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Constraints and symmetries in theories of interacting spin-2 fields
Stockholm University, Faculty of Science, Department of Physics.ORCID iD: 0000-0001-5346-1044
2020 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

The Hassan-Rosen bimetric theory describes two interacting spin-2 fields, one massless and one massive. In this thesis, a complete canonical analysis of this theory is performed in the metric formulation and all constraints are computed. In particular, a secondary constraint, whose existence was in doubt, is shown to exist and evaluated explicitly, bringing the total number of constraints up to six. This, together with general covariance, is enough to eliminate the Boulware-Deser ghost and ensure that the theory propagates the appropriate seven degrees of freedom. The requirement that the constraints are preserved in time leads to a linear relation between the lapse functions of the two metrics. Knowing the explicit form of the ratio of the lapses is necessary for solving initial value problems. The ratio is computed for the special case where the metrics share the same spherical symmetry.

Since the bimetric theory is diffeomorphism invariant, it must contain four first class constraints whose Poisson brackets form a certain algebra. In general, it is possible to use this algebra to identify a metric. In this thesis, the four first class constraints of bimetric theory are identified and it is shown that their Poisson brackets indeed forms the algebra required by diffeomorphism invariance. However, the metric identified from the algebra turns out not to be unique, but to depend on a choice of variables. Additionally, it need not coincide with the gravitational metric.

The candidate nonlinear partially massless bimetric theory is also investigated in this thesis. It is shown that for this theory, the partially massless symmetry cannot be extended beyond cubic order in the action. This result is generalized to the most general two derivative theory of only two interacting spin-2 fields, showing that such a theory cannot possess the partially massless symmetry beyond cubic order.

Place, publisher, year, edition, pages
Stockholm: Department of Physics, Stockholm University , 2020. , p. 69
Keywords [en]
modified gravity, bimetric theory, spin-2 fields, classical field theory, partially massless symmetry
National Category
Physical Sciences
Research subject
Theoretical Physics
Identifiers
URN: urn:nbn:se:su:diva-176348ISBN: 978-91-7797-960-9 (print)ISBN: 978-91-7797-961-6 (electronic)OAI: oai:DiVA.org:su-176348DiVA, id: diva2:1375365
Public defence
2020-02-21, FA32, AlbaNova universitetscentrum, Roslagstullsbacken 21, Stockholm, 13:00 (English)
Opponent
Supervisors
Available from: 2020-01-29 Created: 2019-12-04 Last updated: 2020-01-17Bibliographically approved
List of papers
1. Analysis of constraints and their algebra in bimetric theory
Open this publication in new window or tab >>Analysis of constraints and their algebra in bimetric theory
2018 (English)In: Journal of High Energy Physics (JHEP), ISSN 1126-6708, E-ISSN 1029-8479, no 8, article id 182Article in journal (Refereed) Published
Abstract [en]

We perform a canonical analysis of the bimetric theory in the metric formulation, computing the constraints and their algebra explicitly. In particular, we compute a secondary constraint, that has been argued to exist earlier, and show that it has the correct form to eliminate the ghost. We also identify a set of four first class constraints that generate the algebra of general covariance. The covariance algebra naturally determines a spacetime metric for the theory. However, in bimetric theory, this metric is not unique but depends on how the first class constraints are identified.

Keywords
Classical Theories of Gravity, Cosmology of Theories beyond the SM
National Category
Physical Sciences
Research subject
Theoretical Physics
Identifiers
urn:nbn:se:su:diva-160168 (URN)10.1007/JHEP08(2018)182 (DOI)000443007200004 ()
Available from: 2018-09-17 Created: 2018-09-17 Last updated: 2019-12-18Bibliographically approved
2. On the ratio of lapses in bimetric relativity
Open this publication in new window or tab >>On the ratio of lapses in bimetric relativity
2019 (English)In: Classical and quantum gravity, ISSN 0264-9381, E-ISSN 1361-6382, Vol. 36, no 22, article id 225013Article in journal (Refereed) Published
Abstract [en]

The two lapse functions in the Hassan–Rosen bimetric theory are not independent. Without knowing the relation between them, one cannot evolve the equations in the 3+1 formalism. This work computes the ratio of lapses for the spherically symmetric case, which is a prerequisite for numerical bimetric relativity.

Keywords
modified gravity, bimetric relativity, ghost-free bimetric theory
National Category
Physical Sciences
Research subject
Theoretical Physics
Identifiers
urn:nbn:se:su:diva-176349 (URN)10.1088/1361-6382/ab497a (DOI)000494436100002 ()
Available from: 2019-12-02 Created: 2019-12-02 Last updated: 2020-01-31Bibliographically approved
3. Gauge and global symmetries of the candidate partially massless bimetric gravity
Open this publication in new window or tab >>Gauge and global symmetries of the candidate partially massless bimetric gravity
2016 (English)In: Physical Review D: covering particles, fields, gravitation, and cosmology, ISSN 2470-0010, E-ISSN 2470-0029, Vol. 94, no 12, article id 124055Article in journal (Refereed) Published
Abstract [en]

In this paper we investigate a particular ghost-free bimetric theory that exhibits the partially massless ( PM) symmetry at quadratic order. At this order the global SO(1,4) symmetry of the theory is enhanced to SO(1,5). We show that this global symmetry becomes inconsistent at cubic order, in agreement with a previous calculation. Furthermore, we find that the PM symmetry of this theory cannot be extended beyond cubic order in the PM field. More importantly, it is shown that the PM symmetry cannot be extended to quartic order in any theory with one massless and one massive spin-2 fields.

National Category
Physical Sciences
Research subject
Theoretical Physics
Identifiers
urn:nbn:se:su:diva-139381 (URN)10.1103/PhysRevD.94.124055 (DOI)000391017700010 ()
Available from: 2017-02-07 Created: 2017-02-06 Last updated: 2019-12-18Bibliographically approved

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