Bounds on the Nonminimal Coupling of the Higgs Boson to Gravity

Atkins, Michael; Calmet, Xavier

doi:10.1103/physrevlett.110.051301

Cited by 75 publications

(112 citation statements)

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“…The discovery of the Higgs boson and precision measurements of its couplings to fermions and bosons at the LHC can be used to set a limit on ξ . One finds that |ξ | < 2.6 × 10 15 [13]. Clearly very little is known about the values of c i and ξ .…”

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confidence: 99%

Higgs Starobinsky inflation

2016

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In this paper we point out that Starobinsky inflation could be induced by quantum effects due to a large nonminimal coupling of the Higgs boson to the Ricci scalar. The Higgs Starobinsky mechanism provides a solution to issues attached to large Higgs field values in the early universe which in a metastable universe would not be a viable option. We verify explicitly that these large quantum corrections do not destabilize Starobinsky's potential.The idea that inflation may be due to degrees of freedom already present in the standard model of particle physics or quantum general relativity is extremely attractive and has received much attention in the recent years. In particular two models stand out by their simplicity and elegance. Higgs inflation [1][2][3] with a large non-minimal coupling of the Higgs boson H to the Ricci scalar (ξ H † H R) and Starobinsky's inflation model [4] based on R 2 gravity are both minimalistic and perfectly compatible with the latest Planck data.These two models should not be considered as physics beyond the standard model but rather both operators ξ H † H R and R 2 are expected to be generated when general relativity is coupled to the standard model of particle physics. We will come back to that point shortly. The aim of this paper is to point out an intriguing distinct possibility, namely that Starobinsky inflation is generated by quantum effects due to a large non-minimal coupling of the Higgs boson to the Ricci scalar. In that framework, we do not need to posit that the Higgs boson starts at a high field value in the early universe which would alleviate constraints coming from the requirement of having a stable Higgs potential even for large Higgs field values [5][6][7].We shall now argue that both terms necessary for Higgs inflation or Starobinsky's model are naturally present when the standard model of particle physics is coupled to general relativity. While the quantization of general relativity remains one of the outstanding challenges of theoretical a e-mail: x.calmet@sussex.ac.uk b e-mail: ibere.kuntz@sussex.ac.uk physics, it is possible to use effective field theory methods below the energy scale M at which quantum gravitational effects are expected to become large. The energy scale M is usually assumed to be of the order of the Planck scale where we have restricted our considerations to dimension four operators which are expected to dominate at least at low energies. Note that we are using the Weyl basis and the following notations: R stands for the Ricci scalar, R μν for the Ricci tensor, E = R μνρσ R μνρσ − 4R μν R μν + R 2 , C 2 = E + 2R μν R μν − 2/3R 2 , the dimensionless ξ is the non-minimal coupling of the Higgs boson H to the Ricci scalar, the coefficients c i are dimensionless free parameters, the cosmological constant C is of order of 10 −3 eV, the Higgs boson vacuum expectation value, v = 246 GeV contributes to the value of the Planck scale,L SM contains all the usual standard model interactions (including mass terms for neutrinos), and finally L DM descr...

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confidence: 99%

Higgs Starobinsky inflation

2016

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“…The LHC data can be used to set a limit on the value of the Higgs boson non-minimal coupling to space-time curvature: one finds that |ξ | > 2.6 × 10 15 is excluded at the 95% C.L. [30]. Very little is known about higher dimensional operators.…”

Section: Xavier Calmetmentioning

confidence: 99%

Quantum Black Holes and Effective Quantum Gravity Approaches

Calmet

2015

Springer Proceedings in Physics

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One of the most exciting developments in theoretical physics in the last 20 years has been the realization that the scale of quantum gravity could be in the TeV region instead of the usually assumed 10 19 GeV. Indeed, the strength of gravity can be affected by the size of potential extra-dimensions [1][2][3][4] or the quantum fluctuations of a large hidden sector of particles [5]. A dramatic signal of quantum gravity in the TeV region would be the production of small black holes in high energy collisions of particles at colliders. The possibility of creating small black holes at colliders has led to some wonderful theoretical works on the formation of black holes in the collisions of particles.Long before studying the production of such black holes in the high energy collisions of particles became fashionable, in the 1970's Penrose proved that a closed trapped surface forms when two shockwaves traveling at energies much larger than the Planck scale even when the impact parameter is non-zero. Unfortunately, he never published his work. The result was independently rediscovered by Eardley and Giddings in 2002 [6] when the high energy community started to discuss the formation of black holes at colliders. Earlier estimate of the production cross section had been done using the hoop conjecture. Some did not trust the hoop conjecture, thinking that in the collision of particles the situation was too asymmetrical to trust this conjecture. The paper of Eardley and Giddings settled the issue. Proving the formation of a closed trapped surface is enough to establish gravitational collapse and hence the formation of a black hole. This work was extended by Hsu [7] into the semi-classical region using path integral methods. One could thus claim with confidence that black holes with masses 5 to 20 times the Planck scale, depending on the model of quantum gravity, could form in the collision of particles at the CERN LHC is the Planck scale was low enough. Early phenomenological studies can be found in [8][9][10][11][12][13][14].

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“…This procedure for Einstein-Gauss-Bonnet theory in higher dimensions is not trivial. Fortunately, we can reduce this problem to a Schrödinger type equation (19), with the potential given by…”

Section: Tensor Perturbationsmentioning

confidence: 99%

“…Equation (19) can be solved using the familiar WKB approach, where an approximate WKB solution is found at both regions I and II, and matched with the approximated solution found around the peak of the potential. To reconcile the boundary conditions (21) with the matching, the modes should obey the constraint…”

Section: Scalar Perturbationsmentioning

confidence: 99%

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Quasinormal modes of a black hole with a cloud of strings in Einstein–Gauss–Bonnet gravity

Graça

Salako

Bezerra

2017

Int. J. Mod. Phys. D

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The quasinormal modes for a scalar field in the background spacetime corresponding to a black hole, with a cloud of strings, in Einstein-Gauss-Bonnet gravity, and the tensor quasinormal modes corresponding to perturbations in such spacetime, were both calculated using the WKB approximation. In the obtained results we emphasize the role played by the parameter associated with the string cloud, comparing them with the results already obtained for the Boulware-Deser metric. We also study how the GaussBonnet correction to general relativity affects the results for the quasinormal modes, comparing them with the same background in general relativity.

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Bounds on the Nonminimal Coupling of the Higgs Boson to Gravity

Abstract: We derive the first bound on the value of the Higgs boson non-minimal coupling to the Ricci scalar. We show that the recent discovery of the Higgs boson at the Large Hadron Collider at CERN implies that the non-minimal coupling is smaller than 2.6 × 10 15 .

Cited by 75 publications

References 19 publications

Higgs Starobinsky inflation

Higgs Starobinsky inflation

Quantum Black Holes and Effective Quantum Gravity Approaches

Quasinormal modes of a black hole with a cloud of strings in Einstein–Gauss–Bonnet gravity

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