arXiv subjects

Angnis Schmidt-May

Publications and source records attributed to Angnis Schmidt-May.

35 records · Page 2Linked to original sources

arXiv2016

Nonlinear interactions for massive spin-2 fields

We give a basic introduction to ghost-free nonlinear theories involving massive spin-2 fields, focussing on bimetric theory. After motivating the construction of such models from field theoretical considerations, we review the linear theories for massive and massless spin-2 fluctuations propagating on maximally symmetric backgrounds. The structure of general nonlinear spin-2 interactions is explained before we specialise to the ghost-free case. We review the maximally symmetric solutions of bimetric theory, its mass spectrum and the parameter limit which brings the theory close to general relativity. Finally we discuss applications of bimetric theory to cosmology with particular emphasis on the role of the general relativity limit.

gr-qc↗

arXiv2015

Extended Weyl Invariance in a Bimetric Model and Partial Masslessness

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 10-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.

hep-th↗

arXiv2015

On Partially Massless Bimetric Gravity

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.

hep-th↗

arXiv2015

Higher Derivative Gravity and Conformal Gravity From Bimetric and Partially Massless Bimetric Theory

In this paper we establish the correspondence between ghost-free bimetric theory and a class of higher derivative gravity actions, including conformal gravity and New Massive Gravity. We also characterize the relation between the respective equations of motion and classical solutions. We illustrate that, in this framework, the spin-2 ghost of higher derivative gravity is an artifact of the truncation to a 4-derivative theory. The analysis also gives a relation between the proposed partially massless (PM) bimetric theory and conformal gravity, showing, in particular, the equivalence of their equations of motion at the 4-derivative level. For the PM bimetric theory this provides further evidence for the existence of an extra gauge symmetry and the associated loss of a propagating mode away from de Sitter backgrounds. The new symmetry is an extension of Weyl symmetry which also suggests the PM bimetric theory as a ghost-free completion of conformal gravity.

hep-th↗

arXiv2015

Bimetric gravity is cosmologically viable

Bimetric theory describes gravitational interactions in the presence of an extra spin-2 field. Previous work has suggested that its cosmological solutions are generically plagued by instabilities. We show that by taking the Planck mass for the second metric, $M_f$, to be small, these instabilities can be pushed back to unobservably early times. In this limit, the theory approaches general relativity with an effective cosmological constant which is, remarkably, determined by the spin-2 interaction scale. This provides a late-time expansion history which is extremely close to $Λ$CDM, but with a technically-natural value for the cosmological constant. We find $M_f$ should be no larger than the electroweak scale in order for cosmological perturbations to be stable by big-bang nucleosynthesis. We further show that in this limit the helicity-0 mode is no longer strongly-coupled at low energy scales.

gr-qc↗

arXiv2015

Mass eigenstates in bimetric theory with matter coupling

In this paper we study the ghost-free bimetric action extended by a recently proposed coupling to matter through a composite metric. The equations of motion for this theory are derived using a method which avoids varying the square-root matrix that appears in the matter coupling. We make an ansatz for which the metrics are proportional to each other and find that it can solve the equations provided that one parameter in the action is fixed. In this case, the proportional metrics as well as the effective metric that couples to matter solve Einstein's equations of general relativity including a matter source. Around these backgrounds we derive the quadratic action for perturbations, diagonalized into a massive and a massless spin-2 fluctuation. We find that only the massless spin-2 mode interacts with matter; a result which is independent of the remaining parameters of the theory.

gr-qc↗

arXiv2014

A link between ghost-free bimetric and Eddington-inspired Born-Infeld theory

We provide an auxiliary field formulation of the full ghost-free bimetric theory which avoids the explicit presence of a square-root matrix in the action. This description always allows for a branch of solutions where the auxiliary fields can be integrated out to give back the ghost-free theory. For certain parameter regions the two formulations are dynamically equivalent, but in the general case another branch of solutions also exists. We show that this second branch, with certain restrictions on the parameters of the theory, is dynamically equivalent to Eddington-inspired Born-Infeld gravity. This establishes a definite connection between two seemingly unrelated theories of modified gravity.

hep-th↗

arXiv2014

Particular Solutions in Bimetric Theory and Their Implications

Ghost-free bimetric theory can describe gravity in the presence of an extra spin-2 field. We study certain aspects of dynamics in this theory: (1) 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. (2) 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 exits, its symmetry will not survive in the massive gravity limit.

hep-th↗

arXiv2014

Absence of ghost in a new bimetric-matter coupling

Interactions in bimetric theory, which can describe gravity in the presence of an extra spin-2 field, are severely constrained by the requirement of the absence of the Boulware-Deser ghost instability. Recently an interesting new matter coupling was proposed in terms of a composite metric but it was claimed to reintroduce the ghost. In this paper we carry out a nonlinear Hamiltonian analysis of this new matter coupling and show that it is indeed ghost-free. The analysis involves using a new set of variables that naturally appear in the relation between the metric and vielbein formulations of bimetric theory. In terms of these variables we show that the new matter coupling does not reduce the number of constraints in bimetric theory and hence does not reintroduce the Boulware-Deser ghost.

hep-th↗

arXiv2014

Radiative Inflation and Dark Energy RIDEs Again after BICEP2

Following the ground-breaking measurement of the tensor-to-scalar ratio $r = 0.20^{+0.07}_{- 0.05}$ by the BICEP2 collaboration, we perform a statistical analysis of a model that combines Radiative Inflation with Dark Energy (RIDE) based on the $M^2 |Φ|^2 \ln \left(|Φ|^2/Λ^2 \right)$ potential and compare its predictions to those based on the traditional chaotic inflation $M^2|Φ|^2$ potential. We find a best-fit value in the RIDE model of $r=0.18$ as compared to $r=0.17$ in the chaotic model, with the spectral index being $n_S=0.96$ in both models.

hep-ph↗

arXiv2014

Consistent Bimetric Theory and its Application to Cosmology

Recently, the construction of ghost-free nonlinear massive spin-2 interactions solved a long outstanding problem in classical field theory. The consistent formulation requires a second rank-two tensor (or metric) and therefore has the form of a bimetric theory. Besides providing the solution to an old problem in field theory, ghost-free bimetric theory also has an interesting phenomenology: Its homogeneous and isotropic background solutions can reproduce the expansion history of the universe without any input of vacuum energy.

gr-qc↗

arXiv2013

On Consistent Theories of Massive Spin-2 Fields Coupled to Gravity

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.

hep-th↗

arXiv2012

Bimetric Theory and Partial Masslessness with Lanczos-Lovelock Terms in Arbitrary Dimensions

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 analyze 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 3 and 4 dimensions. But on adding Lanczos-Lovelock terms to the bimetric action it is found that higher derivative nonlinear PM theories 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 5, 6 and 8 dimensions but show that none exist in 7 dimensions.

hep-th↗

arXiv2012

Proof of Consistency of Nonlinear Massive Gravity in the Stuckelberg Formulation

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.

hep-th↗

arXiv2011

Ghost-free Massive Gravity with a General Reference Metric

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.

hep-th↗

arXiv2011

Cosmological Solutions in Bimetric Gravity and their Observational Tests

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 while 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.

gr-qc↗

arXiv2011

Radiative Inflation and Dark Energy

We propose a model based on radiative symmetry breaking that combines inflation with Dark Energy and is consistent with the WMAP 7-year regions. The radiative inflationary potential leads to the prediction of a spectral index 0.955 \lesssim n_S \lesssim 0.967 and a tensor to scalar ratio 0.142 \lesssim r \lesssim 0.186, both consistent with current data but testable by the Planck experiment. The radiative symmetry breaking close to the Planck scale gives rise to a pseudo Nambu-Goldstone boson with a gravitationally suppressed mass which can naturally play the role of a quintessence field responsible for Dark Energy. Finally, we present a possible extra dimensional scenario in which our model could be realised.

hep-ph↗