Enrico Barausse (Institut d’Astrophysique de Paris/CNRS, France)

The implications of GW
detections for GR extensions
The 3rd International KMI Symposium“Quest for the Origin of Particles and the Universe”

January 5th-7th, 2017

“2.9” GW detections

Why important?

First direct detection of GWs (indirect evidence from binary pulsars)

High BH masses imply formation in weak-wind/low-metallicity environment

Opens up era of multi-band EM+GW astronomy

Test GR for the first time in strong-field (UNewton~c2) and highly relativistic(v~c) regime This talk: why we expect GWs to be different in theories that extend GR, andwhat is the physics behind these differences

GWs in GR & beyond GR

Analytic (BH perturbation theory)“Analytic” 

(Post-Newtonian)

Numerical relativity
Focus on inspiral (where we can make predictions in modified gravity theories)

Some general consideration on merger (if time allows)

No ringdown tests (anyway possible only with third generation/space-based detector, cf
Berti, Sesana, EB, Cardoso, Belczynski 2016)

No propagation effects (weak constraints on GR alternatives unless EM counterpart)Beyond GR: how?
Lovelock’s theorem

Figure adapted from Berti, EB et al 2015

Generic way to modify GR is to add extra fields!

How to couple extra fields?
Satisfy weak equivalence principle (i.e. universality of free
fall for bodies with weak self-gravity) by avoiding
coupling extra fields to matter (i.e. no fifth forces at treelevel)

But extra fields usually couple non-minimally to metric, so
gravity mediates effective interaction between matter andnew field in strong gravity regimes (Nordtvedt effect)

Equivalence principle violated for strongly gravitating
bodiesStrong EP violations
For strongly gravitating bodies, gravitational binding energy gives large
contribution to total mass, but binding energy depends on extra fields!
Examples:Brans-Dicke, scalar-tensor theories: Geff ∝ GN/φ, but φ in which star is immersed depends on
cosmology, presence of other starg

Lorentz-violating gravity (Einstein-aether, Horava):
preferred frame exists for gravitational physics
gravitational mass of strongly gravitating bodies depends onvelocity wrt preferred frame

If gravitational mass depends on fields, deviations from GR motion
already at geodesics levelsensitivities or charges or hairs, i.e. response to change in field boundary conditions

Strong EP violations and GW emission
Whenever strong equivalence principle is violated, monopolar anddipolar radiation may be produced

In electromagnetism, no monopolar radiation because electric charge
conservation is implied by Maxwell eqs

In GR, no monopolar or dipolar radiation because energy and linear
momentum conservation is implied by Einstein eqs e.g.

not a wave!

In GR extensions, effective coupling matter-extra fields in strong
gravity regimes
energy and momentum transfer between
bodies and extra field, monopolar and dipolar GW emission, modified
quadrupole formula

Dipolar emission dominant for quasi-circular systems;

1.5 PN effect vs 2.5 PN in GR! But effect depends on nature of bodies

(Absence of) dipolar emission in binary pulsars

(Absence of) dipolar emission in binary pulsars

An example: Lorentz-violating gravity(= infrared limitof Horava gravity)

No ghosts+no gradient instabilities+solar system tests+absence of Cherenkov gravitational radiation (to agreewith cosmic rays)

(Absence of) dipolar emission in binary pulsars

An example: Lorentz-violating gravity

khronometrictheoryNo ghosts+no gradient instabilities+solar system tests+absence of Cherenkov gravitational radiation (to agreewith cosmic rays)+cosmology

(Absence of) dipolar emission in binary pulsars

An example: Lorentz-violating gravity

Yagi, Blas, EB & Yunes 2014

khronometrictheoryEinstein-aether
theoryNo ghosts+no gradient instabilities+solar system tests+absence of Cherenkov gravitational radiation (to agreewith cosmic rays)+cosmology+pulsars

(Absence of) dipolar emission in binary pulsars

Damour-Esposito-Farese scalar-tensor theory

Generalizes Fierz-Jordan-Brans-Dicke by introducing linear coupling
β between scalar and curvature, besides constant coupling α: ⇤' ⇠ ↵R + 'R
Strongly non linear effects
inside NS (“spontaneous scalarization”)

Figure credits: Wex, private comm.

Dipolar emission in BH binaries?
Not present in Fierz-Jordan-Brans-Dicke-like theories (e.g.
Damour-Esposito-Farese theory) because R=0 in vacuum⇤' ⇠ ↵R + 'R
Loophole: non-trivial (cosmological) boundary conditions

But other curvature invariants do not vanish in vacuum, e.g.
Kretschmann, Gauss-Bonnet, PontryaginDipolar emission in BH binaries?
Not present in Fierz-Jordan-Brans-Dicke-like theories (e.g.
Damour-Esposito-Farese theory) because R=0 in vacuum⇤' ⇠ ↵R + 'R
Loophole: non-trivial (cosmological) boundary conditions

But other curvature invariants do not vanish in vacuum, e.g.
Kretschmann, Gauss-Bonnet, PontryaginDipolar emission in BH binaries?
Not present in Fierz-Jordan-Brans-Dicke-like theories (e.g.
Damour-Esposito-Farese theory) because R=0 in vacuum⇤' ⇠ ↵R + 'R
Loophole: non-trivial (cosmological) boundary conditions

But other curvature invariants do not vanish in vacuum, e.g.
Kretschmann, Gauss-Bonnet, Pontryagin

Caveats

f1 = const: f(R) gravity = FJBD like theory with a potential
f1 ≠ const: higher-order field equations, Ostrogradsky ghost

Ostrogradsky ghost f3 = const: same dynamics as GR (Pontryagin density is 4D topological invariant)f3 ≠ const: dynamical Chern-Simons, Ostrogradsky ghost f4 = const: same dynamics as GR (Gauss-Bonnet term is 4D topological invariant)f4 ≠ const: dilatonic Gauss-Bonnet gravity, 2nd-order field eqs, no Ostrogradsky ghost)
In shift-symmetric dilatonic Gauss-Bonnet [f4(φ) = φ], sensitivities (and thus dipole
emission) are zero for NS but NOT for BHs (EB & Yagi 2015, Yagi, Stein & Yunes 2015)

More general theories (with extra vector or tensor dof’s) predict dipole emission

also (though not exclusively) in BH binaries

Constraints on dipolar emission

from direct detections
Weak bounds from advanced detectors

Better for 3rd-gen detectors, e.g. Lorentz violating gravity (Hansen, Yunes, Yagi 2015)

Multi-band observations of GW150914-like/intermediate-mass binary BHs
Also visible by eLISA if 6 links and 5 year mission!
(Sesana 2016, Amaro-Seoane & Santamaria 2009) 

High-frequency noise is crucial!

Astrophysical stochastic background may screen
primordial ones

Figures from Sesana 2016

Tests of BH-BH dipole emission

Pulsar constrain |B| ≲ 2 x 10-9, GW150914-like systems + eLISA
will constrain same dipole term in BH-BH systems to comparable
accuracy

From EB, Yunes & Chamberlain 2016

How about merger?
Possible surprises/

highly non-linear dynamics?

Need numerical-relativity simulations: prerequisite is that Cauchy problem be wellposed (e.g. that eqs be strongly hyperbolic, i.e. wave eqs)

True for FJBD-like scalar-tensor theories (i.e. with NO galileon terms), but GR
dynamics in vacuum (modulo boundary/initial conditions, mass term)

True in flat-space & spherical symmetry for Lorentz-violating gravity andgalileons; dynamics differs from GR both in vacuum and matter, but no generalformulation/simulations

Cauchy problem easier to formulate if theory interpreted as EFT (eg ChernSimons)Smoking-gun scalar effects?
Earlier plunge than in GR for LIGO NS-NS sources, in DEF scalar-tensor theories

EB, Palenzuela, Ponce & Lehner 2013, 2014;
also Shibata, Taniguchi, Okawa & Buonanno 2014, 2015; Sennett & Buonanno 2016

Detectable with custom-made templates but also by ppE or “cut” waveforms(Sampson et al 2015)

Caused by induced scalarization of one (spontaneously scalarized) star on theother, or by dynamical scalarization of an initially non-scalarized binary

Spontaneous/dynamical scalarization
as “phase transitions”

Figure from Esposito-Farese, gr-qc/0402007

Can we learn something from BH-BH
GW detections without NR simulations?
Dynamics is perturbative in v/c(as also shown by binary pulsars
and solar-system tests!)

In (some) theories with screening,
the PN expansion becomes NONperturbative

Galileon/Horndeski screening
Generalized Galileon action is most generic with 2nd order eqs

Galleons also arise in massive gravity

p

gn
L =
K( , X)
16⇡G

h

2

2

i

G3 ( , X)⇤ + G4 ( , X)R + @X G4 ( , X) (⇤ )(rµ r⌫ )
h
io
1
3
2
3
+G5 ( , X)Gµ⌫ rµ r⌫@X G5 ( , X) (⇤ )3 (⇤ ) (rµ r⌫ ) + 2 (rµ r⌫ )6

X⌘rµ rµ /2(rµ r⌫ )2 ⌘ rµ r⌫ r⌫ rµ3(rµ r⌫ ) ⌘ rµ r⇢ r⇢ r⌫ r⌫ rµNon-linear field eqs allow “Vainshtein mechanism”⇤ + @X G3 [(⇤ )2 (rµ r⌫ )2 Rµ⌫ rµ r⌫ ] + ... = ...
"r
#
rV3
d
r3
GM (r)
/ 3
1+ 3
1
dr
rV
r
r2
Scalar effects only arise for r>> rV (Vainshtein radius)Non-perturbative PN expansion in Horndeski with Vainshtein mechanism

Vainshtein radius rv is effective size of point passIf rv ≳ λ, we have a problem! (de Rham, Matas & Tolley 2012, Chu & Trodden
2013, EB & Yagi 2015)

WKB analysis predicts all multipole moments radiate with same strength inbinary systems (de Rham, Matas & Tolley 2012)

An example: acceleration-based
screening à la MOND
Similar to Lorentz-violating
gravity, e.g. TeVeS, generalized
Einstein-Aether theories: dipole
radiation in BH and NS binaries

Intrinsically non-linear
dynamics: strong couplingwhen trying to recover
GR at high accelerations

may occur

Bonetti & EB 2015

(Future) ringdown tests
Tests of the no-hair theorem:

Difficult with advanced detectors
because little SNR in ringdownTests of no-hair theorem by BH ringdown

Berti, Sesana, EB,

Cardoso, Belczynski, PRL in press, 2016

Constraints on massive fields around spinning BHs
Spinning BH + massive fields with Compton wavelength comparable to event
horizon radius are unstable under superradiance (Cardoso, Pani, Berti, Brito,
Arvanitaki, etc)

Scenario explored for Proca field, axion-like particles, massive graviton, etc

Instability endpoint unclear, but might be BH with scalar hair (Cardoso, Pani, Brito,
Witek, Herdeiro, etc)

Caveat: instability must be faster than system’s timescale (e.g. Salpeter time,orbital time, formation time, etc)

Pani et al 2012

Arvanitaki et al 2016

Ringdown’s sensitivity to near-horizon physics
Deviations away from Kerr geometry near horizon (e.g. firewalls, gravastars, wormholes,etc) can produce significant changes in QNM spectrum

Deviations taketo show up in time-domain signal because QNMs
generated at the circular null orbit (Damour & Solodukhin 2007, EB, Cardoso & Pani
2014, Cardoso, Franzin & Pani 2016) and coordinate time diverges on horizon

Need “matter” with high viscosity to explain absence of hydrodynamic modes;
possible with NS matter+large B, but not with boson stars (Yunes, Yagi & Pretorius 2016);

Schwarzschild BH of mass M+thin shell of 0.01 M at r0

Cardoso, Franzin & Pani 2016

EB, Cardoso & Pani 2014

r0 =60 M, shell of mass M, Gaussian wavepacket initially at ISCO

Conclusions

Conclusions
GR extensions already tightly constrained by binary pulsars/ solar system

Conclusions
GR extensions already tightly constrained by binary pulsars/ solar system
Direct GW detections push tests to more extreme regimes (strong
gravitational fields, relativistic velocities) and different objects

Conclusions
GR extensions already tightly constrained by binary pulsars/ solar system
Direct GW detections push tests to more extreme regimes (strong
gravitational fields, relativistic velocities) and different objects
Perturbative effects are small and may require more detections

Conclusions
GR extensions already tightly constrained by binary pulsars/ solar system
Direct GW detections push tests to more extreme regimes (strong
gravitational fields, relativistic velocities) and different objects
Perturbative effects are small and may require more detections
Non-perturbative “smoking-gun” effects may be present, probably firstdetectable by parametrized tests if present

Conclusions
GR extensions already tightly constrained by binary pulsars/ solar system

Direct GW detections push tests to more extreme regimes (strong
gravitational fields, relativistic velocities) and different objects

Perturbative effects are small and may require more detections

Non-perturbative “smoking-gun” effects may be present, probably firstdetectable by parametrized tests if present

Thank you!

ありがとうございました!

Beyond GR: why?
1=BH-BH systems with aLIGO/aVirgo/KAGRA

2=NS-NS systems with aLIGO/aVirgo/KAGRA, 

3=BH-BH with eLISA, 

4=BH- BH with PTAs

Beyond GR: why?
1=BH-BH systems with aLIGO/aVirgo/KAGRA

2=NS-NS systems with aLIGO/aVirgo/KAGRA, 

3=BH-BH with eLISA, 

4=BH- BH with PTAs

Evidence for Dark Sector from systems with a < 10-10 m/s2
~ c/H0 : need screening!

Beyond GR: why?
1=BH-BH systems with aLIGO/aVirgo/KAGRA

2=NS-NS systems with aLIGO/aVirgo/KAGRA, 

3=BH-BH with eLISA, 

4=BH- BH with PTAs

Evidence for Dark Sector from systems with a < 10-10 m/s2
~ c/H0 : need screening!

GR never tested in highly relativistic AND strong-field regime

Beyond GR: why?
strong field and/or relativistic

1=BH-BH systems with aLIGO/aVirgo/KAGRA

2=NS-NS systems with aLIGO/aVirgo/KAGRA, 

3=BH-BH with eLISA, weak field andnon-relativistic

4=BH- BH with PTAs

Evidence for Dark Sector from systems with a < 10-10 m/s2
~ c/H0 : need screening!

GR never tested in highly relativistic AND strong-field regime

Strong-equivalence principle violations
by thought experiments (Dicke 1969)

Energy balance gives

Tests of dipolar emission with GWs
Difficulty is to calculate sensitivities

Since they are response to field boundary conditions, needto calculate compact-object solution for different
boundary conditions

Calculation needs to be done exactly (no extrapolation of
weak field approximation) and (for NS) for different EOS’s
Example: NS
sensitivities 

in Lorentz violating
gravity (Yagi, Blas, EB and
Yunes et al 2014)

Dipolar emission in BH binaries?
Ostrogradsky instabilities not enough to rule dynamical Chern-Simons out
from EFT standpoint (Yagi, Stein & Yunes 2015)

If dCS interpreted as EFT, deviations from GR in GW emission in BH-BH
appear at high PN orders (3PN in fluxes, 2PN in waveforms, if spinning BHBH, NS-NS; 5PN in waveforms/fluxes for non-spinning BH-BH, 6PN for nonspinning NS-NS), cf Yagi, Yunes & Tanaka 2012

In dilatonic Gauss-Bonnet, dipolar -1PN term in fluxes & waveforms, for both
NS-NS and BH-BH

In shift-symmetric dilatonic Gauss-Bonnet [f4(φ) = φ], sensitivities (and thus
dipole emission) are zero for NS but NOT for BHs (EB & Yagi 2015, Yagi,
Stein & Yunes 2015)

Dipolar BH-BH fluxes expected also in theories with vector fields (Horava
gravity, Einstein-aether, TeVeS, etc) or tensor fields (bi-metric massive
gravity)Other inspiral effects: mass changes
Emparan-Fabbri-Kaloper-Tanaka conjecture:

In braneworld models, Hawking evaporation may be enhanced due to large
number of horizon degrees of freedom (cf AdS-CFT), and evaporation may
be interpreted classically from 5D viewpoint

Caveat: brane-localized BH solutions computed numerically and do not seemto support conjecture

Accretion of Dark Energy with w < -1 (“phantom energy”; allows for CTC’s,
wormholes, big rip…)

Phenomenological time variation of G

-4 PN effects

Summary: inspiral effects

Tables from Yunes, Yagi & Pretorius 2016

Inspired effects mappable to parametric formalisms (ppE, TIGER,…):

Caveat: ppE parameters may depend on sources (e.g. sensitivities
different in NSs and BHs), so stacking may not be physically meaningful!

BH QNM calculations in modified theories
Calculation often non-trivial because formulation in terms of wave eqs needed (ifelliptic sector present, need to worry about boundary conditions, etc)

Excitation amplitudes can only be calculated by full numerical-relativity simulation

Extra fields lead to different GW polarizations, each may have its own horizon 

Linked to question of (linear) stability, c.f. e.g. massive fields in Kerr

In eikonal limit, QNM frequencies and decay times linked to orbital frequencies andinstability timescales of circular null geodesics, i.e. “QNM produced at the light ring”
Eikonal limit fractional deviations from GR in LV gravity

EB, Jacobson & Sotiriou 2011

Propagation effects
Direct searches for extra polarizations beyond quadrupole (need a network)

Modified propagation velocity: - e.g. LV gravity, Horndeski, etc- Must be superluminal to avoid Cherenkov- Strong constraints from binary pulsars- Weak GW constraints from time of arrival
at different detectors (Blas et al 2016) 

- Strong bounds if EM counterpart

e.g. Horndeski/beyond-Horndeski theories(Jimenez, Piazza, Velten 2015)

αH and cT are theory’s parameters(αH = 0 in Horndeski)Propagation effects
Modified dispersion relations

Generically predicted by quantum-gravity theories

Pros: effects accumulate over distance, mappable to ppE phase term 

Cons: GWs have low energies compares to cosmic rays/Planck scale

Tables from Yunes, Yagi & Pretorius 2016

Actual tests with GW150914
Constraints on deviations from GR’s PN parameters

Actual tests with GW150914
Bounds on graviton’s mass

No constraints on extra polarizations

GR tests with direct detections

Parametric inspiral-based tests (ppE, TIGER,…):probe similar physics to binary pulsars (e.g. -1PN terms
constrained by pulsars in NS-NS systems)…

.. but since sensitivities depend on source, -1PN term may bepresent in BH-BH system or in NS-NS systems if NS mass >1.4 MsunCaveat: stacking may not be physically meaningful!

GR tests with direct detections
Parametric ringdown tests, i.e. tests of the no-hair theorem:tDifficult with advanced detectors because little SNR in
ringdown

Direct searches for extra polarizations beyond quadrupole

Need a detector network / many-pulsar timing array

Propagation effects (bounds on graviton mass, graviton
oscillations in biometric gravity)

GW detectors

Next-generation detectors

eLISA: selected as ESA’ s
L3 mission (Pathfinder
mission underway; launch2028-2034)

ET: design study funded;
2020s?

Current PTA limits

Figure courtesy of A. Sesana

Binary pulsars
Binary system of stars on circular orbits has time changing
mass quadrupole
GW emission GWs carry energy and angular momentum away from system,
binding energy gets more and more negative and binary
shrinks

Indirect detection by binary pulsar systems (e.g. Hulse-Taylor
pulsar)Compact-object binaries
are main GW sources
Adv LIGO/Virgo: stellar-mass range,i.e. NS-NS up to z ~ 0.1, NS-BH, BH-BH up to z ~ 0.5 - 1

ET: stellar and intermediate mass range,i.e. NS-NS, BH-NS, NS-NS at z < 5, IMBH-IMBH, BHIMBH, NS-IMBH at z < 10 - 15

PTA: supermassive range, i.e. SMBH-SMBH at z < 1

eLISA: supermassive range,i.e. SMBH-SMBH at z < 10 - 15; IMBH-SMBH at z < 5,
BH-SMBH, NS-SMBH at z < 1