Steven Dubovsky

Causality, analyticity and an IR obstruction to UV completion

We argue that certain apparently consistent low-energy effective field theories described by local, Lorentzinvariant Lagrangians, secretly exhibit macroscopic non-locality and cannot be embedded in any UV theory whose S-matrix satisfies canonical analyticity constraints. The obstruction involves the signs of a set of leading irrelevant operators, which must be strictly positive to ensure UV analyticity. An IR manifestation of this restriction is that the “wrong” signs lead to superluminal fluctuations around non-trivial backgrounds, making it impossible to define local, causal evolution, and implying a surprising IR breakdown of the effective theory. Such effective theories can not arise in quantum field theories or weakly coupled string theories, whose S-matrices satisfy the usual analyticity properties. This conclusion applies to the DGP brane-world model modifying gravity in the IR, giving a simple explanation for the difficulty of embedding this model into controlled stringy backgrounds, and to models of electroweak symmetry breaking that predict negative anomalous quartic couplings for the W and Z. Conversely, any experimental support for the DGP model, or measured negative signs for anomalous quartic gauge boson couplings at future accelerators, would constitute direct evidence for the existence of superluminality and macroscopic non-locality unlike anything previously seen in physics, and almost incidentally falsify both local quantum field theory and perturbative string theory.

Null energy condition and superluminal propagation

We study whether a violation of the null energy condition necessarily implies the presence of instabilities. We prove that this is the case in a large class of situations, including isotropic solids and fluids relevant for cosmology. On the other hand we present several counter-examples of consistent effective field theories possessing a stable background where the null energy condition is violated. Two necessary features of these counter-examples are the lack of isotropy of the background and the presence of superluminal modes. We argue that many of the properties of massive gravity can be understood by associating it to a solid at the edge of violating the null energy condition. We briefly analyze the difficulties of mimicking u H > 0 in scalar tensor theories of gravity.

Phases of massive gravity

We systematically study the most general Lorentz-violating graviton mass invariant under three-dimensional Eucledian group using the explicitly covariant language. We find that at general values of mass parameters the massive graviton has six propagating degrees of freedom, and some of them are ghosts or lead to rapid classical instabilities. However, there is a number of different regions in the mass parameter space where massive gravity can be described by a consistent low-energy effective theory with cutoff

Brane world: disappearing massive matter

\sim\sqrt{mM_{Pl}}

Spontaneous breaking of Lorentz invariance, black holes and perpetuum mobile of the 2nd kind

free of rapid instabilities and vDVZ discontinuity. Each of these regions is characterized by certain fine-tuning relations between mass parameters, generalizing the Fierz--Pauli condition. In some cases the required fine-tunings are consequences of the existence of the subgroups of the diffeomorphism group that are left unbroken by the graviton mass. We found two new cases, when the resulting theories have a property of UV insensitivity, i.e. remain well behaved after inclusion of arbitrary higher dimension operators without assuming any fine-tunings among the coefficients of these operators, besides those enforced by the symmetries. These theories can be thought of as generalizations of the ghost condensate model with a smaller residual symmetry group. We briefly discuss what kind of cosmology can one expect in massive gravity and argue that the allowed values of the graviton mass may be quite large, affecting growth of primordial perturbations, structure formation and, perhaps, enhancing the backreaction of inhomogeneities on the expansion rate of the Universe.We systematically study the most general Lorentz-violating graviton mass invariant under three-dimensional Eucledian group. We find that at general values of mass parameters the massive graviton has six propagating degrees of freedom, and some of them are ghosts or lead to rapid classical instabilities. However, there is a number of different regions in the mass parameter space where massive gravity is described by a consistent low-energy effective theory with cutoff ~ (mMPl)1/2. This theory is free of rapid instabilities and vDVZ discontinuity. Each of these regions is characterized by certain fine-tuning relations between mass parameters, generalizing the Fierz–Pauli condition. In some cases the required fine-tunings are consequences of the existence of the subgroups of the diffeomorphism group that are left unbroken by the graviton mass. We found two new cases, when the resulting theories have a property of UV insensitivity, i.e. remain well behaved after inclusion of arbitrary higher dimension operators without assuming any fine-tunings among the coefficients of these operators, besides those enforced by the symmetries. These theories can be thought of as generalizations of the ghost condensate model with a smaller residual symmetry group. We briefly discuss what kind of cosmology can one expect in massive gravity and argue that the allowed values of the graviton mass may be quite large, affecting growth of primordial perturbations, structure formation and, perhaps, enhancing the backreaction of inhomogeneities on the expansion rate of the Universe.

Elevated platelet intracellular calcium concentration in bipolar depression

In a brane (domain wall) scenario with an infinite extra dimension and localized gravity, bulk fermions and scalars often have bound states with zero 4-dimensional mass. In this way massless matter residing on the brane may be obtained. We consider what happens when one tries to introduce small, but non-vanishing mass to these matter fields. We find that the discrete zero modes turn into quasi-localized states with finite 4-dimensional mass and finite width. The latter is due to tunneling of massive matter into extra dimension. We argue that this phenomenon is generic to fields that can have bulk modes. We also point out that in theories meant to describe massive scalars, the 4-dimensional scalar potential has, in fact, power-law behavior at large distances.

A measure of de Sitter entropy and eternal inflation

We study the effect of spontaneous breaking of Lorentz invariance on black hole thermodynamics. We consider a scenario where Lorentz symmetry breaking manifests itself by the difference of maximal velocities attainable by particles of different species in a preferred reference frame. The Lorentz breaking sector is represented by the ghost condensate. We find that the notions of black hole entropy and temperature loose their universal meaning. In particular, the standard derivation of the Hawking radiation yields that a black hole does emit thermal radiation in any given particle species, but with temperature depending on the maximal attainable velocity of this species. We demonstrate that this property implies violation of the second law of thermodynamics, and hence, allows construction of a perpetuum mobile of the 2nd kind. We discuss possible interpretation of these results.

Calcium antagonists in mania: A double-blind study of verapamil

Baseline and thrombin-stimulated free intracellular calcium concentrations in blood platelets were significantly higher in untreated depressed bipolar patients than in untreated unipolar depressed patients or controls. Platelet intracellular calcium ion concentrations in euthymic-treated bipolar patients were equivalent to control values, suggesting but not proving a state-dependent change in intracellular calcium ion dynamics in bipolar depression. Unipolar and some subsets of bipolar patients appear not to exhibit this change.

Effective field theory for hydrodynamics: thermodynamics, and the derivative expansion

We show that in any model of non-eternal inflation satisfying the null energy condition, the area of the de Sitter horizon increases by at least one Planck unit in each inflationary e-folding. This observation gives an operational meaning to the finiteness of the entropy S_dS of an inflationary de Sitter space eventually exiting into an asymptotically flat region: the asymptotic observer is never able to measure more than e^(S_dS) independent inflationary modes. This suggests a limitation on the amount of de Sitter space outside the horizon that can be consistently described at the semiclassical level, fitting well with other examples of the breakdown of locality in quantum gravity, such as in black hole evaporation. The bound does not hold in models of inflation that violate the null energy condition, such as ghost inflation. This strengthens the case for the thermodynamical interpretation of the bound as conventional black hole thermodynamics also fails in these models, strongly suggesting that these theories are incompatible with basic gravitational principles.

Intracellular calcium signalling in peripheral cells of patients with bipolar affective disorder.

Five of seven acutely manic patients improved significantly when taking verapamil but not placebo in a double-blind crossover study. This finding adds support to two other formal studies of verapamil, several case reports of verapamil in manic patients, and one small study of nifedipine suggesting that some calcium antagonists may have antimanic properties. Indirect evidence links this antimanic action to correction of a disturbance of intracellular calcium dynamics in affective disorders. However, the effectiveness of calcium antagonist drugs could also be related to some property other than interference with the action of calcium within brain neurons.