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Proof of consistency of nonlinear massive gravity in the Stuckelberg formulation
Stockholm University, Faculty of Science, Department of Physics.
Stockholm University, Faculty of Science, Department of Physics. Stockholm University, Faculty of Science, The Oskar Klein Centre for Cosmo Particle Physics (OKC).
Stockholm University, Faculty of Science, Department of Physics. Stockholm University, Faculty of Science, The Oskar Klein Centre for Cosmo Particle Physics (OKC).
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.

Place, publisher, year, edition, pages
2012. Vol. 715, no 4-5, 335-339 p.
Keyword [en]
Massive gravity
National Category
Physical Sciences
Research subject
Theoretical Physics
Identifiers
URN: urn:nbn:se:su:diva-81262DOI: 10.1016/j.physletb.2012.07.018ISI: 000308617500010OAI: oai:DiVA.org:su-81262DiVA: diva2:560582
Note

AuthorCount:3;

Available from: 2012-10-15 Created: 2012-10-15 Last updated: 2017-12-07Bibliographically approved
In thesis
1. Unravelling Consistent Spin-2 Interactions
Open this publication in new window or tab >>Unravelling Consistent Spin-2 Interactions
2012 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

Recently, a unique formulation of a classically consistent theory of massive spin-2 fields has emerged. In this thesis I address a few of the primary questions that arise once such a theory is available.

I will discuss cosmological solutions in a bimetric setup and show that, as far as the background evolution is concerned, a theory of interacting spin-2 fields remain a viable option to the mainstream ΛCDM concordance model. In general, the bimetric solutions are quite different from general relativistic solutions and hence in many situations will not be supported by observations. I highlight a particularly useful class of bimetric solutions which mimic general relativity exactly at the background level. This class of solutions is very special since it both uniquely provide the maximally symmetric vacuum solutions in the absence of matter sources as well as uniquely provide a massive Fierz-Pauli wave equation for perturbations of these backgrounds. This allow us a clear interpretation of the spectrum of perturbations in terms of mass eigenstates. I provide a nonlinear extension of these mass eigenstates into nonlinear fields which are not true mass eigenstates but still provide useful input into the theoretical understanding of the theory. These nonlinear extensions are particularly interesting both with respect to parameterizing generic deviations of the bimetric solutions to general relativistic solutions, as well as providing further insight into some unresolved questions related to ``massive gravity" in maximally symmetric backgrounds, such as the illusive nature of the Higuchi bound and its accompanying linear on-shell gauge invariance.

The special structure of the consistent interacting theory provides the basic tool to start to unravel some of the mysteries connected with spin-2 fields, with hope to reinvestigate many fundamental open questions explicitly related to the gravitational sector of field theory.

Place, publisher, year, edition, pages
Stockholm: Department of Physics, Stockholm University, 2012. 135 p.
Keyword
Modified Gravity, Massive Spin-2, Spin-2 Interactions
National Category
Physical Sciences
Research subject
Theoretical Physics
Identifiers
urn:nbn:se:su:diva-83258 (URN)978-91-7447-618-7 (ISBN)
Public defence
2013-01-28, FA32, AlbaNova University Center, Roslagstullsbacken 21, Stockholm, 14:00 (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 5: Submitted. Paper 6: Submitted.

 

Available from: 2013-01-07 Created: 2012-12-06 Last updated: 2012-12-14Bibliographically approved
2. Consistent Nonlinear Interactions for the Graviton
Open this publication in new window or tab >>Consistent Nonlinear Interactions for the Graviton
2012 (English)Licentiate thesis, comprehensive summary (Other academic)
Abstract [en]

This thesis investigates various aspects of massive gravity and bimetric gravity which be- long to a certain class of modifications of general relativity. It provides an introduction to linear massive gravity in flat backgrounds, before reviewing the construction of consistent nonlinear massive gravity that avoids the Boulware-Deser ghost instability. We discuss the structure of the ghost-free action and summarize the consistency proofs for massive gravity in arbitrary backgrounds, using two different formulations. Thereafter we reca- pitulate the generalization of massive gravity to consistent bimetric models of gravity, in which we then solve the equations of motion with a homogeneous, isotropic ansatz and discuss implications for cosmology.

Place, publisher, year, edition, pages
Department of Physis, Stockholm University, 2012. 63 p.
National Category
Astronomy, Astrophysics and Cosmology
Identifiers
urn:nbn:se:su:diva-77173 (URN)
Available from: 2013-01-30 Created: 2012-06-01 Last updated: 2013-01-30Bibliographically approved
3. Classically Consistent Theories of Interacting Spin-2 Fields
Open this publication in new window or tab >>Classically Consistent Theories of Interacting Spin-2 Fields
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:nbn:se:su:diva-96167 (URN)978-91-7447-791-7 (ISBN)
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

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Hassan, FawadSchmidt-May, Angnisvon Strauss, Mikael
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