Brout-Englert-Higgs monopoles: particlelike solutions in modified gravity Sandrine Schl¨ ogel UNamur (naXys) & UCLouvain (CP3) FFP14 - July 17, 2014 Particlelike distributions of the Higgs field nonminimally coupled to gravity, A. F¨ uzfa, M. Rinaldi, S.S. , PRL 111 (2013) 121103 Particlelike solutions of modified gravity: the Higgs monopoles, S.S., M. Rinaldi, F. Staelens, A. F¨ uzfa , arXiv:1405.5476 (accepted by PRD) S. Schl¨ ogel (UNamur-UCL) BEH monopoles FFP14 - July 17, 2014 1 / 15
Motivations General relativity (GR) and the Standard Model cannot explain (satisfactorily) Current cosmic acceleration without coincidence issues Dark matter effects Flatness and horizon problems ( primordial inflation ) ... but never been faulted by observations/experiments as well ! − → Modified gravity ( scalar-tensor theory , F(R), massive gravity, extra dimensions...)? Constraints on deviations from GR Solar-system constraints (e.g. Cassini probe) Astrophysical tests (e.g. binary pulsar) Experimental tests (e.g. torsion balance) S. Schl¨ ogel (UNamur-UCL) BEH monopoles FFP14 - July 17, 2014 2 / 15
BEH field, partner of the metric? Why the BEH field? Only fundamental scalar field detected (up to now) Elementary particles mass generation Partner to gravity? Some simplifications Unitary gauge � � 1 0 φ ( x ) = √ v + h ( x ) 2 Coupling between the BEH field to matter in modified gravity not considered so far Greenwood, Kaiser, Sfakianakis, PRD 87 (2013): 064021 Rinaldi, Eur.Phys.J.Plus (2014) 129: 56 S. Schl¨ ogel (UNamur-UCL) BEH monopoles FFP14 - July 17, 2014 3 / 15
(New) Higgs inflation (New) Higgs inflation The Standard Model Higgs boson as the inflaton, Phys. Lett. B 659 (2008) 703, F. L. Bezrukov and M. Shaposhnikov S. Schl¨ ogel (UNamur-UCL) BEH monopoles FFP14 - July 17, 2014 4 / 15
(New) Higgs inflation Viable inflation? New Higgs inflation (2008): Very early model (’80): ”minimally coupled BEH field” ”non-minimally coupled BEH field” m 2 m 2 R − 1 16 π R − 1 2 ( ∂φ ) 2 − V ( φ ) 2 ( ∂φ ) 2 − V ( φ ) pl pl � 1 + ξφ 2 � L = L = 16 π S. Schl¨ ogel (UNamur-UCL) BEH monopoles FFP14 - July 17, 2014 5 / 15
(New) Higgs inflation New Higgs inflation, a viable model? Constraint: Non-minimal coupling ξ > 10 4 At high energy: equivalent to R 2 inflation Favoured by Planck data Ruled out by BICEP 2 results (no tensor modes) Planck 2013 results. J. Martin, C. Ringeval, V. Venin XXII. Constraints on inflation arXiv:1303.3787 S. Schl¨ ogel (UNamur-UCL) BEH monopoles FFP14 - July 17, 2014 6 / 15
Higgs monopoles Higgs monopoles S. Schl¨ ogel (UNamur-UCL) BEH monopoles FFP14 - July 17, 2014 7 / 15
Higgs monopoles Introduction Solutions in static spherically symmetric spacetime � � m 2 1 + ξ R − 1 2 ( ∂ H ) 2 − V ( H )+ L mat [ ψ m , g µ ν ] pl H 2 L = 16 π m 2 pl H = m pl h ˜ v , v = 246 GeV / m pl ˜ with V ( H ) = λ H 2 − v 2 � 2 � 4 Standard Model potential parameters Matter = top-hat density profile Distribution of the BEH field around compact objects? Deviations from GR? S. Schl¨ ogel (UNamur-UCL) BEH monopoles FFP14 - July 17, 2014 8 / 15
Higgs monopoles Effective dynamics Klein-Gordon equation � h = − dV eff dh with V eff = − V + ξ h 2 R 16 π In cosmology (FLRW metric, scale factor a ( t ) ) d 2 h dt 2 + 3 da dh dt = dV eff a dt dh h=1 For compact objects (Schwarzschild coordinates) � � λ ′ − ν ′ − 2 − dV eff h ′′ − h ′ = r dh S. Schl¨ ogel (UNamur-UCL) BEH monopoles FFP14 - July 17, 2014 9 / 15
Higgs monopoles Higgs monopole solutions ξ = 10, m = 10 6 kg , s = 0 . 75 Particlelike solutions: 1.5 Convergence towards the vev Globally regular Finite energy 1 Asympotically flat Higgs field (vev) In GR, unrealistic homogeneous solution only 0.5 ( h = 1 everywhere) Parameters Compactness s = r s R with 0 r s , the Schwarzschild radius and R , the radius Baryonic mass m −0.5 −4 −2 0 2 4 10 10 10 10 10 Non-minimal coupling ξ r/r S S. Schl¨ ogel (UNamur-UCL) BEH monopoles FFP14 - July 17, 2014 10 / 15
Higgs monopoles Monopole family 8 D 6 ξ h c m s 10 3 kg 10 4 0 . 1 A - 5.37 4 10 6 kg 0 . 88 B - 0.21 10 10 6 kg 10 6 2 C 1.077 0 . 01 C 10 4 kg h 0 . 47 D 7.88 60 0 B Notice: no astrophysical objects −2 −4 A −6 −2 0 2 4 10 10 10 10 r/r S S. Schl¨ ogel (UNamur-UCL) BEH monopoles FFP14 - July 17, 2014 11 / 15
Higgs monopoles Deviations from GR ξ = 60, s = 0 . 2 (neutron star) Astrophysical objects: h c − → 1 2.5 No observable deviations from GR with SM potential parameters 2 Even for big values of ξ h c Vev vs Planck scale 1.5 (”hierarchy problem”) 1 Only one solution, different 5 6 7 8 9 10 10 10 10 10 10 10 m than GR ! S. Schl¨ ogel (UNamur-UCL) BEH monopoles FFP14 - July 17, 2014 12 / 15
Higgs monopoles Amplification mechanism (I) m = 10 3 kg ξ = 64 . 6 (solid line) ξ = 64 . 7 (dotted line) 20000 120 100 15000 80 h c 60 40 10000 h c 20 5000 64 62 60 58 0.8 56 0.6 0 54 0.4 52 0.2 50 ξ s 0.44 0.45 0.46 0.47 0.48 0.49 0.5 0.51 0.52 0.53 s S. Schl¨ ogel (UNamur-UCL) BEH monopoles FFP14 - July 17, 2014 13 / 15
Higgs monopoles Amplification mechanism (II) m = 10 2 kg, ξ = 10 4 20 15 10 5 h c 0 −5 −10 Critical ξ : h c − → ∞ for some s (or R ) −15 Phase transition h ∞ − → ± 1 −20 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 Constraint on ξ : forbidden s (or R ) s → No (monopole) solution ! S. Schl¨ ogel (UNamur-UCL) BEH monopoles FFP14 - July 17, 2014 14 / 15
Higgs monopoles Conclusions and perspectives Conclusion: New particlelike solution: Higgs monopole Different than GR and usual scalar-tensor theory (no potential) Negligible deviations from GR (SM potential parameters) General amplification mechanism Perspectives: Coupling BEH field to matter (cosmology and compact objects) Unitary gauge Possible formation during gravitational collapse and stability? Remnants? Generalization of amplification mechanism (other potential) Application to boson stars S. Schl¨ ogel (UNamur-UCL) BEH monopoles FFP14 - July 17, 2014 15 / 15
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