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Unravelling Consistent Spin-2 Interactions
Stockholm University, Faculty of Science, Department of Physics. (CoPS)
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 [en]
Modified Gravity, Massive Spin-2, Spin-2 Interactions
National Category
Physical Sciences
Research subject
Theoretical Physics
Identifiers
URN: urn:nbn:se:su:diva-83258ISBN: 978-91-7447-618-7 (print)OAI: oai:DiVA.org:su-83258DiVA: diva2:575082
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
List of papers
1. Brane induced gravity, its ghost and the cosmological constant problem
Open this publication in new window or tab >>Brane induced gravity, its ghost and the cosmological constant problem
2011 (English)In: Journal of Cosmology and Astroparticle Physics, ISSN 1475-7516, E-ISSN 1475-7516, no 1, 020- p.Article in journal (Refereed) Published
Abstract [en]

Brane Induced Gravity is regarded as a promising framework for addressing the cosmological constant problem, but it also suffers from a ghost instability for parameter values that make it phenomenologically viable. We carry out a detailed analysis of codimension > 2 models employing gauge invariant variables in a flat background approximation. It is argued that using instead a curved background sourced by the brane would not resolve the ghost issue, unless a very specific condition is satisfied (if satisfiable at all). As for other properties of the model, from an explicit analysis of the 4-dimensional graviton propagator we extract a mass, a decay width and a momentum dependent modification of the gravitational coupling for the spin 2 mode. In the flat space approximation, the mass of the problematic spin 0 ghost is instrumental in filtering out a brane cosmological constant. The mass replaces a background curvature that would have had the same function. The optical theorem is used to demonstrate the suppression of graviton leakage into the uncompactified bulk. Then, we derive the 4-dimensional effective action for gravity and show that general covariance is spontaneously broken by the bulk-brane setup. This provides a natural realization of the gravitational Higgs mechanism. We also show that the addition of extrinsic curvature dependent terms has no bearing on linearized brane gravity.

Keyword
modified gravity, cosmological applications of theories with extra dimensions
National Category
Astronomy, Astrophysics and Cosmology
Research subject
Theoretical Physics
Identifiers
urn:nbn:se:su:diva-68376 (URN)10.1088/1475-7516/2011/01/020 (DOI)000286802900020 ()
Note

AuthorCount:3;

Available from: 2012-01-04 Created: 2012-01-03 Last updated: 2017-12-08Bibliographically 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

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