arXiv subjects

Angnis Schmidt-May

Publications and source records attributed to Angnis Schmidt-May.

At least 19 recordsLinked to original sources

arXiv2020

Vainshtein Screening in Bimetric Cosmology

We demonstrate that the instabilities in linear cosmological perturbations in bimetric theory are the manifestation of the non-linear Vainshtein mechanism on an FRW background. The spin-2 mass serves as the cosmological Vainshtein scale in this case. This allows us to quantitatively address early universe cosmology. In particular, in a global analysis, we study data from the cosmic microwave background radiation and local measurements of the Hubble flow. We show that bimetric cosmology resolves the discrepancy in the local and early-time measurements of the Hubble scale via an effective phantom dark energy component.

gr-qc↗

arXiv2020

Physical parameter space of bimetric theory and SN1a constraints

Bimetric theory describes a massless and a massive spin-2 field with fully non-linear (self-)interactions. It has a rich phenomenology and has been successfully tested with several data sets. However, the observational constraints have not been combined in a consistent framework, yet. We propose a parametrization of bimetric solutions in terms of the effective cosmological constant $Λ$ and the mass $m_\mathrm{FP}$ of the spin-2 field as well as its coupling strength to ordinary matter $\barα$. This simplifies choosing priors in statistical analysis and allows to directly constrain these parameters with observational data not only from local systems but also from cosmology. By identifying the physical vacuum of bimetric theory these parameters are uniquely determined. We work out the dictionary for the new parametrization for various submodels and present the implied consistency constraints on the physical parameter space. We then apply the dictionary to derive observational constraints from SN1a on the physical parameters. As a result we find that even self-accelerating models with a heavy spin-2 field are in perfect agreement with current supernova data.

gr-qc↗

arXiv2020

The Unified Standard Model

The aim of this work is to find a simple mathematical framework for our established description of particle physics. We demonstrate that the particular gauge structure, group representations and charge assignments of the Standard Model particles are all captured by the algebra M(8,$\mathbb{C})$ of complex 8$\times$8 matrices. This algebra is well motivated by its close relation to the normed division algebra of octonions. (Anti-)particle states are identified with basis elements of the vector space M(8,$\mathbb{C})$. Gauge transformations are simply described by the algebra acting on itself. Our result shows that all particles and gauge structures of the Standard Model are contained in the tensor product of all four normed division algebras, with the quaternions providing the Lorentz representations. Interestingly, the space M(8,$\mathbb{C})$ contains two additional elements independent of the Standard Model particles, hinting at a minimal amount of new physics.

hep-th↗

arXiv2020

The complete theory of Maxwell and Proca fields

We present the most general ghost-free classical Lagrangian containing first-order derivatives and describing interacting real Abelian spin-one fields on Minkowski spacetime. We study both massive Proca and massless Maxwell fields and allow for a non-linear realization of mass, in the form of derivative self-interactions. Within this context, our construction notoriously extends the existing literature, which is limited to the case of a single Proca field and to multiple interacting Proca fields in the presence of a global rotational symmetry. In the limit of a single Proca field, we reproduce the known healthy interaction terms. We provide the necessary and sufficient conditions to ensure ghost-freedom in any multi-field setup. We observe that, in general, the said conditions are not satisfied by the rotationally symmetric multi-Proca interactions suggested so far, which implies that they propagate ghosts. Our theory admits a plethora of applications in a wide range of subjects. For illustrative purposes, we provide concrete proposals in holographic condensed matter and black hole physics.

hep-th↗

arXiv2020

The Maxwell-Proca theory: definition and construction

We present a systematic construction of the most general first order Lagrangian describing an arbitrary number of interacting Maxwell and Proca fields on Minkowski spacetime. To this aim, we first formalize the notion of a Proca field, in analogy to the well known Maxwell field. Our definition allows for a non-linear realization of the Proca mass, in the form of derivative self-interactions. Consequently, we consider so-called generalized Proca/vector Galileons. We explicitly demonstrate the ghost-freedom of this complete Maxwell-Proca theory by obtaining its constraint algebra. We find that, when multiple Proca fields are present, their interactions must fulfill non-trivial differential relations in order to ensure the propagation of the correct number of degrees of freedom. These relations had so far been overlooked, which means previous multi-Proca proposals generically contain ghosts. This is a companion paper to arXiv:1905.06968 [hep-th]. It puts on a solid footing the theory there introduced.

hep-th↗

arXiv2019

Bimetric cosmology is compatible with local tests of gravity

Recently, Kenna-Allison et.al. claimed that bimetric gravity cannot give rise to a viable cosmological expansion history while at the same time being compatible with local gravity tests. In this note we review that claim and combine various results from the literature to provide several simple counter examples. We conclude that the results of Kenna-Allison et.al. cannot hold in general.

gr-qc↗

arXiv2019

Gravity with antisymmetric components

This work proposes a new gravitational theory formulated in terms of the vierbein field. The vierbein contains components which can be shifted by local Lorentz transformations and therefore do not show up in the spacetime metric. These components are given dynamics and become physical in our setup. They enter the massless theory in the form of an antisymmetric tensor field which makes the action reminiscent of the bosonic sector of supergravity. We then demonstrate that both the metric and the antisymmetric tensor can be made massive by adding a potential term for the vierbein. The form of this mass potential is inspired by ghost-free massive gravity. We confirm the absence of additional and potentially pathological degrees of freedom in an ADM analysis. However, at the linearized level around maximally symmetric solutions, the fluctuation of the antisymmetric tensor has a tachyonic mass pole.

hep-th↗

arXiv2019

Vierbein interactions with antisymmetric components

In this work we propose a new gravitational setup formulated in terms of two interacting vierbein fields. The theory is the fully diffeomorphism and local Lorentz invariant extension of a previous construction which involved a fixed reference vierbein. Certain vierbein components can be shifted by local Lorentz transformations and do not enter the associated metric tensors. We parameterize these components by an antisymmetric tensor field and give them a kinetic term in the action, thereby promoting them to dynamical variables. In addition, the action contains two Einstein-Hilbert terms and an interaction potential whose form is inspired by ghost-free massive gravity and bimetric theory. The resulting theory describes the interactions of a massless spin-2, a massive spin-2 and an antisymmetric tensor field. It can be generalized to the case of multiple massive spin-2 fields and multiple antisymmetric tensor fields. The absence of additional and potentially pathological degrees of freedom is verified in an ADM analysis. However, the antisymmetric tensor fluctuation around the maximally symmetric background solution has a tachyonic mass pole.

hep-th↗

arXiv2018

4D spin-2 fields from 5D Chern-Simons theory

We consider a 5-dimensional Chern-Simons gauge theory for the isometry group of Anti-de-Sitter spacetime, $\operatorname{AdS}_{4+1}\simeq\operatorname{SO}(4,2)$, and invoke different dimensional reduction schemes in order to relate it to 4-dimensional spin-2 theories. The AdS gauge algebra is isomorphic to a parametrized 4-dimensional conformal algebra, and the gauge fields corresponding to the generators of non-Abelian translations and special conformal transformations reduce to two vierbein fields in $D=4$. Besides these two vierbeine, our reduction schemes leave only the Lorentz spin connection as an additional dynamical field in the 4-dimensional theories. We identify the corresponding actions as particular generalizations of Einstein-Cartan theory, conformal gravity and ghost-free bimetric gravity in first-order form.

gr-qc↗

arXiv2018

Interactions of multiple spin-2 fields beyond pairwise couplings

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. Here we present a class of spin-2 theories with genuine multi-field 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 multi-vierbein interactions generated are not always expressible in terms of the associated metrics.

hep-th↗

arXiv2018

Ghost-free infinite derivative gravity

We present the construction of a gravitational action including an infinite series of higher derivative terms. The outcome is a classically consistent completion of a well-studied quadratic curvature theory. The closed form for the full action is ghost-free bimetric theory, describing the interactions of a massive and a massless spin-2 field. At energies much smaller than the spin-2 mass scale, the theory reduces to general relativity. For energies comparable to the spin-2 mass, the higher derivative terms completing the Einstein-Hilbert action capture the effects of the additional massive spin-2 field. The theory is only ghost-free when the full series of higher derivatives is kept.

gr-qc↗

arXiv2018

Ghost-free completion of an effective matter coupling in bimetric theory

We consider a particular set of ghost-free interactions for three spin-2 fields in which we freeze out the dynamics of the metric tensor that couples to the matter sector. Integrating out the non-dynamical degrees of freedom in vacuum results in a ghost-free bimetric theory. In the presence of the matter source, which we treat as a small perturbation, the equations for the non-dynamical field can be solved perturbatively for its vierbein. This results in ghost-free bimetric theory in vierbein formulation with a modified matter coupling. To lowest order in matter perturbations, we precisely obtain an effective matter coupling that has been suggested earlier in the literature. This coupling contains a linear combination of the two vierbeine whose corresponding metric fluctuation coincides with the massless spin-2 mode. In the past, bimetric theory with this symmetric coupling has been treated as an effective theory valid at low energies without a ghost-free completion. Our results demonstrate that the effective matter coupling can be rendered entirely ghost-free by including the higher-order corrections obtained from the trimetric setup.

hep-th↗

arXiv2018

Dark matter scenarios with multiple spin-2 fields

We study ghost-free multimetric theories for $(N+1)$ tensor fields with a coupling to matter and maximal global symmetry group $S_N\times(Z_2)^N$. Their mass spectra contain a massless mode, the graviton, and $N$ massive spin-2 modes. One of the massive modes is distinct by being the heaviest, the remaining $(N-1)$ massive modes are simply identical copies of each other. All relevant physics can therefore be understood from the case $N=2$. Focussing on this case, we compute the full perturbative action up to cubic order and derive several features that hold to all orders in perturbation theory. The lighter massive mode does not couple to matter and neither of the massive modes decay into massless gravitons. We propose the lighter massive particle as a candidate for dark matter and investigate its phenomenology in the parameter region where the matter coupling is dominated by the massless graviton. The relic density of massive spin-2 can originate from a freeze-in mechanism or from gravitational particle production, giving rise to two different dark matter scenarios. The allowed parameter regions are very different from those in scenarios with only one massive spin-2 field and more accessible to experiments.

hep-th↗

arXiv2017

Structures in multiple spin-2 interactions

We study generalisations of ghost-free bimetric theory which involve more than two spin-2 fields. The consistent interactions can enter in the form of two different couplings and in the majority of this work we concentrate on the simpler one. The corresponding action involves one metric coupled to $N$ tensor fields which do not interact with each other. We derive maximally symmetric solutions to the multimetric equations of motion and identify the mass eigenstates in the linearised theory around these backgrounds. Our results are then applied to the problem of singling out multimetric models which possess certain additional structures. In particular, we look for a relation between scale invariant background solutions, the perturbative emergence of Weyl invariance and the presence of partially massless spin-2 fields in the linear theory. Our findings generalise known results in bimetric theory and allow us to point out similarities and differences between the bi- and multimetric models.

gr-qc↗

arXiv2016

Heavy spin-2 Dark Matter

We provide further details on a recent proposal addressing the nature of the dark sectors in cosmology and demonstrate that all current observations related to Dark Matter can be explained by the presence of a heavy spin-2 particle. Massive spin-2 fields and their gravitational interactions are uniquely described by ghost-free bimetric theory, which is a minimal and natural extension of General Relativity. In this setup, the largeness of the physical Planck mass is naturally related to extremely weak couplings of the heavy spin-2 field to baryonic matter and therefore explains the absence of signals in experiments dedicated to Dark Matter searches. It also ensures the phenomenological viability of our model as we confirm by comparing it with cosmological and local tests of gravity. At the same time, the spin-2 field possesses standard gravitational interactions and it decays universally into all Standard Model fields but not into massless gravitons. Matching the measured DM abundance together with the requirement of stability constrains the spin-2 mass to be in the 1 to 100 TeV range.

hep-th↗

arXiv2016

Linear spin-2 fields in most general backgrounds

We derive the full perturbative equations of motion for the most general background solutions in ghost-free bimetric theory in its metric formulation. Clever field redefinitions at the level of fluctuations enable us to circumvent the problem of varying a square-root matrix appearing in the theory. This greatly simplifies the expressions for the linear variation of the bimetric interaction terms. We show that these field redefinitions exist and are uniquely invertible if and only if the variation of the square-root matrix itself has a unique solution, which is a requirement for the linearised theory to be well-defined. As an application of our results we examine the constraint structure of ghost-free bimetric theory at the level of linear equations of motion for the first time. We identify a scalar combination of equations which is responsible for the absence of the Boulware-Deser ghost mode in the theory. The bimetric scalar constraint is in general not manifestly covariant in its nature. However, in the massive gravity limit the constraint assumes a covariant form when one of the interaction parameters is set to zero. For that case our analysis provides an alternative and almost trivial proof of the absence of the Boulware-Deser ghost. Our findings generalise previous results in the metric formulation of massive gravity and also agree with studies of its vielbein version.

hep-th↗

arXiv2016

Gravitational Origin of Dark Matter

Observational evidence for the existence of Dark Matter is limited to its gravitational effects. The extensive program for dedicated searches has yielded null results so far, challenging the most popular models. Here we propose that this is the case because the very existence of cold Dark Matter is a manifestation of gravity itself. The consistent bimetric theory of gravity, the only known ghost-free extension of General Relativity involving a massless and a massive spin-2 field, automatically contains a perfect Dark Matter candidate. We demonstrate that the massive spin-2 particle can be heavy, stable on cosmological scales, and that it interacts with matter only through a gravitational type of coupling. Remarkably, these features persist in the same region of parameter space where bimetric theory satisfies the current gravity tests. We show that the observed Dark Matter abundance can be generated via freeze-in and suggest possible particle physics and gravitational signatures of our bimetric Dark Matter model.

hep-ph↗

arXiv2016

Recent developments in bimetric theory

This review is dedicated to recent progress in the field of classical, interacting, massive spin-2 theories, with a focus on ghost-free bimetric theory. We will outline its history and its development as a nontrivial extension and generalisation of nonlinear massive gravity. We present a detailed discussion of the consistency proofs of both theories, before we review Einstein solutions to the bimetric equations of motion in vacuum as well as the resulting mass spectrum. We introduce couplings to matter and then discuss the general relativity and massive gravity limits of bimetric theory, which correspond to decoupling the massive or the massless spin-2 field from the matter sector, respectively. More general classical solutions are reviewed and the present status of bimetric cosmology is summarised. An interesting corner in the bimetric parameter space which could potentially give rise to a nonlinear theory for partially massless spin-2 fields is also discussed. Relations to higher-curvature theories of gravity are explained and finally we give an overview of possible extensions of the theory and review its formulation in terms of vielbeins.

hep-th↗