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Classically Consistent Theories of Interacting Spin-2 Fields
Stockholm University, Faculty of Science, Department of Physics.
2013 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

This doctoral thesis comprises a study of recently developed nonlinear theories for massive spin-2 fields that go by the names of Massive Gravity and Bimetric Theory. As we demonstrate in a Hamiltonian analysis, the construction of these theories avoids the notorious Boulware-Deser ghost instability that generically plagues nonlinear spin-2 interactions and renders their description inconsistent. We explore the mass spectrum of ghost-free Bimetric Theory and reformulate its action in terms of nonlinear mass eigenstates. A generalized version of the theory with multiple vielbein interactions is reviewed and then reexpressed in terms of metrics. Homogeneous and isotropic solutions to the equations of motion in Bimetric Theory are derived and discussed in the context of cosmology. We furthermore single out particular values for the parameters in the bimetric interaction potential for which the theory could potentially contain an additional gauge redundancy. This establishes a unique candidate for a nonlinear theory of a partially massless spin-2 field. Finally, we reveal a close connection of Bimetric Theory to a certain class of higher-curvature theories for gravity and offer a solution to their ghost problems. In particular we find that, in four space-time dimensions, the bimetric candidate for nonlinear partial masslessness is closely related to Conformal Gravity.

Place, publisher, year, edition, pages
Stockholm: Department of Physics, Stockholm University , 2013. , 134 p.
National Category
Physical Sciences
Research subject
Theoretical Physics
Identifiers
URN: urn:nbn:se:su:diva-96167ISBN: 978-91-7447-791-7 (print)OAI: oai:DiVA.org:su-96167DiVA: diva2:663715
Public defence
2013-12-12, sal FA32, AlbaNova Universitetscentrum, Roslagstullsbacken 21, Stockholm, 13:30 (English)
Opponent
Supervisors
Note

At the time of the doctoral defense, the following papers were unpublished and had a status as follows: Paper 4: Submitted. Paper 6: Submitted. Paper 8: Manuscript.

Available from: 2013-11-20 Created: 2013-11-12 Last updated: 2013-11-12Bibliographically approved
List of papers
1. Ghost free massive gravity with a general reference metric
Open this publication in new window or tab >>Ghost free massive gravity with a general reference metric
2012 (English)In: Journal of High Energy Physics (JHEP), ISSN 1126-6708, E-ISSN 1029-8479, no 2, 026- p.Article in journal (Refereed) Published
Abstract [en]

Theories of massive gravity inevitably include an auxiliary reference metric. Generically, they also contain an inconsistency known as the Boulware-Deser ghost. Recently, a family of non-linear massive gravity actions, formulated with a flat reference metric, were proposed and shown to be ghost free at the complete non-linear level. In this paper we consider these non-linear massive gravity actions but now formulated with a general reference metric. We extend the proof of the absence of the Boulware-Deser ghost to this case. The analysis is carried out in the ADM formalism at the complete non-linear level. We show that in these models there always exists a Hamiltonian constraint which, with an associated secondary constraint, eliminates the ghost. This result considerably extends the range of known consistent non-linear massive gravity theories. In addition, these theories can also be used to describe a massive spin-2 field in an arbitrary, fixed gravitational background. We also discuss the positivity of the Hamiltonian.

Keyword
Classical Theories of Gravity, Cosmology of Theories beyond the SM
National Category
Astronomy, Astrophysics and Cosmology
Identifiers
urn:nbn:se:su:diva-80131 (URN)10.1007/JHEP02(2012)026 (DOI)000301451200026 ()
Note

AuthorCount:3;

Available from: 2012-09-18 Created: 2012-09-12 Last updated: 2017-12-07Bibliographically approved
2. Cosmological solutions in bimetric gravity and their observational tests
Open this publication in new window or tab >>Cosmological solutions in bimetric gravity and their observational tests
Show others...
2012 (English)In: Journal of Cosmology and Astroparticle Physics, ISSN 1475-7516, E-ISSN 1475-7516, no 3, 042- p.Article in journal (Refereed) Published
Abstract [en]

We obtain the general cosmological evolution equations for a classically consistent theory of bimetric gravity. Their analytic solutions are demonstrated to generically allow for a cosmic evolution starting out from a matter dominated FLRW universe and relaxing towards a de Sitter (anti-de Sitter) phase at late cosmic time. In particular, we examine a subclass of models which contain solutions that are able to reproduce the expansion history of the cosmic concordance model inspite of the nonlinear couplings of the two metrics. This is demonstrated explicitly by fitting these models to observational data from Type Ia supernovae, Cosmic Microwave Background and Baryon Acoustic Oscillations. In the appendix we comment on the relation to massive gravity.

Keyword
modified gravity, dark energy theory
National Category
Astronomy, Astrophysics and Cosmology
Research subject
Theoretical Physics
Identifiers
urn:nbn:se:su:diva-83245 (URN)10.1088/1475-7516/2012/03/042 (DOI)000302949600042 ()
Available from: 2012-12-06 Created: 2012-12-06 Last updated: 2017-12-07Bibliographically approved
3. Proof of consistency of nonlinear massive gravity in the Stuckelberg formulation
Open this publication in new window or tab >>Proof of consistency of nonlinear massive gravity in the Stuckelberg formulation
2012 (English)In: Physics Letters B, ISSN 0370-2693, E-ISSN 1873-2445, Vol. 715, no 4-5, 335-339 p.Article in journal (Refereed) Published
Abstract [en]

We address some recent concerns about the absence of the Boulware-Deser ghost in the Stuckelberg formulation of nonlinear massive gravity. First we provide general arguments for why any ghost analysis in the Stuckelberg formulation has to agree with existing consistency proofs that have been carried out without using Stuckelberg fields. We then demonstrate the absence of the ghost at the completely nonlinear level in the Stuckelberg formulation of the minimal massive gravity action. The constraint that removes the ghost field and the associated secondary constraint that eliminates its conjugate momentum are computed explicitly, confirming the consistency of the theory in the Stuckelberg formulation.

Keyword
Massive gravity
National Category
Physical Sciences
Research subject
Theoretical Physics
Identifiers
urn:nbn:se:su:diva-81262 (URN)10.1016/j.physletb.2012.07.018 (DOI)000308617500010 ()
Note

AuthorCount:3;

Available from: 2012-10-15 Created: 2012-10-15 Last updated: 2017-12-07Bibliographically approved
4. Metric Formulation of Ghost-Free Multivielbein Theory
Open this publication in new window or tab >>Metric Formulation of Ghost-Free Multivielbein Theory
(English)In: Journal of High Energy Physics (JHEP), ISSN 1126-6708, E-ISSN 1029-8479Article in journal (Refereed) Submitted
Abstract [en]

We formulate the recently proposed ghost-free theory of multiple interacting vielbeins in terms of their corresponding metrics. This is achieved by reintroducing all local Lorentz invariances broken by the multivielbein interaction potential which, in turn, allows us to explicitly separate the gauge degrees of freedom in the vielbeins from the components of the metrics by an appropriate gauge choice. We argue that the gauge choice does not spoil the no-ghost proof of the multivielbein theory, hence the multimetric theory is ghost-free. We further show the on-shell equivalence of the metric and vielbein descriptions, first in general and thereafter in two illustrative examples.

National Category
Physical Sciences
Research subject
Theoretical Physics
Identifiers
urn:nbn:se:su:diva-83248 (URN)
Available from: 2012-12-06 Created: 2012-12-06 Last updated: 2017-12-07Bibliographically approved
5. On Consistent Theories of Massive Spin-2 Fields Coupled to Gravity
Open this publication in new window or tab >>On Consistent Theories of Massive Spin-2 Fields Coupled to Gravity
2013 (English)In: Journal of High Energy Physics (JHEP), ISSN 1126-6708, E-ISSN 1029-8479, no 5, 086- p.Article in journal (Refereed) Published
Abstract [en]

We consider the issues that arise out of interpreting the ghost-free bimetric theory as a theory of a spin-2 field coupled to gravity. This requires identifying a gravitational metric and parameterizing deviations of the resulting theory from general relativity. To this end, we first consider the most general bimetric backgrounds for which a massless and a massive spin-2 fluctuation with Fierz-Pauli mass exist. These backgrounds coincide with solutions in general relativity. Based on this, we obtain nonlinear extensions of the massive and massless spin-2 fields. The background value of the nonlinear massive field parameterizes generic deviations of the bimetric theory from GR. It is also shown that the nonlinear massless field does not have standard ghost-free matter couplings, and hence cannot represent the gravitational metric. However, an appropriate gravitational metric can still be identified in the weak gravity limit. Hence in the presence of other neutral spin-2 fields, the weak gravity limit is crucial for compatibility with general relativity. We also write down the action in terms of the nonlinear massive spin-2 field and obtain its ghost-free couplings to matter. The discussion is then generalized to multimetric theories.

Keyword
Classical Theories of Gravity, Cosmology of Theories beyond the SM
National Category
Physical Sciences
Research subject
Theoretical Physics
Identifiers
urn:nbn:se:su:diva-83250 (URN)10.1007/JHEP05(2013)086 (DOI)000321375600003 ()
Available from: 2012-12-06 Created: 2012-12-06 Last updated: 2017-12-07Bibliographically approved
6. On Partially Massless Bimetric Gravity
Open this publication in new window or tab >>On Partially Massless Bimetric Gravity
(English)In: Journal of High Energy Physics (JHEP), ISSN 1126-6708, E-ISSN 1029-8479Article in journal (Refereed) Submitted
Abstract [en]

We extend the notion of the Higuchi bound and partial masslessness to ghost-free nonlinear bimetric theories. This can be achieved in a simple way by first considering linear massive spin-2 perturbations around maximally symmetric background solutions, for which the linear gauge symmetry at the Higuchi bound is easily identified. Then, requiring consistency between an appropriate subset of these transformations and the dynamical nature of the backgrounds, fixes all but one parameter in the bimetric interaction potential. This specifies the theory up to the value of the Fierz-Pauli mass and leads to the unique candidate for nonlinear partially massless bimetric theory.

National Category
Subatomic Physics Astronomy, Astrophysics and Cosmology
Research subject
Theoretical Physics
Identifiers
urn:nbn:se:su:diva-83251 (URN)
Available from: 2012-12-06 Created: 2012-12-06 Last updated: 2017-12-07Bibliographically approved
7. Bimetric theory and partial masslessness with Lanczos-Lovelock terms in arbitrary dimensions
Open this publication in new window or tab >>Bimetric theory and partial masslessness with Lanczos-Lovelock terms in arbitrary dimensions
2013 (English)In: Classical and quantum gravity, ISSN 0264-9381, E-ISSN 1361-6382, Vol. 30, no 18, 184010- p.Article in journal (Refereed) Published
Abstract [en]

Ghost-free bimetric theories describe nonlinear interactions of massive and massless spin-2 fields and, hence, provide a natural framework for investigating the phenomenon of partial masslessness for massive spin-2 fields at the nonlinear level. In this paper we analyse the spectrum of the ghost-free bimetric theory in arbitrary dimensions. Using a recently proposed construction, we identify the candidate nonlinear partially massless (PM) theories. It is shown that, in a 2-derivative setup, nonlinear PM theories can exist only in three and four dimensions. But on adding Lanczos-Lovelock terms to the bimetric action it is found that higher derivative nonlinear PM theories could also exist in higher dimensions. This is consistent with existing results on the direct construction of cubic vertices with PM gauge symmetry. We obtain the candidate nonlinear PM theories in five, six and eight dimensions but find that none exist in seven dimensions.

National Category
Astronomy, Astrophysics and Cosmology
Identifiers
urn:nbn:se:su:diva-94859 (URN)10.1088/0264-9381/30/18/184010 (DOI)000324236700011 ()
Note

AuthorCount:3;

Available from: 2013-10-17 Created: 2013-10-16 Last updated: 2017-12-06Bibliographically approved
8. Higher Derivative Gravity and Conformal Gravity From Bimetric and Partially Massless Bimetric Theory
Open this publication in new window or tab >>Higher Derivative Gravity and Conformal Gravity From Bimetric and Partially Massless Bimetric Theory
(English)Manuscript (preprint) (Other academic)
National Category
Natural Sciences Astronomy, Astrophysics and Cosmology
Identifiers
urn:nbn:se:su:diva-96166 (URN)
Available from: 2013-11-12 Created: 2013-11-12 Last updated: 2013-11-14Bibliographically approved

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