System

Binary Black Hole

Mergers

Galactic Dynamics

GRNot GR

In Gravitational Wave Physics

Solar System

Binary Black Hole

MergersNot GRGR


Weak Field Theories


Example: Scalar Tensor Theories

17

Definition:

Main Effect:

Dominant Observables:

Spontaneous Scalarization

Stars acquire scalar charge +

Grav. and Inertial center of mass do not coincide

Faster Orbital Decay

Damour+Esposito-Farese, PRD 54 (’96) Palenzuela, et al, PRD 97 (’13), 89 (’14).

Screened Dipole Gravitational Wave

Emission

Effective Coupling to Matter:


Constraints on Weak Field Theories

18

Scalarizable Scalar-Tensor:

(similar constraints for TeVeS and for massive Brans-Dicke) Freire, et al, MRAS 18 (’12).

Alsing, et al, PRD 85, (’12).


Strong Field Theories


Example: Quadratic Gravity

20

Definition:

Main Effects:

Dominant Observables:

Chirping of Gravitational Wave Phase

Alexander & Yunes, Phys. Rept 480 (’09) Yunes & Stein, PRD 83 (’11)

certain choices of couplings lead to Einstein-Dilaton-Gauss-Bonnet theory or dynamical Chern-Simons gravity.

dCS. Gravitational Parity Violation, inverse no-hair theorem.

Requires observation of late inspiral & merger


Constraints on Strong Field Theories

21

Extremely weak from Solar System (GPB)

dCS

Projected GW constraints

Yagi, Yunes & Tanaka, PRL 109 (’12)

Current constraints

Constraint Contours on

in km.


Parametrized Post-Einsteinian


Strong FieldWeak Field

GR Signal/ppE Templates, 3-sigma constraints, SNR = 20

Yunes & Hughes, 2010, Cornish, Sampson, Yunes & Pretorius, 2011 Sampson, Cornish, Yunes 2013.

Newt 1PN 1.5 2 2.5 3 3.5

aLIGO projected bounds

Double Binary Pulsar bounds

Projected Gravitational Wave Constraints

h(f) = hGR(f) (1 + ↵fa) ei�fb


At our doorstep...

• is the Pontryagin density.

• is either a dynamical field that evolves.

24

Firs

t Loc

k

LIG

O In

dia?

aLIG

Oac

cept

ance

aLIG

Oin

stal

latio

nst

art

Stra

in N

oise

[1/s

qrt(

Hz)

]

S5 S6

YearN

ow

Earl

y ru

ns:

LIG

O O

nly?

Full

Lock

Adv

Kag

ra

Virg

o


Non GR injection, extracted with GR templates (blue) and ppE templates (red). GR template extraction is “wrong” by much more than the systematic

(statistical) error. “Fundamental Bias”

Non-GR Signal/GR Templates, SNR = 20

12

0.01

0.1

10 20 30 40 50

beta

unc

erta

inty

SNR

actual values1/SNR

FIG. 14: The scaling of the parameter estimation error inthe ppE parameter β for an aLIGO simulation with ppE pa-rameters (a,α, b,β) = (0, 0,−1.25, 0.1). The parameter errorsfollow the usual 1/SNR scaling.

0

0.01

0.02

0.03

0.04

0.05

0.06

0.005 0.01 0.015 0.02 0.025 0.03

1

100

10000

1e+06

1.0

- FF

Baye

s Fa

ctor

β

Bayes FactorFitting Factor

FIG. 15: The log Bayes factors and (1 − FF) plotted as afunction of β for a ppE injection with parameters (a,α, b,β) =(0, 0,−1.25,β). The predicted link between the fitting factorand Bayes factor is clearly apparent.

the log Bayes factor is equal to

logB = χ2min/2 + ∆ logO

= (1− FF2)SNR2

2+ ∆ logO . (25)

Thus, up to the difference in the log Occam factors,∆ logO, the log Bayes factor should scale as 1−FF whenFF ∼ 1. This link is confirmed in Figure 15.

E. Parameter Biases

If we assume that nature is described by GR, but intruth another theory is correct, this will result in therecovery of the wrong parameters for the systems we arestudying. For instance, when looking at a signal thathas non-zero ppE phase parameters, a search using GRtemplates will return the incorrect mass parameters, asillustrated below.

2.8 2.82 2.84 2.86 2.88 2.9 2.92 2.94ln(M)

BF = 0.3β = 1

2.75 2.8 2.85 2.9 2.95ln(M)

BF = 5.6β = 5

2.65 2.7 2.75 2.8 2.85 2.9 2.95ln(M)

BF = 322β = 10

2.4 2.5 2.6 2.7 2.8 2.9ln(M)

BF = 3300β = 20

FIG. 16: Histograms showing the recovered log total massfor GR and ppE searches on ppE signals. As the source getsfurther from GR, the value for total mass recovered by theGR search moves away from the actual value.

Perhaps the most interesting point to be made withthis study is that the GR templates return values of thetotal mass that are completely outside the error rangeof the (correct) parameters returned by the ppE search,even before the signal is clearly discernible from GR. Werefer to this parameter biasing as ‘stealth bias’, as it isnot an effect that would be easy to detect, even if onewere looking for it.

This ‘stealth bias’ is also apparent when the ppE αparameter is non-zero. As one would expect, when a GRtemplate is used to search on a ppE signal that has non-zero amplitude corrections, the parameter that is mostaffected is the luminosity distance. We again see the biasof the recovered parameter becoming more apparent asthe signal differs more from GR. In this study, becausewe held the injected luminosity distance constant insteadof the injected SNR, the uncertainty in the recovered lu-minosity distance changes considerably between the dif-ferent systems. In both cases shown, however, the re-covered posterior distribution from the search using GRtemplates has zero weight at the correct value of lumi-nosity distance, even though the Bayes factor does notfavor the ppE model over GR.

V. CONCLUSION

The two main results of this study are that the ppEwaveforms can constrain higher order deviations from GR(terms involving higher powers of the orbital velocity)much more tightly than pulsar observations, and thatthe parameters recovered from using GR templates torecover the signals from an alternative theory of gravitycan be significantly biased, even in cases where it is notobvious that GR is not the correct theory of gravity. Wealso see that the detection efficiency of GR templates canbe seriously compromised if they are used to characterizedata that is not described by GR.

13

30 40 50 60 70 80 90 100 110DL (Gpc)

BF = 1 ppEGR

injected value

30 40 50 60 70 80 90 100 110DL(Gpc)

BF = 53 ppEGR

injected value

FIG. 17: Histograms showing the recovered values for lumi-nosity distance from GR and ppE searches on a LISA binaryat redshift z = 7. Both signals have a = 0.5, and were in-jected with a luminosity distance of 70.5 Gpc. The top plothas α = 3.0 and the bottom has α = 2.5. As the Bayes factorfavors the ppE model more strongly, the bias in the recov-ered luminosity distance from the GR search becomes morepronounced.

The current study makes several simplifying assump-tions about the waveforms: we consider only the inspi-ral stage for non-spinning black holes on circular orbits,and include just the leading order ppE corrections to thewaveforms. In future work we plan to include a marginal-ization over these higher order corrections. Including thismarginalization will be more realistic, as the ppE for-malism allows for many higher order corrections to thewaveform. Marginalizing over the higher order terms willweaken the bounds on the leading order ppE parame-ters, though probably not by that much since they aresub-dominant terms.

Another subject that we will examine in the futureis the affect on our analysis of multiple detections. Si-multaneously characterizing several systems with differ-ent mass ratios should allow us to constrain all six ppEparameters and not just the four we used in this study.Looking at several systems simultaneously should also al-low us to detect deviations from GR that are smaller than

those we could confidently infer with a single detection,as the evidence for the ppE hypothesis will accumulatewith the additional data.

We also plan to perform a study similar to that doneby Arun et al. [24–26], in which the exponents ai, bi arefixed at the values found in the PN expansion of GR, andcompare their Fisher matrix based bounds to those fromBayesian inference.

Finally, we will look at LISA observations of galacticwhite-dwarf binaries to see if the brighter systems, whichmay have SNRs in the hundreds, may allow us to beatthe pulsar bounds across the entire ppE parameter space.The brightest white-dwarf systems will have u ∼ 10−8 →10−7 (for comparison the ‘golden’ double pulsar system,PSR J0737-3039A has u = 3.94× 10−9), and these smallvalues for u make the ppE effects, which scale as ua andub, much larger than for black hole inspirals when a, b <0.

The chance to test the validity of Einstein’s theoryof gravity is one of the most exciting opportunities thatgravitational wave astronomy will afford to the scientificcommunity. Without the appropriate tools, however, ourability to perform these tests is sharply curtailed. Thisanalysis has shown that the ppE template family couldbe an effective means of detecting and characterizing de-viations from GR, and also that assuming that our GRwaveforms are correct could lead to lessened detectionefficiency and biased parameter estimates if gravity isdescribed by and alternative theory. We have identifiedseveral areas of future investigation, and will continue tostudy this area in depth.

Acknowledgments

We thank Patrick Brady, Curt Cutler, Ben Owen,David Spergel, Xavier Siemens, Paul Steinhardt andMichelle Vallisneri for detailed comments and sugges-tions. We are very grateful to Martin Weinberg and WillFarr for making their direct evidence integration codesavailable to us, and for helping us to understand the re-sults. N. J. and L. S. acknowledge support from theNSF Award 0855407 and NASA grant NNX10AH15G.N. Y. and F. P. acknowledge support from the NSF grantPHY-0745779, and FP acknowledges the support of theAlfred P. Sloan Foundation.

[1] C. M. Will, Living Reviews in Relativity 9 (2006), URLhttp://www.livingreviews.org/lrr-2006-3.

[2] N. Yunes and F. Pretorius, Phys. Rev. D80, 122003(2009), 0909.3328.

[3] B. F. Schutz, J. Centrella, C. Cutler, and S. A. Hughes(2009), 0903.0100.

[4] C. M. Will, Phys. Rev. D57, 2061 (1998), gr-qc/9709011.[5] C. M. Will and N. Yunes, Class. Quant. Grav. 21, 4367

(2004), gr-qc/0403100.[6] E. Berti, A. Buonanno, and C. M. Will, Class. Quant.

Grav. 22, S943 (2005), gr-qc/0504017.[7] A. Stavridis and C. M. Will, Phys. Rev. D80, 044002

(2009), 0906.3602.[8] K. G. Arun and C. M. Will, Class. Quant. Grav. 26,

155002 (2009), 0904.1190.[9] D. Keppel and P. Ajith, Phys. Rev. D82, 122001 (2010),

Cornish, Sampson, Yunes & Pretorius, 2011

Fundamental Bias


Sampson, 2013

Ignoring Fundamental Bias...injection=(not-ruled out) ppE template=GR

Fitting Factor Deteriorates

Physical Parameters Completely Biased

YunesGW Probes of Extreme Gravity 27Vallisneri & Yunes, 2013

Stealth Bias

Fundamental Bias that we can’t detect!SNR needed to detect a

GR deviationSNR needed for fundamental bias error

to be larger than systematic error

Overt BiasNegligible Bias

Stealth Bias


Sampson, Cornish & Yunes, 2013

Bayes Factor between a 1-parameter ppE template and a GR template (red) and between a 2-parameter ppE template and a GR template (blue), given a non-GR

injection with 3 phase deformations, as a function of the magnitude of the leading-order phase deformation.

Simple ppE Performance


The Need for Accuracy

• “C-tensor”:

29Quantum Noise (Amelino-Camelia)


Gravitational Wave Detectors

• is the Pontryagin density.

• is either a dynamical field that evolves.

30

Bounce light off mirrors and look for interference pattern when the light

recombines.

LHO

LLO Virgo/AdV

GEO

KAGRA

Ligo-India

Detectors


Yunes & Pretorius, PRD 2009 Mirshekari, Yunes & Will, PRD 2012 Chatziioannou, Yunes & Cornish, PRD 2012

I. Parametrically deform the Hamiltonian.

II. Parametrically deform the RR force.

III. Deform waveform generation.

IV. Parametrically deform g propagation.

h = hGR (1 + �fa) ei�fb

Result: To leading PN order and leading GR deformation

Parameterized post-Einsteinian Framework

A = AGR + �A�AH,RR = ↵H,RRv

aH,RR

h = F+h+ + F⇥h⇥ + Fshs + . . .

E2g = p2gc

4 + ↵p↵g

h(f) = hGR(f) (1 + ↵fa) ei�fb

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