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  • 1.
    Apolo, Luis
    et al.
    Stockholm University, Faculty of Science, Department of Physics. Stockholm University, Faculty of Science, The Oskar Klein Centre for Cosmo Particle Physics (OKC).
    Hassan, S. Fawad
    Stockholm University, Faculty of Science, Department of Physics. Stockholm University, Faculty of Science, The Oskar Klein Centre for Cosmo Particle Physics (OKC).
    Non-linear partially massless symmetry in an SO(1,5) continuation of conformal gravity2017In: Classical and quantum gravity, ISSN 0264-9381, E-ISSN 1361-6382, Vol. 34, no 10, article id 105005Article in journal (Refereed)
    Abstract [en]

    We construct a non-linear theory of interacting spin-2 fields that is invariant under the partially massless (PM) symmetry to all orders. This theory is based on the SO(1, 5) group, in analogy with the SO(2, 4) formulation of conformal gravity, but has a quadratic spectrum free of ghost instabilities. The action contains a vector field associated with a local SO(2) symmetry which is manifest in the vielbein formulation of the theory. We show that, in a perturbative expansion, the SO(2) symmetry transmutes into the PM transformations of a massive spin-2 field. In this context, the vector field is crucial to circumvent earlier obstructions to an order-by-order construction of PM symmetry. Although the non-linear theory lacks enough first class constraints to remove all helicity-0 modes from the spectrum, the PM transformations survive to all orders. The absence of ghosts and strong coupling effects at the non-linear level are not addressed here.

  • 2. Barack, Leor
    et al.
    Cardoso, Vitor
    Nissanke, Samaya
    Sotiriou, Thomas P.
    Askar, Abbas
    Belczynski, Chris
    Bertone, Gianfranco
    Bon, Edi
    Blas, Diego
    Brito, Richard
    Bulik, Tomasz
    Burrage, Clare
    Byrnes, Christian T.
    Caprini, Chiara
    Chernyakova, Masha
    Chruściel, Piotr
    Colpi, Monica
    Ferrari, Valeria
    Gaggero, Daniele
    Gair, Jonathan
    García-Bellido, Juan
    Hassan, Sayed Fawad
    Stockholm University, Faculty of Science, Department of Physics. Stockholm University, Faculty of Science, The Oskar Klein Centre for Cosmo Particle Physics (OKC).
    Heisenberg, Lavinia
    Hendry, Martin
    Heng, Ik Siong
    Herdeiro, Carlos
    Hinderer, Tanja
    Horesh, Assaf
    Kavanagh, Bradley J.
    Kocsis, Bence
    Kramer, Michael
    Le Tiec, Alexandre
    Mingarelli, Chiara
    Nardini, Germano
    Nelemans, Gijs
    Palenzuela, Carlos
    Pani, Paolo
    Perego, Albino
    Porter, Edward K.
    Rossi, Elena M.
    Schmidt, Patricia
    Sesana, Alberto
    Sperhake, Ulrich
    Stamerra, Antonio
    Stein, Leo C.
    Tamanini, Nicola
    Tauris, Thomas M.
    Arturo Urena-López, L.
    Vincent, Frederic
    Volonteri, Marta
    Wardell, Barry
    Wex, Norbert
    Yagi, Kent
    Abdelsalhin, Tiziano
    Ángel Aloy, Miguel
    Amaro-Seoane, Pau
    Annulli, Lorenzo
    Arca-Sedda, Manuel
    Bah, Ibrahima
    Barausse, Enrico
    Barakovic, Elvis
    Benkel, Robert
    Bennett, Charles L.
    Bernard, Laura
    Bernuzzi, Sebastiano
    Berry, Christopher P. L.
    Berti, Emanuele
    Bezares, Miguel
    Juan Blanco-Pillado, Jose
    Blázquez-Salcedo, Jose Luis
    Bonetti, Matteo
    Bošković, Mateja
    Bosnjak, Zeljka
    Bricman, Katja
    Brügmann, Bernd
    Capelo, Pedro R.
    Carloni, Sante
    Cerdá-Durán, Pablo
    Charmousis, Christos
    Chaty, Sylvain
    Clerici, Aurora
    Coates, Andrew
    Colleoni, Marta
    Collodel, Lucas G.
    Compère, Geoffrey
    Cook, William
    Cordero-Carríon, Isabel
    Correia, Miguel
    de la Cruz-Dombriz, Álvaro
    Czinner, Viktor G.
    Destounis, Kyriakos
    Dialektopoulos, Kostas
    Doneva, Daniela
    Dotti, Massimo
    Drew, Amelia
    Eckner, Christopher
    Edholm, James
    Emparan, Roberto
    Erdem, Recai
    Ferreira, Miguel
    Ferreira, Pedro G.
    Finch, Andrew
    Font, Jose A.
    Franchini, Nicola
    Fransen, Kwinten
    Gal'tsov, Dmitry
    Ganguly, Apratim
    Gerosa, Davide
    Glampedakis, Kostas
    Gomboc, Andreja
    Goobar, Ariel
    Stockholm University, Faculty of Science, Department of Physics. Stockholm University, Faculty of Science, The Oskar Klein Centre for Cosmo Particle Physics (OKC).
    Gualtieri, Leonardo
    Guendelman, Eduardo
    Haardt, Francesco
    Harmark, Troels
    Hejda, Filip
    Hertog, Thomas
    Hopper, Seth
    Husa, Sascha
    Ihanec, Nada
    Ikeda, Taishi
    Jaodand, Amruta
    Jetzer, Philippe
    Jimenez-Forteza, Xisco
    Kamionkowski, Marc
    Kaplan, David E.
    Kazantzidis, Stelios
    Kimura, Masashi
    Kobayashi, Shiho
    Kokkotas, Kostas
    Krolik, Julian
    Kunz, Jutta
    Lämmerzahl, Claus
    Lasky, Paul
    Lemos, José P. S.
    Said, Jackson Levi
    Liberati, Stefano
    Lopes, Jorge
    Luna, Raimon
    Ma, Yin-Zhe
    Maggio, Elisa
    Mangiagli, Alberto
    Montero, Marina Martinez
    Maselli, Andrea
    Mayer, Lucio
    Mazumdar, Anupam
    Messenger, Christopher
    Ménard, Brice
    Minamitsuji, Masato
    Moore, Christopher J.
    Mota, David
    Nampalliwar, Sourabh
    Nerozzi, Andrea
    Nichols, David
    Nissimov, Emil
    Obergaulinger, Martin
    Obers, Niels A.
    Oliveri, Roberto
    Pappas, George
    Pasic, Vedad
    Peiris, Hiranya
    Stockholm University, Faculty of Science, Department of Physics. Stockholm University, Faculty of Science, The Oskar Klein Centre for Cosmo Particle Physics (OKC).
    Petrushevska, Tanja
    Pollney, Denis
    Pratten, Geraint
    Rakic, Nemanja
    Racz, Istvan
    Radia, Miren
    Ramazanoglu, Fethi M.
    Ramos-Buades, Antoni
    Raposo, Guilherme
    Rogatko, Marek
    Rosca-Mead, Roxana
    Rosinska, Dorota
    Rosswog, Stephan
    Stockholm University, Faculty of Science, Department of Physics. Stockholm University, Faculty of Science, The Oskar Klein Centre for Cosmo Particle Physics (OKC).
    Ruiz-Morales, Ester
    Sakellariadou, Mairi
    Sanchis-Gual, Nicolás
    Salafia, Om Sharan
    Samajdar, Anuradha
    Sintes, Alicia
    Smole, Majda
    Sopuerta, Carlos
    Souza-Lima, Rafael
    Stalevski, Marko
    Stergioulas, Nikolaos
    Stevens, Chris
    Tamfal, Tomas
    Torres-Forne, Alejandro
    Tsygankov, Sergey
    Ünlütürk, Kivanç I.
    Valiante, Rosa
    van de Meent, Maarten
    Velhinho, José
    Verbin, Yosef
    Vercnocke, Bert
    Vernieri, Daniele
    Vicente, Rodrigo
    Vitagliano, Vincenzo
    Weltman, Amanda
    Whiting, Bernard
    Williamson, Andrew
    Witek, Helvi
    Wojnar, Aneta
    Yakut, Kadri
    Yan, Haopeng
    Yazadjiev, Stoycho
    Zaharijas, Gabrijela
    Zilhão, Miguel
    Black holes, gravitational waves and fundamental physics: a roadmap2019In: Classical and quantum gravity, ISSN 0264-9381, E-ISSN 1361-6382, Vol. 36, no 14, article id 143001Article, review/survey (Refereed)
    Abstract [en]

    The grand challenges of contemporary fundamental physics dark matter, dark energy, vacuum energy, inflation and early universe cosmology, singularities and the hierarchy problem all involve gravity as a key component. And of all gravitational phenomena, black holes stand out in their elegant simplicity, while harbouring some of the most remarkable predictions of General Relativity: event horizons, singularities and ergoregions. The hitherto invisible landscape of the gravitational Universe is being unveiled before our eyes: the historical direct detection of gravitational waves by the LIGO-Virgo collaboration marks the dawn of a new era of scientific exploration. Gravitational-wave astronomy will allow us to test models of black hole formation, growth and evolution, as well as models of gravitational-wave generation and propagation. It will provide evidence for event horizons and ergoregions, test the theory of General Relativity itself, and may reveal the existence of new fundamental fields. The synthesis of these results has the potential to radically reshape our understanding of the cosmos and of the laws of Nature. The purpose of this work is to present a concise, yet comprehensive overview of the state of the art in the relevant fields of research, summarize important open problems, and lay out a roadmap for future progress. This write-up is an initiative taken within the framework of the European Action on 'Black holes, Gravitational waves and Fundamental Physics'.

  • 3.
    Hassan, Fawad
    et al.
    Stockholm University, Faculty of Science, Department of Physics.
    Schmidt-May, Angnis
    Stockholm University, Faculty of Science, Department of Physics. Stockholm University, Faculty of Science, The Oskar Klein Centre for Cosmo Particle Physics (OKC).
    von Strauss, Mikael
    Stockholm University, Faculty of Science, Department of Physics. Stockholm University, Faculty of Science, The Oskar Klein Centre for Cosmo Particle Physics (OKC).
    Proof of consistency of nonlinear massive gravity in the Stuckelberg formulation2012In: Physics Letters B, ISSN 0370-2693, E-ISSN 1873-2445, Vol. 715, no 4-5, p. 335-339Article in journal (Refereed)
    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.

  • 4.
    Hassan, S. Fawad
    et al.
    Stockholm University, Faculty of Science, Department of Physics. Stockholm University, Faculty of Science, The Oskar Klein Centre for Cosmo Particle Physics (OKC).
    Hofmann, Stefan
    von Strauss, Mikael
    Stockholm University, Faculty of Science, Department of Physics. Stockholm University, Faculty of Science, The Oskar Klein Centre for Cosmo Particle Physics (OKC).
    Brane induced gravity, its ghost and the cosmological constant problem2011In: Journal of Cosmology and Astroparticle Physics, ISSN 1475-7516, E-ISSN 1475-7516, no 1, p. 020-Article in journal (Refereed)
    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.

  • 5.
    Hassan, S. Fawad
    et al.
    Stockholm University, Faculty of Science, Department of Physics. Stockholm University, Faculty of Science, The Oskar Klein Centre for Cosmo Particle Physics (OKC).
    Lundkvist, Anders
    Stockholm University, Faculty of Science, Department of Physics. Stockholm University, Faculty of Science, The Oskar Klein Centre for Cosmo Particle Physics (OKC).
    Analysis of constraints and their algebra in bimetric theory2018In: Journal of High Energy Physics (JHEP), ISSN 1126-6708, E-ISSN 1029-8479, no 8, article id 182Article in journal (Refereed)
    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.

  • 6.
    Hassan, S. Fawad
    et al.
    Stockholm University, Faculty of Science, Department of Physics. Stockholm University, Faculty of Science, The Oskar Klein Centre for Cosmo Particle Physics (OKC).
    Rosen, Rachel A.
    Bimetric gravity from ghost-free massive gravity2012In: Journal of High Energy Physics (JHEP), ISSN 1126-6708, E-ISSN 1029-8479, Vol. 1202, article id 126Article in journal (Refereed)
    Abstract [en]

    Generically, non-linear bimetric theories of gravity suffer from the same Boulware-Deser ghost instability as non-linear theories of massive gravity. However, recently proposed theories of massive gravity have been shown to be ghost-free. These theories are formulated with respect to a flat, non-dynamical reference metric. In this work we show that it is possible to give dynamics to the reference metric in such a way that the consistency of the theory is maintained. The result is a non-linear bimetric theory of a massless spin-2 field interacting with a massive spin-2 field that is free of the Boulware-Deser ghost. To our knowledge, this is the first construction of such a ghost-free bimetric theory.

  • 7.
    Hassan, S. Fawad
    et al.
    Stockholm University, Faculty of Science, Department of Physics. Stockholm University, Faculty of Science, The Oskar Klein Centre for Cosmo Particle Physics (OKC).
    Rosen, Rachel A.
    Confirmation of the secondary constraint and absence of ghost in massive gravity and bimetric gravity2012In: Journal of High Energy Physics (JHEP), ISSN 1126-6708, E-ISSN 1029-8479, no 4, article id 123Article in journal (Refereed)
    Abstract [en]

    In massive gravity and in bimetric theories of gravity, two constraints are needed to eliminate the two phase-space degrees of freedom of the Boulware-Deser ghost. For recently proposed non-linear theories, a Hamiltonian constraint has been shown to exist and an associated secondary constraint was argued to arise as well. In this paper we explicitly demonstrate the existence of the secondary constraint. Thus the Boulware-Deser ghost is completely absent from these non-linear massive gravity theories and from the corresponding bimetric theories. Equivalently, this proves the existence of classically ghost-free theories of massive spin-2 fields, in both fixed and dynamical gravitational backgrounds.

  • 8.
    Hassan, S. Fawad
    et al.
    Stockholm University, Faculty of Science, Department of Physics. Stockholm University, Faculty of Science, The Oskar Klein Centre for Cosmo Particle Physics (OKC).
    Rosen, Rachel A.
    On non-linear actions for massive gravity2011In: Journal of High Energy Physics (JHEP), ISSN 1126-6708, E-ISSN 1029-8479, no 7, p. 009-Article in journal (Refereed)
    Abstract [en]

    In this work we present a systematic construction of the potentially ghost-free non-linear massive gravity actions. The most general action can be regarded as a 2-parameter deformation of a minimal massive action. Further extensions vanish in 4 dimensions. The general mass term is constructed in terms of a deformed determinant from which this property can clearly be seen. In addition, our formulation identifies non-dynamical terms that appear in previous constructions and which do not contribute to the equations of motion. We elaborate on the formal structure of these theories as well as some of their implications.

  • 9.
    Hassan, S. Fawad
    et al.
    Stockholm University, Faculty of Science, Department of Physics. Stockholm University, Faculty of Science, The Oskar Klein Centre for Cosmo Particle Physics (OKC).
    Rosen, Rachel A.
    Stockholm University, Faculty of Science, Department of Physics. Stockholm University, Faculty of Science, The Oskar Klein Centre for Cosmo Particle Physics (OKC).
    Resolving the Ghost Problem in Nonlinear Massive Gravity2012In: Physical Review Letters, ISSN 0031-9007, E-ISSN 1079-7114, Vol. 108, no 4, article id 041101Article in journal (Refereed)
    Abstract [en]

    We analyze the ghost issue in the recently proposed models of nonlinear massive gravity in the Arnowitt-Deser-Misner formalism. We show that, in the entire two-parameter family of actions, the Hamiltonian constraint is maintained at the complete nonlinear level and we argue for the existence of a nontrivial secondary constraint. This implies the absence of the pathological Boulware-Deser ghost to all orders. To our knowledge, this is the first demonstration of the existence of a consistent theory of massive gravity at the complete nonlinear level, in four dimensions.

  • 10.
    Hassan, S. Fawad
    et al.
    Stockholm University, Faculty of Science, Department of Physics. Stockholm University, Faculty of Science, The Oskar Klein Centre for Cosmo Particle Physics (OKC).
    Rosen, Rachel A.
    Schmidt-May, Angnis
    Stockholm University, Faculty of Science, Department of Physics. Stockholm University, Faculty of Science, The Oskar Klein Centre for Cosmo Particle Physics (OKC).
    Ghost free massive gravity with a general reference metric2012In: Journal of High Energy Physics (JHEP), ISSN 1126-6708, E-ISSN 1029-8479, no 2, p. 026-Article in journal (Refereed)
    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.

  • 11.
    Hassan, S. Fawad
    et al.
    Stockholm University, Faculty of Science, Department of Physics.
    Schmidt-May, Angnis
    Interactions of Multiple Spin-2 Fields beyond Pairwise Couplings2019In: Physical Review Letters, ISSN 0031-9007, E-ISSN 1079-7114, Vol. 122, no 25, article id 251101Article in journal (Refereed)
    Abstract [en]

    Thus far, all known ghost-free interactions of multiple spin-2 fields have involved at most pairwise couplings of the fields, which are direct generalizations of bimetric interactions. We present a class of spin-2 theories with genuine multifield interactions and explicitly demonstrate the absence of ghost instabilities. The construction involves integrating out a nondynamical field in a theory of spin-2 fields with only pairwise ghost-free interactions. The new multivierbein interactions generated are not always expressible in terms of the associated metrics.

  • 12.
    Hassan, S. Fawad
    et al.
    Stockholm University, Faculty of Science, Department of Physics. Stockholm University, Faculty of Science, The Oskar Klein Centre for Cosmo Particle Physics (OKC).
    Schmidt-May, Angnis
    von Strauss, Mikael
    Extended Weyl invariance in a bimetric model and partial masslessness2016In: Classical and quantum gravity, ISSN 0264-9381, E-ISSN 1361-6382, Vol. 33, no 1, article id 015011Article in journal (Refereed)
    Abstract [en]

    We revisit a particular ghost-free bimetric model which is related to both partial masslessness (PM) and conformal gravity. Linearly, the model propagates six instead of seven degrees of freedom not only around de Sitter but also around flat spacetime. Nonlinearly, the equations of motion can be recast in the form of expansions in powers of curvatures, and exhibit a remarkable amount of structure. In this form, the equations are shown to be invariant under scalar gauge transformations, at least up to six orders in derivatives, the lowest order term being a Weyl scaling of the metrics. The terms at two-derivative order reproduce the usual PM gauge transformations on de Sitter backgrounds. At the four-derivative order, a potential obstruction that could destroy the symmetry is shown to vanish. This in turn guarantees the gauge invariance to at least six-orders in derivatives. This is equivalent to adding up to ten-derivative corrections to conformal gravity. More generally, we outline a procedure for constructing the gauge transformations order by order as an expansion in derivatives and comment on the validity and limitations of the procedure. We also discuss recent arguments against the existence of a PM gauge symmetry in bimetric theory and show that, at least in their present form, they are evaded by the model considered here. Finally, we argue that a bimetric approach to PM theory is more promising than one based on the existence of a fundamental PM field.

  • 13.
    Hassan, S. Fawad
    et al.
    Stockholm University, Faculty of Science, Department of Physics. Stockholm University, Faculty of Science, The Oskar Klein Centre for Cosmo Particle Physics (OKC).
    Schmidt-May, Angnis
    Stockholm University, Faculty of Science, Department of Physics. Stockholm University, Faculty of Science, The Oskar Klein Centre for Cosmo Particle Physics (OKC).
    von Strauss, Mikael
    Stockholm University, Faculty of Science, Department of Physics. Stockholm University, Faculty of Science, The Oskar Klein Centre for Cosmo Particle Physics (OKC).
    Metric Formulation of Ghost-Free Multivielbein TheoryIn: Journal of High Energy Physics (JHEP), ISSN 1126-6708, E-ISSN 1029-8479Article in journal (Refereed)
    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.

  • 14.
    Hassan, S. Fawad
    et al.
    Stockholm University, Faculty of Science, Department of Physics. Stockholm University, Faculty of Science, The Oskar Klein Centre for Cosmo Particle Physics (OKC).
    Schmidt-May, Angnis
    Stockholm University, Faculty of Science, Department of Physics. Stockholm University, Faculty of Science, The Oskar Klein Centre for Cosmo Particle Physics (OKC).
    von Strauss, Mikael
    Stockholm University, Faculty of Science, Department of Physics. Stockholm University, Faculty of Science, The Oskar Klein Centre for Cosmo Particle Physics (OKC).
    On Consistent Theories of Massive Spin-2 Fields Coupled to Gravity2013In: Journal of High Energy Physics (JHEP), ISSN 1126-6708, E-ISSN 1029-8479, no 5, p. 086-Article in journal (Refereed)
    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.

  • 15.
    Hassan, S. Fawad
    et al.
    Stockholm University, Faculty of Science, Department of Physics. Stockholm University, Faculty of Science, The Oskar Klein Centre for Cosmo Particle Physics (OKC).
    Schmidt-May, Angnis
    Stockholm University, Faculty of Science, Department of Physics. Stockholm University, Faculty of Science, The Oskar Klein Centre for Cosmo Particle Physics (OKC).
    von Strauss, Mikael
    Stockholm University, Faculty of Science, Department of Physics. Stockholm University, Faculty of Science, The Oskar Klein Centre for Cosmo Particle Physics (OKC).
    On partially massless bimetric gravity2013In: Physics Letters B, ISSN 0370-2693, E-ISSN 1873-2445, Vol. 726, no 4-5, p. 834-838Article in journal (Refereed)
    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.

  • 16.
    Hassan, S. Fawad
    et al.
    Stockholm University, Faculty of Science, Department of Physics. Stockholm University, Faculty of Science, The Oskar Klein Centre for Cosmo Particle Physics (OKC).
    Schmidt-May, Angnis
    Stockholm University, Faculty of Science, Department of Physics. Stockholm University, Faculty of Science, The Oskar Klein Centre for Cosmo Particle Physics (OKC).
    von Strauss, Mikael
    Stockholm University, Faculty of Science, Department of Physics. Stockholm University, Faculty of Science, The Oskar Klein Centre for Cosmo Particle Physics (OKC).
    On Partially Massless Bimetric GravityIn: Journal of High Energy Physics (JHEP), ISSN 1126-6708, E-ISSN 1029-8479Article in journal (Refereed)
    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.

  • 17.
    Hassan, S. Fawad
    et al.
    Stockholm University, Faculty of Science, Department of Physics. Stockholm University, Faculty of Science, The Oskar Klein Centre for Cosmo Particle Physics (OKC).
    Schmidt-May, Angnis
    Stockholm University, Faculty of Science, Department of Physics. Stockholm University, Faculty of Science, The Oskar Klein Centre for Cosmo Particle Physics (OKC).
    von Strauss, Mikael
    Particular solutions in bimetric theory and their implications2014In: International Journal of Modern Physics D, ISSN 0218-2718, Vol. 23, no 13, article id 1443002Article in journal (Refereed)
    Abstract [en]

    Ghost-free bimetric theory can describe gravity in the presence of an extra spin-2 field. In this paper, we study certain aspects of dynamics in this theory: (i) It is shown that if either of the metrics is an Einstein solution, then the other is always forced to be Einstein, too. For a class of bimetric models, this constraint is stronger and as soon as one metric is Einstein, the other metric is forced to be proportional to it. As a consequence, the models in this class avoid a branch of pathological solutions that exhibit determinant singularities or nonlinear ghosts. These constraints persists in a generalized form when sources are included, but are destroyed in the massive gravity limit of the theory. (ii) For another class of bimetric models, we show the existence of solutions that do not admit a massive gravity limit. A bimetric model that could exhibit a nonlinear version of partially massless symmetry belongs to both these classes. It is argued that if such a model exist, its symmetry will not survive in the massive gravity limit.

  • 18.
    Hassan, Sayed Fawad
    et al.
    Stockholm University, Faculty of Science, Department of Physics. Stockholm University, Faculty of Science, The Oskar Klein Centre for Cosmo Particle Physics (OKC).
    Kocic, Mikica
    Stockholm University, Faculty of Science, Department of Physics. Stockholm University, Faculty of Science, The Oskar Klein Centre for Cosmo Particle Physics (OKC).
    On the local structure of spacetime in ghost-free bimetric theory and massive gravity2018In: Journal of High Energy Physics (JHEP), ISSN 1126-6708, E-ISSN 1029-8479, no 5, article id 099Article in journal (Refereed)
    Abstract [en]

    The ghost-free bimetric theory describes interactions of gravity with another spin-2 field in terms of two Lorentzian metrics. However, if the two metrics do not admit compatible notions of space and time, the formulation of the initial value problem becomes problematic. Furthermore, the interaction potential is given in terms of the square root of a matrix which is in general nonunique and possibly nonreal. In this paper we show that both these issues are evaded by requiring reality and general covariance of the equations. First we prove that the reality of the square root matrix leads to a classification of the allowed metrics in terms of the intersections of their null cones. Then, the requirement of general covariance further restricts the allowed metrics to geometries that admit compatible notions of space and time. It also selects a unique definition of the square root matrix. The restrictions are compatible with the equations of motion. These results ensure that the ghost-free bimetric theory can be defined unambiguously and that the two metrics always admit compatible 3+1 decompositions, at least locally. In particular, these considerations rule out certain solutions of massive gravity with locally Closed Causal Curves, which have been used to argue that the theory is acausal.

  • 19.
    Hassan, Sayed Fawad
    et al.
    Stockholm University, Faculty of Science, Department of Physics. Stockholm University, Faculty of Science, The Oskar Klein Centre for Cosmo Particle Physics (OKC).
    Schmidt-May, Angnis
    Stockholm University, Faculty of Science, Department of Physics. Stockholm University, Faculty of Science, The Oskar Klein Centre for Cosmo Particle Physics (OKC).
    von Strauss, Mikael
    Stockholm University, Faculty of Science, Department of Physics. Stockholm University, Faculty of Science, The Oskar Klein Centre for Cosmo Particle Physics (OKC).
    Bimetric theory and partial masslessness with Lanczos-Lovelock terms in arbitrary dimensions2013In: Classical and quantum gravity, ISSN 0264-9381, E-ISSN 1361-6382, Vol. 30, no 18, p. 184010-Article in journal (Refereed)
    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.

  • 20.
    Hassan, S.Fawad
    et al.
    Stockholm University, Faculty of Science, Department of Physics.
    von Strauss, Mikael
    Stockholm University, Faculty of Science, Department of Physics.
    Schmidt-May, Angnis
    Stockholm University, Faculty of Science, Department of Physics.
    Higher Derivative Gravity and Conformal Gravity From Bimetric and Partially Massless Bimetric TheoryManuscript (preprint) (Other academic)
  • 21.
    von Strauss, Mikael
    et al.
    Stockholm University, Faculty of Science, Department of Physics. Stockholm University, Faculty of Science, The Oskar Klein Centre for Cosmo Particle Physics (OKC).
    Schmidt-May, Angnis
    Stockholm University, Faculty of Science, Department of Physics. Stockholm University, Faculty of Science, The Oskar Klein Centre for Cosmo Particle Physics (OKC).
    Enander, Jonas
    Stockholm University, Faculty of Science, Department of Physics. Stockholm University, Faculty of Science, The Oskar Klein Centre for Cosmo Particle Physics (OKC).
    Mörtsell, Edvard
    Stockholm University, Faculty of Science, Department of Physics. Stockholm University, Faculty of Science, The Oskar Klein Centre for Cosmo Particle Physics (OKC).
    Hassan, S. Fawad
    Stockholm University, Faculty of Science, Department of Physics. Stockholm University, Faculty of Science, The Oskar Klein Centre for Cosmo Particle Physics (OKC).
    Cosmological solutions in bimetric gravity and their observational tests2012In: Journal of Cosmology and Astroparticle Physics, ISSN 1475-7516, E-ISSN 1475-7516, no 3, p. 042-Article in journal (Refereed)
    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.

1 - 21 of 21
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