alternative theories and gravitational waves · e. babichev and c. charmousis, jhep 1408, 106...
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Alternative theories and gravitational waves
Thomas P. Sotiriou
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New physics?
Is there new gravitational physics (much) below the Planck scale?
❖ Cosmological constant problem
❖ BHs and QFT (firewall and friends)
❖ Dark matter
Thomas P. Sotiriou – DAMTP, September 23rd and 24th, 2019
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taken from arXiv:1903.09221
Probing a new regime?
Thomas P. Sotiriou – DAMTP, September 23rd and 24th, 2019
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Modelling new physics
To be tested with GW it
has to leave an imprint on BHs/NSs
has to persist in the classical regime
to be modelled! (i.e. we need equations!)
Hence we can test
deviations from GR
extensions of the standard model with a strong gravity imprint
In both cases, we are looking for new fields!
Thomas P. Sotiriou – DAMTP, September 23rd and 24th, 2019
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Lovelock and GR
Lovelock’s theorem leads to GR under assumptions:
4 dimensions
Covariance
Second order equations
No extra fields
Locality
Not all of them are equally important for phenomenology!
Thomas P. Sotiriou – DAMTP, September 23rd and 24th, 2019
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Extracting new physicsStep-by-step guide for your favourite candidate:
Study compact objects and determine their properties �Signatures: hair, tidal properties, etc.
Model the inspiral (post-Newtonian)�Signatures: new polarizations, dephasing, tidal effects…
Model the ringdown (perturbation theory)�Signatures: different QNM spectrum �Hurdle: non-separability, non-trivial background
Do full-blown numerics to get the merger�Signatures: various/unknown �Hurdle: initial value formulation and well-posedness
Thomas P. Sotiriou – DAMTP, September 23rd and 24th, 2019
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Neutron stars beyond GR Ambiguity in EOS, degeneracy with changes in gravity Binary pulsar constraints
There is notable progress…
I-Love-Q and 3-moment relations ��
Moments related to observables in scalar-tensor theories
K. Yagi and N. Yunes, Science 341, 365-368 (2013)�G. Pappas and T. Apostolatos, PRL 112, 121101 (2014)
G. Pappas and T.P.S., PRD 91, 044011 (2015);�MNRAS 453, 2862-2876 (2015)
A. Coates, M. Horbatsch and T.P.S., PRD 95, 084003 (2017);�A. Coates, N. Franchini and T.P.S., PRD 97, 064013 (2018).
…but it assumes that the microphysics is unaffected.
Thomas P. Sotiriou – DAMTP, September 23rd and 24th, 2019
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Testing gravity
Lorentz symmetry �Einstein-aether theory, Horava gravity
Mass of the graviton �massive and bimetric gravity
Parity �dynamical Chern-Simons gravity
Looking under the lamppost approach:
Testing principles approach:
E.g. most general scalar-tensor theory
Thomas P. Sotiriou – DAMTP, September 23rd and 24th, 2019
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Brans-Dicke theory
Solutions with constant are admissible and are GR solutions.
The action of the theory is
and the corresponding field equations are
Thomas P. Sotiriou – DAMTP, September 23rd and 24th, 2019
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Brans-Dicke theory
However, they are not the only ones. E.g. for
around static, spherically symmetric stars a nontrivial configuration is necessary and
So, hiding the scalar requires, either a very large mass (short range) or a very large Brans-Dicke parameter
Thomas P. Sotiriou – DAMTP, September 23rd and 24th, 2019
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Scalar-tensor theory
Jordan frame action:
Redefinitions:
Einstein frame action:
Thomas P. Sotiriou – DAMTP, September 23rd and 24th, 2019
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Screening
In spherical symmetry + Einstein frame
Chameleon
Symmetron
Effective potentials can designed to yield a large mass locally
Known examples:
K. Hinterbichler and J. Khoury, Phys. Rev. Lett. 104, 231301 (2010)
J. Khoury and A. Weltman, Phys. Rev. Lett. 93, 171104 (2004)
Thomas P. Sotiriou – DAMTP, September 23rd and 24th, 2019
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Spontaneous scalarization
There is need for models where new physics “appears” when gravity gets strong
Example: A theory with an extra scalar field that
If then the theory will admit GR solutions around matter!
However they will not necessarily be the only ones...
The non-GR configuration is preferred for sufficiently large central density
T. Damour and G. Esposito-Farese, Phys. Rev. Lett. 70, 2220 (1993)
In Einstein frame
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Tachyonic instability
Taken from G. Esposito-Farese, arXiv:gr-cq/0402007
Severely constrained by binary pulsar tests, unless there is a mass.
This model only works for stars
Thomas P. Sotiriou – DAMTP, September 23rd and 24th, 2019
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Scalarization and matter
Matter can induce scalarization of black holes
Scalarization can drive a gravitational Higgs mechanism: suitably coupling to matter leads to strong gravity deviations from the Standard Model.
V. Cardoso, I. P. Carucci, P. Pani and T. P. S., Phys. Rev. Lett. 111, 111101 (2013); Phys. Rev. D 88, 044056 (2013).
A. Coates, M.Horbatsch, and T.P.S., Phys. Rev. D 95, 084003 (2017)�N. Franchini, A Coates, and T.P.S., Phys. Rev. D 97, 064013 (2018)
Thomas P. Sotiriou – DAMTP, September 23rd and 24th, 2019
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Scalar fields in BH spacetimes
S.W. Hawking, Comm. Math. Phys. 25, 152 (1972).
stationary, as the endpoint of collapse
asymptotically flat, i.e. isolated
The equation
admits only the trivial solution in a BH spacetime that is
The same is true for the equation
with the additional assumption of local stability
T. P. S. and V. Faraoni, Phys. Rev. Lett. 108, 081103 (2012)
Thomas P. Sotiriou – DAMTP, September 23rd and 24th, 2019
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No difference from GR?
Actually there is... Perturbations are different!
They even lead to new effects, e.g. superradiance
In general, relaxing the symmetries of the scalar can lead to “hairy” solutions.
Cosmic evolution or matter could also lead to scalar “hair”
E. Barausse and T.P.S., Phys. Rev. Lett. 101, 099001 (2008).
A. Arvanitaki and S. Dubovksy, Phys. Rev. D 83, 044026 (2011) R. Brito, V. Cardoso and P. Pani, Lect.Notes Phys. 906, 1 (2015)
T. Jacobson, Phys. Rev. Lett. 83, 2699 (1999); M. W. Horbatsch and C. P. Burgess, JCAP 1205, 010 (2012). V. Cardoso, I. P. Carucci, P. Pani and T. P. S., Phys. Rev. Lett. 111, 111101 (2013)
C. A. R. Herdeiro and E. Radu, Phys. Rev. Lett. 112, 221101 (2014).
Thomas P. Sotiriou – DAMTP, September 23rd and 24th, 2019
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Generalized Galileons
One can actually have terms in the action with more than 2 derivatives and still have second order equations:
Inspired by galileons: scalars that enjoy galilean symmetry
It includes well-know terms, such asA. Nicolis, R. Rattazzi and E. Trincherini, Phys. Rev. D 79, 064036 (2009)
G. W. Horndeski, Int. J. Theor. Phys. 10, 363 (1974) C. Deffayet et al., Phys. Rev. D 80, 064015 (2009)
P. Kanti et al., Phys. Rev. D 54, 5049 (1996).
Known “hairy” solutions! For example, for the coupling
Thomas P. Sotiriou – DAMTP, September 23rd and 24th, 2019
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No-hair for shift-symmetric generalised galileons
L. Hui, A. Nicolis, Phys. Rev. Lett. 110, 241104 (2013).
Staticity and spherical symmetry Asymptotic flatness must be finite on the horizon Restrictions on the dependence of on
Generalized Galileons
Assumptions:
Straightforward generalisation to slowly-rotating solutions
Hairy black holes with (linearly) time-dependent hair exist
T.P.S. and S.-Y. Zhou, Phys. Rev. Lett. 112, 251102 (2014);� Phys. Rev. D 90, 124063 (2014).
E. Babichev and C. Charmousis, JHEP 1408, 106 (2014)
Thomas P. Sotiriou – DAMTP, September 23rd and 24th, 2019
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A simple exception
Consider the action
The corresponding scalar equation is
The Gauss-Bonnet term does not vanish in BH spacetimes!
T.P.S. and S.-Y. Zhou, Phys. Rev. Lett. 112, 251102 (2014);� Phys. Rev. D 90, 124063 (2014).
See also: P. Kanti et al., PRD 54, 5049 (1996).
Thomas P. Sotiriou – DAMTP, September 23rd and 24th, 2019
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Perturbative solution
To first order in
metric is Schwarzschild
non-trivial scalar profile:
Singular scalar on the horizon!
Regularity on the horizon implies
The scalar charge is fixed to be
Thomas P. Sotiriou – DAMTP, September 23rd and 24th, 2019
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Non-perturbative effects
The finite area singularity is not present in the perturbative solution
Black holes have a minimum size!
Perturbative treatments breaks down at roughly the radius of the naked singularity
Thomas P. Sotiriou – DAMTP, September 23rd and 24th, 2019
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Dynamical formation of hair
First evidence that hair form from collapse�
Stars have zero scalar charge
R. Benkel, T.P.S. and H. Witek, PRD 94 (R), 121503 (2016);� CQG 34, 064001 (2017)
N. Yunes and L. C. Stein, PRD 83, 104002 (2011).
Thomas P. Sotiriou – DAMTP, September 23rd and 24th, 2019
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Black hole scalarization
No-hair theorem for the action
provided that ,
That is, for the equation
trivial solutions are unique if admissible, if the effective mass is positive
But if it is negative then there can be“scalarization”!
H. O. Silva, J. Sakstein, L. Gualtieri, T.P.S, and E. Berti, PRL 120, 131104 (2018)
See also: D. D. Doneva and S. S. Yazadjiev, PRL 120, 131103 (2018)
Thomas P. Sotiriou – DAMTP, September 23rd and 24th, 2019
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Nonlinear quenching
❖ Quadratic coupling (minimal model) leads to radially unstable scalarized solutions
❖ Exponential coupling is not
❖ quadratic coupling scalar EOM linear in the scalar
❖ large metric backreaction necessary to quench the instability
❖ …or nonlinearity in the scalar, e.g. standard �potential term will do!
Explanation:J. L. Blazquez-Sacedo et al., Phys. Rev. D 98, 084011 (2018)
H. O. Silva et al., arXiv:1812.05590 [gr-qc]
C. F. B. Macedo et al., arXiv:190306784 [gr-qc]
Thomas P. Sotiriou – DAMTP, September 23rd and 24th, 2019
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Models of scalarization
❖ and lead to DEF model
❖ trades the��coupling for a disformal coupling with matter
Minimal action for tachyonic instability
Most general up to field redefinition and nonlinear completion:
N. Andreou, N. Franchini, G. Ventagli, and T.P.S, arXiv:1904.06365 [gr-qc]
Thomas P. Sotiriou – DAMTP, September 23rd and 24th, 2019
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Perspectives
Scalarization might be the mechanism that “screens” new physics at low curvatures
Basic principle: a linear instability in strong field quenched by nonlinear effects
Others fields? Vectorisation, tensorisation
Other instabilities?
nonlinear terms
F. M. Ramazanoglu, Phys. Rev. D 96, 064009 (2017) L. Annulli, V. Cardoso, L. Gualtieri, Phys. Rev. D 99, 044038 (2019) …
F. M. Ramazanoglu, Phys. Rev. D 97, 024008 (2018)�C. A. R. Herdeiro and E. Radu, Phys. Rev. D 99, 084039 (2019)�…
Thomas P. Sotiriou – DAMTP, September 23rd and 24th, 2019
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Testing gravity
Lorentz symmetry �Einstein-aether theory, Horava gravity
Mass of the graviton �massive and bimetric gravity
Parity �dynamical Chern-Simons gravity
Looking under the lamppost approach:
Testing principles approach:
E.g. most general scalar-tensor theory
Thomas P. Sotiriou – DAMTP, September 23rd and 24th, 2019
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Einstein-aether theory
The action of the theory is
where
and the aether is implicitly assumed to satisfy the constraint
Most general theory with a unit timelike vector field which is second order in derivatives
T. Jacobson and D. Mattingly, PRD 64, 024028 (2001).
Thomas P. Sotiriou – DAMTP, September 23rd and 24th, 2019
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Hypersurface orthogonality
Now assume
and choose as the time coordinate
Replacing in the action and defining one gets
with and the parameter correspondence
T. Jacobson, PRD 81, 101502 (2010).
Thomas P. Sotiriou – DAMTP, September 23rd and 24th, 2019
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Horava-Lifshitz gravity
The action of the theory is
where
contains all 6th order terms constructed in the same way
contains all 4th order terms constructed with the induced metric and
P. Hořava, PRD 79, 084008 (2009)�D. Blas, 0. Pujolas and S. Sibiryakov, PRL 104, 181302 (2010)
Thomas P. Sotiriou – DAMTP, September 23rd and 24th, 2019
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LV theories in brief
Einstein-aether theoryField content: metric , aether (preferred ‘threading’) Dispersion: Linear UV completion: unknown
Hořava gravityField content: metric , scalar (preferred foliation) Dispersion: non-linear UV completion: known
Thomas P. Sotiriou – DAMTP, September 23rd and 24th, 2019
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LV with linear dispersion relations : effective metrics
…and multiple horizons.
LV with non-linear dispersion relations
space
time
P
Past
Future Simultaneous
…‘universal horizons’. E. Barausse, T. Jacobson and T.P.S., PRD 83, 124043 (2011)�
D. Blas and S. Sibiryakov, PRD 84, 124043 (2011)�M. Colombo, J. Bhattacharyya, and T.P.S., CQG 33, 235003 (2016).
Thomas P. Sotiriou – DAMTP, September 23rd and 24th, 2019
Causal structure
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Spherical collapse
One can make the ansatz
and then the “ -equation” takes the form
Horava gravity has an instantaneous mode!
The universal horizon corresponds to
This foliation was used for simulations �
It does not penetrate the horizon!D. Garfinkle, C. Eling and T. Jacobson, Phys. Rev. D 76, 024003 (2007)
J. Bhattacharyya, A. Coates, M. Colombo, and T.P.S., Phys. Rev. D 93, 064056 (2016).
Thomas P. Sotiriou – DAMTP, September 23rd and 24th, 2019
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Spacetime diagramSi
ngul
arit
y
Universal Horizon Killing Horizon
Constant preferred time
E. Barausse, T. Jacobson and T.P.S., PRD 83, 124043 (2011)
Thomas P. Sotiriou – DAMTP, September 23rd and 24th, 2019
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Penrose diagram
Taken from D. Blas and S. Sibiryakov, Phys. Rev. D 84, 124043 (2011)
Universal HorizonT
Thomas P. Sotiriou – DAMTP, September 23rd and 24th, 2019
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Propagation effects
Strong bound on the mass of the graviton, , But marginally interesting from a theory perspective Weak bounds on in eV range Strong constraint from BNS and EM
This rules out several dark energy models that predict
But we can do better in constraining Lorentz violations by looking for other polarisations!
T.P.S., Phys. Rev. Lett. 120, 041104 (2018);�A. E. Gumrukcuoglu, M. Saravani and T.P.S., Phys. Rev. D 97, 024032 (2018).
Thomas P. Sotiriou – DAMTP, September 23rd and 24th, 2019
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Combined ConstraintsHořava gravity
A. E. Gumrukcuoglu, M. Saravani and T.P.S., PRD 97, 024032 (2018)
Thomas P. Sotiriou – DAMTP, September 23rd and 24th, 2019
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Modeling beyond GR
We need to know what to expect
Parametrizations have limited range of validity
They only get us half way there - they need interpretation in terms of a theory
They give us a false sense of achievement - constraints can be meaningless or not independent
Calibration
We need precision
Why do we need it?
Thomas P. Sotiriou – DAMTP, September 23rd and 24th, 2019
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NR beyond GR: open issues
Establishing well-posedness: Existence, uniqueness and continuous dependence on initial data
Interpreting well/ill-posedness in the context of effective field theory (EFT)
Numerical challenges associated with the above and with having extra fields
Thomas P. Sotiriou – DAMTP, September 23rd and 24th, 2019
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Interesting theories tend to look ill-posed, e.g.
Well-posedness
Lorentz symmetry: Einstein-aether theory, Horava gravity �Faster than light propagation
Mass of the graviton: massive and bimetric gravity �Multiple metrics
Parity: dynamical Chern-Simons gravity �3rd order equations
“Screening” requires nonlinearity and derivative interactions which also leads to seemingly ill-posed theories
No-hair theorems also suggest that obviously well-posed theories are unlikely to be very interesting in strong field
Thomas P. Sotiriou – DAMTP, September 23rd and 24th, 2019
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Sometimes things are better than they seem…
Well-posedness
Einstein-aether theory appears to be well-posed�
Sometimes things are complicated… Horava gravity is an elliptic-hyperbolic problem
Sometimes things are probably just bad
O. Sarbach, E. Barausse, and J. A. Preciado-Lopez, Class. Quant. Grav. 36, 165007 (2019)
Most Horndeski theories are not strongly hyperbolic in a generalized harmonic gauge in weak field�
Numerics suggest that they are ill-posed G. Papallo, and H. S. Reall, Phys. Rev. D 96, 044019 (2017)
J. L. Ripley, and F. Pretorius, Phys. Rev. D 99, 084014 (2019)
D. Blas and S. Sibiryakov, Phys. Rev. D 84, 124043 (2011)�M. Colombo, J. Bhattacharyya, and T.P.S, Class. Quant. Grav. 33, 235003 (2016)�J. Bhattacharyya, A. Coates, M. Colombo, and T.P.S., Phys. Rev. D 93, 064056 (2016)
Thomas P. Sotiriou – DAMTP, September 23rd and 24th, 2019
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NR and EFT
Possible ways to “cure” ill-posedness working perturbatively in the coupling��
Israel-Stewart-like approach
Other?
R. Benkel, T.P.S. and H. Witek, Phys. Rev. D 94 (R), 121503 (2016);� Class. Quant. Grav. 34, 064001 (2017)�M. Okounkova et al., Phys. Rev. D 96, 044020 (2017) H. Witek, L. Gualtieri, P. Pani and T.P.S., Phys. Rev. D 99, 064035 (2019)�M. Okounkova et al., arXiv:1906.08789 [gr-qc]
J. Cayuso, N. Ortiz, and L. Lehner, Phys. Rev. D 96, 084043 (2017)
Can we afford to toss away ill-posed theories? Theories with heavy ghost are examples of “sick”
theories that we use and interpret as EFTs
Thomas P. Sotiriou – DAMTP, September 23rd and 24th, 2019
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Perspectives
GW observations are probing the strong gravity regime
Future detectors will lead to an era of “precision gravity”
…so, there is real motivation for studying the non-linear, dynamical regime beyond GR and probe fundamental physics
Eventually we will need to break degeneracies between astrophysics and fundamental physics
…but we will need new (effective) theories
and we will need to learn how to model systems within these theories
Thomas P. Sotiriou – DAMTP, September 23rd and 24th, 2019