Alternative theories and lternative theories and gravitational - - PowerPoint PPT Presentation

Alternative theories and lternative theories and gravitational waves 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?

Thomas P. Sotiriou – DAMTP, September 23rd and 24th, 2019

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

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

Extracting new physics

Step-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

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

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

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

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

Scalar-tensor theory

Jordan frame action: Redefinitions: Einstein frame action:

Thomas P. Sotiriou – DAMTP, September 23rd and 24th, 2019

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

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

Thomas P. Sotiriou – DAMTP, September 23rd and 24th, 2019

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

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

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

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

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 as

• A. 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

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

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

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

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

• f the naked singularity

Thomas P. Sotiriou – DAMTP, September 23rd and 24th, 2019

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

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

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

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

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

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

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

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

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

LV theories in brief

Einstein-aether theory Field content: metric , aether (preferred ‘threading’) Dispersion: Linear UV completion: unknown Hořava gravity Field content: metric , scalar (preferred foliation) Dispersion: non-linear UV completion: known

Thomas P. Sotiriou – DAMTP, September 23rd and 24th, 2019

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

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

Spacetime diagram

Singularity 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

Penrose diagram

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

Universal Horizon T

Thomas P. Sotiriou – DAMTP, September 23rd and 24th, 2019

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

Combined Constraints

Hořava gravity

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

Thomas P. Sotiriou – DAMTP, September 23rd and 24th, 2019

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

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

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

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

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

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