General Class Of Theories Research Articles

Searching for a fifth force with atomic and nuclear clocks

We consider the general class of theories in which there is a new ultralight scalar field that mediates an equivalence principle violating, long-range force. In such a framework, the Sun and Earth act as sources of the scalar field, leading to potentially observable location-dependent effects on atomic and nuclear spectra. We determine the sensitivity of current and next-generation atomic and nuclear clocks to these effects and compare the results against the existing laboratory and astrophysical constraints on equivalence principle violating fifth forces. We show that, in the future, the annual modulation in the frequencies of atomic and nuclear clocks in the laboratory caused by the eccentricity of Earth's orbit around the Sun may offer the most sensitive probe of this general class of equivalence principle violating theories. Even greater sensitivity can be obtained by placing a precision clock in an eccentric orbit around Earth and searching for time variation in the frequency, as is done in anomalous redshift experiments. In particular, an anomalous redshift experiment based on current clock technology would already have a sensitivity to fifth forces that couple primarily to electrons at about the same level as the existing limits. Our study provides well-defined sensitivity targets to aim for when designing future versions of these experiments.

Constraints on singularity resolution by nonlinear electrodynamics

One of the long standing problems is a quest for regular black hole solutions, in which a resolution of the spacetime singularity has been achieved by some physically reasonable, classical field, before one resorts to the quantum gravity. The prospect of using nonlinear electromagnetic fields for this goal has been limited by the Bronnikov's no-go theorems, focused on Lagrangians depending on the electromagnetic invariant $F_{ab}F^{ab}$ only. We extend Bronnikov's results by taking into account Lagrangians that depend on both electromagnetic invariants, $F_{ab}F^{ab}$ and $F_{ab}\,{\star F^{ab}}$, and prove that the tension between the Lagrangian's Maxwellian weak field limit and boundedness of the curvature invariants persists in more general class of theories.

Parametrized post-Newtonian formalism in higher-order Teleparallel Gravity

We study the parametrized post-Newtonian (PPN) limit of higher-derivative-torsion Modified Teleparallel Gravity. We start from the covariant formulation of modified Teleparallel Gravity by restoring the spin connection of the theory. Then, we perform the post-Newtonian expansion of the tetrad field around the Minkowski background and find the perturbed field equations. We compute the PPN metric for the higher-order Teleparallel Gravity theories which allows us to show that at the post-Newtonian limit this more general class of theories are fully conservative and indistinguishable from General Relativity . In this way, we extend the results that were already found for F(T) gravity in previous works. Furthermore, our calculations reveal the importance of considering a second post-Newtonian (2PN) order approximation or a parametrized post-Newtonian cosmology (PPNC) framework where additional perturbative modes coming from general modifications of Teleparallel Gravity could lead to new observable imprints.

Three dimensional modified gravities as holographic limits of Lancsoz-Lovelock theories

We define a “holographic limit” of Lancsoz-Lovelock theories at the Lagrangian level which gives three-dimensional modified gravity theories. We also show that this limit applies to more general classes of theories in higher dimensions provided that they admit the holographic c-theorem.

Viability of bouncing cosmology in energy-momentum-squared gravity

We analyze the early-time isotropic cosmology in the so-called energy-momentum-squared gravity (EMSG). In this theory, a $T_{\mu\nu}T^{\mu\nu}$ term is added to the Einstein-Hilbert action, which has been shown to replace the initial singularity by a regular bounce. We show that this is not the case, and the bouncing solution obtained does not describe our Universe since it belongs to a different solution branch. The solution branch that corresponds to our Universe, while nonsingular, is geodesically incomplete. We analyze the conditions for having viable regular-bouncing solutions in a general class of theories that modify gravity by adding higher order matter terms. Applying these conditions on generalizations of EMSG that add a $\left(T_{\mu\nu}T^{\mu\nu}\right)^{n}$ term to the action, we show that the case of $n=5/8$ is the only one that can give a viable bouncing solution, while the $n>5/8$ cases suffer from the same problem as EMSG, i.e. they give nonsingular, geodesically incomplete solutions. Furthermore, we show that the $1/2<n<5/8$ cases can provide a nonsingular initially de Sitter solution. Finally, the expanding, geodesically incomplete branch of EMSG or its generalizations can be combined with its contracting counterpart using junction conditions to provide a (weakly) singular bouncing solution. We outline the junction conditions needed for this extension and provide the extended solution explicitly for EMSG. In this sense, EMSG replaces the standard early-time singularity by a singular bounce instead of a regular one.

Hamiltonian and primary constraints of new general relativity

We derive the kinematic Hamiltonian for the so-called "new general relativity" class of teleparallel gravity theories, which is the most general class of theories whose Lagrangian is quadratic in the torsion tensor and does not contain parity violating terms. Our approach makes use of an explicit expression for the flat, in general, nonvanishing spin connection, which avoids the use of Lagrange multipliers, while keeping the theory invariant under local Lorentz transformations. We clarify the relation between the dynamics of the spin connection degrees of freedom and the tetrads. The terms constituting the Hamiltonian of the theory can be decomposed into irreducible parts under the rotation group. Using this, we demonstrate that there are nine different classes of theories, which are distinguished by the occurrence or non-occurrence of certain primary constraints. We visualize these different classes and show that the decomposition into irreducible parts allows us to write the Hamiltonian in a common form for all nine classes, which reproduces the specific Hamiltonians of more restricted classes in which particular primary constraints appear.

Extended cuscuton: formulation

Among single-field scalar-tensor theories, there is a special class called “cuscuton”, which is represented as some limiting case of k-essence in general relativity. This theory has a remarkable feature that the number of propagating degrees of freedom is only two in the unitary gauge in contrast to ordinary scalar-tensor theories with three degrees of freedom. We specify a general class of theories with the same property as the cuscuton in the context of the beyond Horndeski theory, which we dub as the extended cuscuton. We also study cosmological perturbations in the presence of matter in these extended cuscuton theories.

Holography with a Landau pole

Holography for UV-incomplete gauge theories is important but poorly understood. A paradigmatic example is d = 4, mathcal{N}=4 super Yang-Mills coupled to Nf quark flavors, which possesses a Landau pole at a UV scale ΛLP. The dual gravity solution exhibits a UV singularity at a finite proper distance along the holographic direction. Despite this, holographic renormalization can be fully implemented via analytic continuation to an AdS solution. The presence of a UV cut-off manifests itself in several interesting ways. At energies E ≪ ΛLP no pathologies appear, as expected from effective field theory. In contrast, at scales E ≲ ΛLP the gravitational potential becomes repulsive, and at temperatures T ≲ ΛLP the specific heat becomes negative. Although we focus on mathcal{N}=4 super Yang-Mills with flavor, our qualitative results apply to a much more general class of theories, since they only depend on the fact that the metric near the UV singularity is a hyper-scaling violating metric with exponent θ > d − 1.

Exact black hole solutions in shift symmetric scalar-tensor theories

We derive a variety of exact black hole solutions in a subclass of Horndeski's scalar-tensor theory possessing shift symmetry, $\phi\to\phi+c$, and reflection symmetry, $\phi\to-\phi$. The theory admits two arbitrary functions of $X:=-(\partial\phi)^2/2$, and our solutions are constructed without specifying the concrete form of the two functions, implying that black hole solutions in specific scalar-tensor theories found in the literature can be extended to a more general class of theories with shift symmetry. Our solutions include a black hole in the presence of an effective cosmological constant, the Nariai spacetime, the Lifshitz black hole, and other nontrivial solutions, all of which exhibit nonconstant scalar-field profile.

Stability, instability, canonical energy and charged black holes

We use the canonical energy method of Hollands and Wald to study the stability properties of asymptotically flat, stationary solutions to a very general class of theories, consisting of a set of coupled scalar fields and p-form gauge fields, minimally coupled to gravity. We find that, provided certain very weak assumptions are made on the coupling coefficients, the canonical energy method can be extended to this class of theories. In particular, we construct a quadratic form on initial data perturbations, with the properties that on all perturbations indicates stability, while on some perturbation indicates instability. Furthermore, we show that the conditions needed for the existence of allow for a stable definition of asymptotic flatness. Finally, we extend the proof of the Gubser–Mitra conjecture, given by Hollands and Wald, to this class of theories. In particular, this shows that for sufficiently extended, charged black brane solutions to such theories, thermodynamic instability implies dynamical instability.

Collapse of the state vector

Modifications of quantum mechanics are considered, in which the state vector of any system, large or small, undergoes a stochastic evolution. The general class of theories is described, in which the probability distribution of the state vector collapses to a sum of delta functions, one for each possible final state, with coefficients given by the Born rule.

The parameterized post-Newtonian limit of bimetric theories of gravity

We consider the post-Newtonian limit of a general class of bimetric theories of gravity, in which both metrics are dynamical. The established parameterized post-Newtonian approach is followed as closely as possible, although new potentials are found that do not exist within the standard framework. It is found that these theories can evade solar system tests of post-Newtonian gravity remarkably well. We show that perturbations about Minkowski space in these theories contain both massless and massive degrees of freedom, and that in general there are two different types of massive mode, each with a different mass parameter. If both of these masses are sufficiently large then the predictions of the most general class of theories we consider are indistinguishable from those of general relativity, up to post-Newtonian order in a weak-field, low-velocity expansion. In the limit that the massive modes become massless, we find that these general theories do not exhibit a van Dam–Veltman–Zakharov-like discontinuity in their γ parameter, although there are discontinuities in other post-Newtonian parameters as the massless limit is approached. This smooth behaviour in γ is due to the discontinuities from each of the two different massive modes cancelling each other out. Such cancellations cannot occur in special cases with only one massive mode, such as the Isham–Salam–Strathdee theory.

Kahler independence of the G 2-MSSM

The G2-MSSM is a model of particle physics coupled to moduli fields with interesting phenomenology both for colliders and astrophysical experiments. In this paper we consider a more general model - whose moduli Kahler potential is a completely arbitrary G2-holonomy Kahler potential and whose matter Kahler potential is also more general. We prove that the vacuum structure and spectrum of BSM particles is largely unchanged in this much more general class of theories. In particular, gaugino masses are still supressed relative to the gravitino mass and moduli masses. We also consider the effects of higher order corrections to the matter Kahler potential and find a connection between the nature of the LSP and flavor effects.

Hamiltonian analysis of non-chiral Plebanski theory and its generalizations

We consider the non-chiral, full Lorentz group-based Plebanski formulation of general relativity in its version that utilizes the Lagrange multiplier field Φ with ‘internal’ indices. The Hamiltonian analysis of this version of the theory turns out to be simpler than in the previously considered in the literature version with Φ carrying spacetime indices. We then extend the Hamiltonian analysis to a more general class of theories whose action contains scalar invariants constructed from Φ. Such theories have recently been considered in the context of unification of gravity with other forces. We show that these more general theories have six additional propagating degrees of freedom as compared to general relativity. This has not been appreciated in the literature treating them as being not much different from GR.

The attractor mechanism in Gauss-Bonnet gravity

We study extremal black hole solutions of D = 5 Gauss-Bonnet gravity coupled to a system of gauge and scalar fields. As in Einstein gravity, we find that the values of the scalar fields on the horizon must extremize a certain effective potential that depends on the black hole charges. If the matrix of second derivatives of the effective potential at this extremum has positive eigenvalues, we give evidence, based on a near horizon perturbative expansion, that the attractor mechanism continues to hold in this general class of theories. We numerically construct solutions to a particular simple single scalar field model that display the attractor mechanism over a wide range of asymptotic values for the scalar field. We also numerically construct non-extremal solutions and show that the attractor mechanism fails to hold away from extremality.

Sh-Lie Algebras Induced by Gauge Transformations

Traditionally symmetries of field theories are encoded via Lie group actions, or more generally, as Lie algebra actions. A significant generalization is required when “gauge parameters” act in a field dependent way. Such symmetries appear in several field theories, most notably in a “Poisson induced” class due to Schaller and Strobl [SS94] and to Ikeda [Ike94], and employed by Cattaneo and Felder [CF99] to implement Kontsevich's deformation quantization [Kon97]. Consideration of “particles of spin > 2” led Berends, Burgers and van Dam [Bur85,BBvD84,BBvD85] to study “field dependent parameters” in a setting permitting an analysis in terms of smooth functions. Having recognized the resulting structure as that of an sh-Lie algebra (L ∞-algebra), we have now formulated such structures entirely algebraically and applied it to a more general class of theories with field dependent symmetries.

Neutrinos vis-à-vis the six-dimensional standard model

We examine the origin of neutrino masses and oscillations in the context of the six-dimensional standard model. The space-time symmetries of this model explain proton stability and forbid Majorana neutrino masses. The consistency of the six-dimensional theory requires three right-handed neutrinos, and therefore Dirac neutrino masses are allowed. We employ the idea that the smallness of these masses is due to the propagation of the right-handed neutrinos in a seventh, warped dimension. We argue that this class of theories is free of gravitational anomalies. Although an exponential hierarchy arises between the neutrino masses and the electroweak scale, we find that the mass hierarchy among the three neutrino masses is limited by higher-dimension operators. All current neutrino oscillation data, except for the LSND result, are naturally accommodated by our model. In the case of the solar neutrinos, the model leads to the large mixing angle, MSW solution. The mechanism employed, involving three right-handed neutrinos coupled to a scalar in an extra dimension, may explain the features of the neutrino spectrum in a more general class of theories that forbid Majorana masses.

Trial and intertrial durations in Pavlovian conditioning: Issues of learning and performance.

Four experiments assessed the effects of trial (T) and intertrial (I) durations on magazine approach behavior in rats. In Experiments 1 and 2, different groups of animals were conditioned with various combinations of I and T durations. The rate of acquisition, in terms of the number of trials required to reach various acquisition criteria, generally was faster in groups trained with large I:T ratios. There also were differences in rate of acquisition and terminal response rates between groups trained with identical I:T ratios but with different absolute I and T durations. Differences evident at the end of conditioning persisted during a common test with various combinations of I and T durations. Experiments 3 and 4 provided a more specific test of the predictions of 2 general classes of theories and found results that were consistent with those theories that characterize group differences as indicative of differences in learning, rather than in performance.

Forecasting Volatility

This monograph puts together results from several lines of research that I have pursued over a period of years, on the general topic of volatility forecasting for option pricing applications. It is not meant to be a complete survey of the extensive literature on the subject, nor is it a definitive set of prescriptions on how to get the best volatility prediction. While at the outset, I had hoped to find the Best Method to obtain a volatility input for use in pricing options, as the reader will quickly determine, it seems that I have been more successful in uncovering the flaws and difficulties in the methods that are widely used than I have been in determining a single optimal strategy myself.Given that I am not able to reveal the optimal technique for volatility forecasting, the main objective of this work is to share with the reader a variety of observations and thoughts about the general problem of volatility prediction and the ways in which it is customarily approached, that I have arrived at after investigating the issues from a number of different angles. Along with describing the theory and the implementation of the standard techniques, I try to point out several areas in which common procedures and ways of thinking about volatility forecasting turn out to involve assumptions or ideas that do not stand up under close examination.Two major themes emerge, both having to do with the connection, or perhaps more correctly, the possibility of a disconnection between theory and practice in dealing with volatility prediction and its role in option valuation. There are two general classes of theories involved.First, there is the statistical theory used in fitting models of price behavior in financial markets. Section I brings out the distinction between physical processes and economic processes in terms of the stability of their internal structure and the prospects for making accurate predictions about them. We argue that routinely applying the classical estimation methodology appropriate for physical processes to the economic process of price behavior in a financial market can lead one to build models that are too complex and to hold inappropriately high expectations about the potential accuracy of volatility forecasts from those models.The second area of conflict between theory and practice arises in the use of implied volatility from option market prices, because there is a significant disparity between the trading strategies arbitrage–based derivatives valuation models assume investors follow and what options market participants actually do. In theory, the implied volatility is the options market's well–informed prediction of the underlying asset's future volatility. Academic researchers typically treat it as such. In practice, however, the arbitrage trading that is supposed to force option prices into conformance with the market's volatility expectations may not be done very actively at all. In many markets it is very hard to execute, and it also will normally be less profitable and will entail more risk than a simple market making strategy that reacts to the market, maximizes order flow and earns profits from the bid–ask spread. The latter, however, may do little to enforce theoretical pricing against the noisy forces of supply and demand in the market. Thus the implied volatility derived from market option prices need not be a good proxy for the market's best forecast of future volatility of the underlying asset.In both cases, I try to point out important implications for volatility estimation that tend to be overlooked by those following traditional lines of thought. It is my hope that in the end, the reader will acquire a broader perspective to see more clearly what is involved in obtaining the volatility input to a derivatives valuation model, and what questions need to be asked of any proposed technique.

Condensate-smearing effect in inelastic scattering on Bose liquids

It is argued that the response function of a liquid of interacting particles containing a condensate fraction has a nonvanishing width at the quasielastic peak, unlike the otherwise expected \ensuremath{\delta}-function peak for a noninteracting system. The mechanism involved is the scattering of the particles in the system, implying the effect is a many-body one. For systems with regular interactions between the particles, the width vanishes in the asymptotic limit of momentum transfer q\ensuremath{\rightarrow}\ensuremath{\infty}, leading to a \ensuremath{\delta}-function peak in the response, while for singular interactions such as a hard core, a nonzero width remains. The methods used in the argument can be applied to derive a general class of theories describing final-state interactions. The Gersch-Rodriguez broadening formula is derived using these methods.