Alternative theories and gravitational waves · E. Babichev and C. Charmousis, JHEP 1408, 106...

Alternative theories and gravitational waves

Thomas P. Sotiriou

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

taken from arXiv:1903.09221

Probing a new regime?


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!


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!


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


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.


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


Brans-Dicke theory

Solutions with constant are admissible and are GR solutions.

The action of the theory is

and the corresponding field equations are


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


Scalar-tensor theory

Jordan frame action:

Redefinitions:

Einstein frame action:


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)


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


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


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)


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)


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).


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


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)


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).


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


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


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).


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)


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]


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]


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)�…


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


Einstein-aether theory


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).


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).


Horava-Lifshitz gravity


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)


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


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).


Causal structure

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).


Spacetime diagramSi

ngul

arit

y

Universal Horizon Killing Horizon

Constant preferred time

E. Barausse, T. Jacobson and T.P.S., PRD 83, 124043 (2011)


Penrose diagram

Taken from D. Blas and S. Sibiryakov, Phys. Rev. D 84, 124043 (2011)

Universal HorizonT


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).


Combined ConstraintsHořava gravity

A. E. Gumrukcuoglu, M. Saravani and T.P.S., PRD 97, 024032 (2018)


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?


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


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


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)


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


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


Alternative theories and gravitational waves · E. Babichev and C. Charmousis, JHEP 1408, 106...

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