1,643 research outputs found
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.Comment: Latex, 18 pages. Published versio
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.Comment: Latex, 35 pages. Matches published versio
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.Comment: v1: Latex, 11 pages, v2: a comment adde
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, , 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 CDM, but with
a technically-natural value for the cosmological constant. We find 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.Comment: 8+2 pages, 2 tables. Version published in PLB. Minor typo corrections
from v
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.Comment: Latex, 11 pages; references added, discussion extended; matches
published versio
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