Testing GR with Gravitational Waves: Theory-agnostic or Specific Tests?

Kent Yagi

NR beyond GR

University of Virginia

Benasque, June 4th 2018

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Fundamental Pillars in General Relativity (GR)

Kent YagiIntroduction

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Fundamental Pillars in General Relativity (GR)

Kent YagiKent YagiIntroduction

Zoo of Modified Gravity[Bull et al. arXiv:1512.05356]

Kent YagiIntroduction

Theory-agnostic vs Specific Tests

Q: Shall we compare GW data against each theory one by one?

A: More efficient to first carry out theory-agnostic tests, and map them to specific tests.

Kent YagiIntroduction

Outline

Kent YagiOutline

Applications to GW150914 & GW151226

Theory-agnostic Tests

Outline

Kent YagiOutline

Applications to GW150914 & GW151226

Theory-agnostic Tests

(I) PN Tests of GR

(II) Parameterized post-Einsteinian Formalism

(III) Generalized IMRPhenom Waveform

Outline

Kent YagiOutline

Applications to GW150914 & GW151226

Theory-agnostic Tests

(I) PN Tests of GR

(II) Parameterized post-Einsteinian Formalism

(III) Generalized IMRPhenom Waveform

Kent YagiTheory-agnostic

[Abbott et al. PRL 116 061102 (2016)]

Where to start…?

Matched filtering more sensitive to phase than amplitude

Kent Yagi

(I) PN Tests of GR =

7X

k=0

[ k(m1,m2) + kl(m1,m2) ln f ]f(k�5)/3

Non-spinning binary BH at z=1 with LISA [Kramer & Wex (2009), Wex (2014)]

Double Binary Pulsar

[Arun et al. (2006), Mishra et al. (2010)]

Theory-agnostic

GW phase in freq. domain

Outline

Kent YagiOutline

Applications to GW150914 & GW151226

Theory-agnostic Tests

(I) PN Tests of GR

(II) Parameterized post-Einsteinian Formalism

(III) Generalized IMRPhenom Waveform

Kent Yagi

GW Phase in Fourier Domain in GR

Quadrupolar Radiation:

Binding Energy: Kepler’s Law:

dE

dt⇠

...Qij

...Q

ij ⇠ µ2r4f6

f2 ⇠ m

r3

M ⌘✓m3

1 m32

m

◆1/5

E ⇠ µm

r

reduced mass

separation

total mass

⇠ (⇡M f)�5/3chirp mass:

= 2⇡

Z f Z f 0dt

dE

dE

dr

dr

df 00 df00 df 0

(f) = 2⇡

Z f

t(f 0) df 0 = 2⇡

Z f Z f 0dt

df 00 df00 df 0

Theory-agnostic

Kent Yagi

Quadrupolar Radiation:

Binding Energy: Kepler’s Law:

(II) PPE-modified Inspiral Waveform Phase[Yunes & Pretorius PRD80 122003 (2009)]

u ⌘ (⇡Mf)1/3

� = �(A,B)

dE

dt=

✓dE

dt

◆

GR

�1 +B u2q

�

E = EGR

�1 +Au2p

�r(f) ⇠ r(f)GR

�1 +Au2p

�

q PN

⇠ (f)GR + � ub

b = min(2p� 5, 2q � 5)

PPE parameters:

(f) = 2⇡

Z f Z f 0dt

dE

dE

dr

dr

df 00 df00 df 0

Theory-agnostic

Kent Yagi

PPE Mapping to Specific Theories

(↵G ,�G) =

✓� 5

512GM ,� 25

65536GM

◆

˜h(I)GR(f) (1 + ↵ua

) exp

�i� ub

�

[Yunes, Pretorius & Spergel PRD80 122003 (2010)]

PPE inspiral waveform:

Theory-agnostic

Outline

Kent YagiOutline

Applications to GW150914 & GW151226

Theory-agnostic Tests

(I) PN Tests of GR

(II) Parameterized post-Einsteinian Formalism

(III) Generalized IMRPhenom Waveform

Kent Yagi

(III) Generalized IMRPhenom Waveform

[Khan et al. (2015)]

Inspiral-merger-ringdown Phenomonological D (IMRPhenomD) waveform in GR

phenomenological parameters ~p(⌘, �)

phenomenological waveform numerical relativity waveform

symmetric mass ratio

effective dimensionless spin

generalized IMRPhenom (gIMR) waveform

Theory-agnostic

piGR(1 + �pi)

Kent Yagi

(III) Generalized IMRPhenom Waveform

[Khan et al. (2015)]

Inspiral-merger-ringdown Phenomonological D (IMRPhenomD) waveform in GR

phenomenological parameters ~p(⌘, �)

phenomenological waveform numerical relativity waveform

generalized IMRPhenom (gIMR) waveform

Theory-agnostic

possible to model non-GR merger & ringdown(no known mapping to specific theories)

piGR(1 + �pi)

Outline

Kent YagiOutline

Applications to GW150914 & GW151226

Theory-agnostic Tests

Constraining GR Fundamental Pillars[Yunes & Hughes (2010)]

[Yunes, KY & Pretorius (2016)]

ppE

[LIGO-Virgo Collaboration (2016)]

� = � v2n�5

Kent YagiApplications

gIMR

PPE

Constraining GR Fundamental Pillars[Yunes & Hughes (2010)]

[Yunes, KY & Pretorius (2016)]

extra dimension

time varying G

scalar monopole activation

vector field activation

scalar dipole activation

4D equivalence principle

Lorentz invariance

parity invariance

equivalence principle

ppE

[LIGO-Virgo Collaboration (2016)]

� = � v2n�5

Kent YagiApplications

gIMR

PPE

Theoretical Constraints [Yunes, KY & Pretorius PRD (2016)]

Kent YagiApplications

Theoretical Constraints [Yunes, KY & Pretorius PRD (2016)]

Kent YagiApplications

Theoretical Constraints [Yunes, KY & Pretorius PRD (2016)]

graviton dispersion relation: E2 = (p c)2 +A (p c)↵

Kent YagiApplications

Theoretical Constraints [Yunes, KY & Pretorius PRD (2016)]

graviton dispersion relation: E2 = (p c)2 +A (p c)↵

Kent YagiApplications

Important Message

Kent YagiApplications

Conclusions

Takeaway & Future Work

Kent YagiConclusions

Step 1. Carry out theory-agnostic tests

Step 2. Map to specific theories

Need many merger simulations in non-GR theories

Mapping between generic non-GR parameters to specific theoretical coupling constants

Generic non-GR waveforms including merger & ringdown

Takeaway & Future Work

Kent YagiConclusions

Step 1. Carry out theory-agnostic tests

Step 2. Map to specific theories

Need many merger simulations in non-GR theories

Thank You

Generic non-GR waveforms including merger & ringdown

Mapping between generic non-GR parameters to specific theoretical coupling constants