16,764 research outputs found
Matter coupling in partially constrained vielbein formulation of massive gravity
We consider a consistent linear effective vielbein matter coupling without
introducing the Boulware-Deser ghost in ghost-free massive gravity. This is
achieved in the partially constrained vielbein formulation. We first introduce
the formalism and prove the absence of ghost at all scales. As next we
investigate the cosmological application of this coupling in this new
formulation. We show that even if the background evolution accords with the
metric formulation, the perturbations display important different features in
the partially constrained vielbein formulation. We study the cosmological
perturbations of the two branches of solutions separately. The tensor
perturbations coincide with those in the metric formulation. Concerning the
vector and scalar perturbations, the requirement of absence of ghost and
gradient instabilities yields slightly different allowed parameter space.Comment: 25 page
Negative mode problem in false vacuum decay with gravity
There is a single negative mode in the spectrum of small perturbations about
the tunneling solutions describing a metastable vacuum decay in flat spacetime.
This mode is needed for consistent description of decay processes. When gravity
is included the situation is more complicated. An approach based on elimination
of scalar field perturbations shows no negative mode, whereas the recent
approach based on elimination of gravitational perturbations indicates presence
of a negative mode. In this contribution we analyse and compare the present
approaches to the negative mode problem in false vacuum decay with gravity.Comment: 8 pages, 1 eps figure, Talk given at Constrained Dynamics and Quantum
Gravity 99, Villasimius, (Sardinia, Italy), September 14-18, 1999. To apper
in the Proceedings. After this contribution was essentially completed,
further progress in investigation of negative mode problem was made. The
results are summarized in the revised version of gr-qc/000104
Viability of vector-tensor theories of gravity
We present a detailed study of the viability of general vector-tensor
theories of gravity in the presence of an arbitrary temporal background vector
field. We find that there are six different classes of theories which are
indistinguishable from General Relativity by means of local gravity
experiments. We study the propagation speeds of scalar, vector and tensor
perturbations and obtain the conditions for classical stability of those
models. We compute the energy density of the different modes and find the
conditions for the absence of ghosts in the quantum theory. We conclude that
the only theories which can pass all the viability conditions for arbitrary
values of the background vector field are not only those of the pure Maxwell
type, but also Maxwell theories supplemented with a (Lorentz type) gauge fixing
term.Comment: 13 pages, 2 figures, 1 table. Final version to appear in JCA
Relative Entropy Relaxations for Signomial Optimization
Signomial programs (SPs) are optimization problems specified in terms of
signomials, which are weighted sums of exponentials composed with linear
functionals of a decision variable. SPs are non-convex optimization problems in
general, and families of NP-hard problems can be reduced to SPs. In this paper
we describe a hierarchy of convex relaxations to obtain successively tighter
lower bounds of the optimal value of SPs. This sequence of lower bounds is
computed by solving increasingly larger-sized relative entropy optimization
problems, which are convex programs specified in terms of linear and relative
entropy functions. Our approach relies crucially on the observation that the
relative entropy function -- by virtue of its joint convexity with respect to
both arguments -- provides a convex parametrization of certain sets of globally
nonnegative signomials with efficiently computable nonnegativity certificates
via the arithmetic-geometric-mean inequality. By appealing to representation
theorems from real algebraic geometry, we show that our sequences of lower
bounds converge to the global optima for broad classes of SPs. Finally, we also
demonstrate the effectiveness of our methods via numerical experiments
Invariant Set Theory: Violating Measurement Independence without Fine Tuning, Conspiracy, Constraints on Free Will or Retrocausality
Invariant Set (IS) theory is a locally causal ontic theory of physics based
on the Cosmological Invariant Set postulate that the universe can be
considered a deterministic dynamical system evolving precisely on a (suitably
constructed) fractal dynamically invariant set in 's state space. IS theory
violates the Bell inequalities by violating Measurement Independence. Despite
this, IS theory is not fine tuned, is not conspiratorial, does not constrain
experimenter free will and does not invoke retrocausality. The reasons behind
these claims are discussed in this paper. These arise from properties not found
in conventional ontic models: the invariant set has zero measure in its
Euclidean embedding space, has Cantor Set structure homeomorphic to the p-adic
integers () and is non-computable. In particular, it is shown that
the p-adic metric encapulates the physics of the Cosmological Invariant Set
postulate, and provides the technical means to demonstrate no fine tuning or
conspiracy. Quantum theory can be viewed as the singular limit of IS theory
when when is set equal to infinity. Since it is based around a top-down
constraint from cosmology, IS theory suggests that gravitational and quantum
physics will be unified by a gravitational theory of the quantum, rather than a
quantum theory of gravity. Some implications arising from such a perspective
are discussed.Comment: In Proceedings QPL 2015, arXiv:1511.0118
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