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Testing GR with Gravitational Waves: Theory-agnostic or Specific Tests?
Kent Yagi
NR beyond GR
University of Virginia
Benasque, June 4th 2018
Equi
vale
nce
Prin
cipl
e
4 D
imen
sion
s
Fundamental Pillars in General Relativity (GR)
Kent YagiIntroduction
Equi
vale
nce
Prin
cipl
e
4 D
imen
sion
s
Con
stan
t G
Lore
ntz
Inva
rianc
e
Parit
y In
varia
nce
Mas
sles
s G
ravi
ton
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