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 23 rd and 24 th , 2019
Probing a new regime? taken from arXiv:1903.09221 Thomas P. Sotiriou – DAMTP, September 23 rd and 24 th , 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 23 rd and 24 th , 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 23 rd and 24 th , 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 23 rd and 24 th , 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 � K. Yagi and N. Yunes, Science 341, 365-368 (2013) � G. Pappas and T. Apostolatos, PRL 112, 121101 (2014) Moments related to observables in scalar-tensor theories G. Pappas and T.P.S., PRD 91, 044011 (2015); � MNRAS 453, 2862-2876 (2015) …but it assumes that the microphysics is unaffected. A. Coates, M. Horbatsch and T.P.S., PRD 95, 084003 (2017); � A. Coates, N. Franchini and T.P.S., PRD 97, 064013 (2018). Thomas P. Sotiriou – DAMTP, September 23 rd and 24 th , 2019
Testing gravity Testing principles approach: 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: E.g. most general scalar-tensor theory Thomas P. Sotiriou – DAMTP, September 23 rd and 24 th , 2019
Brans-Dicke theory The action of the theory is and the corresponding field equations are Solutions with constant are admissible and are GR solutions. Thomas P. Sotiriou – DAMTP, September 23 rd and 24 th , 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 23 rd and 24 th , 2019
Scalar-tensor theory Jordan frame action: Redefinitions: Einstein frame action: Thomas P. Sotiriou – DAMTP, September 23 rd and 24 th , 2019
Screening In spherical symmetry + Einstein frame Effective potentials can designed to yield a large mass locally Known examples: Chameleon J. Khoury and A. Weltman, Phys. Rev. Lett. 93, 171104 (2004) Symmetron K. Hinterbichler and J. Khoury, Phys. Rev. Lett. 104, 231301 (2010) Thomas P. Sotiriou – DAMTP, September 23 rd and 24 th , 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 In Einstein frame 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) Thomas P. Sotiriou – DAMTP, September 23 rd and 24 th , 2019
Tachyonic instability Severely constrained by binary pulsar tests, unless there is a mass. This model only works for stars Taken from G. Esposito-Farese, arXiv:gr-cq/0402007 Thomas P. Sotiriou – DAMTP, September 23 rd and 24 th , 2019
Scalarization and matter Matter can induce scalarization of black holes V. Cardoso, I. P. Carucci, P. Pani and T. P. S., Phys. Rev. Lett. 111, 111101 (2013); Phys. Rev. D 88, 044056 (2013). Scalarization can drive a gravitational Higgs mechanism: suitably coupling to matter leads to strong gravity deviations from the Standard Model. 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 23 rd and 24 th , 2019
Scalar fields in BH spacetimes The equation admits only the trivial solution in a BH spacetime that is stationary, as the endpoint of collapse asymptotically flat, i.e. isolated S.W. Hawking, Comm. Math. Phys. 25, 152 (1972). 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 23 rd and 24 th , 2019
No difference from GR? Actually there is... Perturbations are different! E. Barausse and T.P.S., Phys. Rev. Lett. 101, 099001 (2008). They even lead to new effects, e.g. superradiance A. Arvanitaki and S. Dubovksy, Phys. Rev. D 83, 044026 (2011) R. Brito, V. Cardoso and P. Pani, Lect.Notes Phys. 906, 1 (2015) In general, relaxing the symmetries of the scalar can lead to “ hairy ” solutions. C. A. R. Herdeiro and E. Radu, Phys. Rev. Lett. 112, 221101 (2014). Cosmic evolution or matter could also lead to scalar “ hair ” 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) Thomas P. Sotiriou – DAMTP, September 23 rd and 24 th , 2019
Generalized Galileons G. W. Horndeski, Int. J. Theor. Phys. 10, 363 (1974) C. Deffayet et al., Phys. Rev. D 80, 064015 (2009) 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 A. Nicolis, R. Rattazzi and E. Trincherini, Phys. Rev. D 79, 064036 (2009) It includes well-know terms, such as Known “ hairy ” solutions! For example, for the coupling P. Kanti et al., Phys. Rev. D 54, 5049 (1996). Thomas P. Sotiriou – DAMTP, September 23 rd and 24 th , 2019
Generalized Galileons No-hair for shift-symmetric generalised galileons Assumptions: 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 Straightforward generalisation to slowly-rotating solutions T.P.S. and S.-Y. Zhou, Phys. Rev. Lett. 112, 251102 (2014); � Phys. Rev. D 90, 124063 (2014). Hairy black holes with (linearly) time-dependent hair exist E. Babichev and C. Charmousis, JHEP 1408, 106 (2014) Thomas P. Sotiriou – DAMTP, September 23 rd and 24 th , 2019
A simple exception T.P.S. and S.-Y. Zhou, Phys. Rev. Lett. 112, 251102 (2014); � Phys. Rev. D 90, 124063 (2014). Consider the action The corresponding scalar equation is The Gauss-Bonnet term does not vanish in BH spacetimes! See also: P. Kanti et al., PRD 54, 5049 (1996). Thomas P. Sotiriou – DAMTP, September 23 rd and 24 th , 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 23 rd and 24 th , 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 of the naked singularity Thomas P. Sotiriou – DAMTP, September 23 rd and 24 th , 2019
Dynamical formation of hair First evidence that hair form from collapse � R. Benkel, T.P.S. and H. Witek, PRD 94 (R), 121503 (2016); � CQG 34, 064001 (2017) Stars have zero scalar charge N. Yunes and L. C. Stein, PRD 83, 104002 (2011). Thomas P. Sotiriou – DAMTP, September 23 rd and 24 th , 2019
Black hole scalarization H. O. Silva, J. Sakstein, L. Gualtieri, T.P.S, and E. Berti, PRL 120, 131104 (2018) 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 ” ! See also: D. D. Doneva and S. S. Yazadjiev, PRL 120, 131103 (2018) Thomas P. Sotiriou – DAMTP, September 23 rd and 24 th , 2019
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