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Massive Gravity in de Sitter Space via Gravitational Higgs Mechanism
High Energy Physics - Theory · Submitted 14 Jul 2010
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim This suggests that no ghost might be present for lower graviton mass values and the full nonlinear theory might be unitary for all values of the graviton mass and the Hubble parameter with no van Dam-Veltman-Zakharov discontinuity.
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In this paper we discuss massive gravity in de Sitter space via gravitational Higgs mechanism, which provides a nonlinear definition thereof. The Higgs scalars are described by a nonlinear sigma model, which includes higher derivative terms required to obtain the Fierz-Pauli mass term. Using the aforesaid non-perturbative definition, we address appearance of an enhanced local symmetry and a null norm state in the linearized massive gravity in de Sitter space at the special value of the graviton mass to the Hubble parameter ratio. By studying full non-perturbative equations of motion, we argue that there is no enhanced symmetry in the full nonlinear theory. We then argue that in the full nonlinear theory no null norm state is expected to arise at the aforesaid special value. This suggests that no ghost might be present for lower graviton mass values and the full nonlinear theory might be unitary for all values of the graviton mass and the Hubble parameter with no van Dam-Veltman-Zakharov discontinuity. We argue that this is indeed the case by studying full nonlinear Hamiltonian for the relevant conformal and helicity-0 longitudinal modes. In particular, we argue that no negative norm state is present in the full nonlinear theory.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | In this paper we discuss massive gravity in de Sitter space via gravitational Higgs mechanism, which provides a nonlinear definition thereof. | contribution 0.95 | 0.78 | 0.06 | asserted 0.98 |
| s1 | The Higgs scalars are described by a nonlinear sigma model, which includes higher derivative terms required to obtain the Fierz-Pauli mass term. | method 0.93 | 0.43 | 0.02 | asserted 1.00 |
| s2 | Using the aforesaid non-perturbative definition, we address appearance of an enhanced local symmetry and a null norm state in the linearized massive gravity in de Sitter space at the special value of the graviton mass to the Hubble parameter ratio. | contribution 0.76 | 0.85 | 0.07 | asserted 0.95 |
| s3 | By studying full non-perturbative equations of motion, we argue that there is no enhanced symmetry in the full nonlinear theory. | result 0.97 | 0.92 | 0.25 | asserted 0.72 |
| s4 | We then argue that in the full nonlinear theory no null norm state is expected to arise at the aforesaid special value. | result 0.95 | 0.83 | 0.17 | hedged possibility 0.68 |
| s5 | This suggests that no ghost might be present for lower graviton mass values and the full nonlinear theory might be unitary for all values of the graviton mass and the Hubble parameter with no van Dam-Veltman-Zakharov discontinuity. | interpretation 0.99 | 0.49 | 0.38 | hedged possibility 0.84 |
| s6 | We argue that this is indeed the case by studying full nonlinear Hamiltonian for the relevant conformal and helicity-0 longitudinal modes. | method 0.79 | 0.92 | 0.18 | asserted 0.88 |
| s7 | In particular, we argue that no negative norm state is present in the full nonlinear theory. | result 0.99 | 0.88 | 0.31 | asserted 0.84 |
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Original abstract
In this paper we discuss massive gravity in de Sitter space via gravitational Higgs mechanism, which provides a nonlinear definition thereof. The Higgs scalars are described by a nonlinear sigma model, which includes higher derivative terms required to obtain the Fierz-Pauli mass term. Using the aforesaid non-perturbative definition, we address appearance of an enhanced local symmetry and a null norm state in the linearized massive gravity in de Sitter space at the special value of the graviton mass to the Hubble parameter ratio. By studying full non-perturbative equations of motion, we argue that there is no enhanced symmetry in the full nonlinear theory. We then argue that in the full nonlinear theory no null norm state is expected to arise at the aforesaid special value. This suggests that no ghost might be present for lower graviton mass values and the full nonlinear theory might be unitary for all values of the graviton mass and the Hubble parameter with no van Dam-Veltman-Zakharov discontinuity. We argue that this is indeed the case by studying full nonlinear Hamiltonian for the relevant conformal and helicity-0 longitudinal modes. In particular, we argue that no negative norm state is present in the full nonlinear theory.
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References
How the literature uses it
6 arXiv papers cite this in 35 sentences
Papers citing it · 21 sentences without a confident label
Builds on it 1 paper
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This is a generalization of the setup of [ref] for the gravitational Higgs mechanism in the de Sitter space to a general background.
Non-perturbative Massive Solutions in Gravitational Higgs Mechanism · Gravitational Higgs Mechanism · 1.00
Cites it as support 3 papers
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Non-perturbatively, even for $β≠1$, the Hamiltonian is bounded from below and the perturbative ghost is merely an artifact of linearization [ref] .[ The full non-perturbative Hamiltonian for the model of [ref] , which has $β=1/2$, in the gravitational Higgs mechanism framework was constructed in [ref] and is expressly positive-definite.
Non-perturbative Massive de Sitter Solutions · Introduction and Summary · 1.00
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As was argued in [ref] , while for $β≠1$ the trace $h$ is a ghost, this is a mere artifact of linearization and non-perturbatively the Hamiltonian is bounded from below.
No vDVZ Discontinuity in Non-Fierz-Pauli Theories · Comments · 0.99
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The non-perturbative Hamiltonian for the relevant degrees of freedom (that is, the conformal and helicity-0 modes) is bounded from below even if $β≠1$ (i.e., when perturbatively the graviton mass term is not of the Fierz-Pauli form and perturbatively the theory is naively non-unitary) [ref] .
Massive Gravity in Extra Dimensions · Why Is the Tensor Structure $(D-1)$-dimensional? · 0.99
Cites it as background 3 papers
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In this section we very briefly review gravitational Higgs mechanism in curved backgrounds – de Sitter was discussed in [ref] , and the general case in [ref] .
Non-perturbative Massive de Sitter Solutions · Gravitational Higgs Mechanism · 1.00
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The graviton acquires mass via spontaneous breaking of the underlying general coordinate reparametrization invariance by scalar vacuum expectation values.[For earlier and subsequent related works, see, e.g., [ref] , and references therein.] In this paper, motivated by the results of [ref] for the gravitational Higgs mechanism in de Sitter space, we study the issue of unitarity of the gravitational Higgs mechanism in the Minkowski background within the setup of [ref] .
Non-perturbative Unitarity of Gravitational Higgs Mechanism · Introduction and Summary · 0.97
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See [ref] for some other aspects of massive gravity on curved space.
Theoretical Aspects of Massive Gravity · Fierz-Pauli gravitons on curved space and partially massless theories · 0.98
What it cites · 16 sentences without a confident label
Compares with 1 paper
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We have been working with ([ref]), while the aforesaid result of [ref] applies to ([ref]).
Gauge Invariances and Phases of Massive Higher Spins in (A)dS · Is there a Ghost? · 0.96
Cites as background 26 papers
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Similarly, components of the massless particle associated with general coordinate reparametrization invariance, the graviton, could acquire mass via gravitational Higgs mechanism [ref] upon spontaneous breaking of diffeomorphism invariance by scalar vacuum expectation values[For earlier and subsequent related works, see, e.g., [ref] , and references therein.].
Massive gravity and structure formation · Introduction and Summary · 0.92
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Similarly, components of the massless particle associated with general coordinate reparametrization invariance, the graviton, could acquire mass via gravitational Higgs mechanism [ref] upon spontaneous breaking of diffeomorphism invariance by scalar vacuum expectation values[For earlier and subsequent related works, see, e.g., [ref] , and references therein.].
Higgs Phenomenon for 4-D Gravity in Anti de Sitter Space · Introduction and Summary · 0.92
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Similarly, components of the massless particle associated with general coordinate reparametrization invariance, the graviton, could acquire mass via gravitational Higgs mechanism [ref] upon spontaneous breaking of diffeomorphism invariance by scalar vacuum expectation values[For earlier and subsequent related works, see, e.g., [ref] , and references therein.].
Effective Field Theory for Massive Gravitons and Gravity in Theory Space · Introduction and Summary · 0.92
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