Massive gravity as a quantum gauge theory

We present a new point of view on the quantization of the massive gravitational field, namely we use exclusively the quantum framework of the second quantization. The Hilbert space of the many-gravitons system is a Fock space F⁺ (H_graviton) where the one-particle Hilbert space H_graviton carries the direct sum of two unitary irreducible representations of the Poincaré group corresponding to two particles of mass m > 0 and spins 2 and 0, respectively. This Hilbert space is canonically isomorphic to a space of the type Ker(Q)/Im(Q) where Q is a gauge charge defined in an extension of the Hilbert space H_graviton generated by the gravitational field h and some ghosts fields u, (which are vector Fermi fields) and v (which is a vector Bose field).Then we study the self interaction of massive gravity in the causal framework. We obtain a solution which goes smoothly to the zero-mass solution of linear quantum gravity up to a term depending on the bosonic ghost field. This solution depends on two real constants as it should be; these constants are related to the gravitational constant and the cosmological constant. In the second order of the perturbation theory we do not need a Higgs field, in sharp contrast to Yang-Mills theory.     

Cosmology of Brane-Induced Gravity Models

We review various aspects of the cosmology of brane-induced gravity models. After recalling some properties of these models, we give the equations governing the cosmological dynamics in a Z ₂ symmetric case. We then discuss properties of two particular solutions of interest, a self-accelerating solution that has been proposed to provide an alternative explanation to the observed late time acceleration of the universe, and a self-flattening solution. The latter is also discussed in relation with the van Dam–Veltman–Zakharov discontinuity.     

Essay: Supersymmetry, the Cosmological Constant, and a Theory of Quantum Gravity in Our Universe

There are many theories of quantum gravity, depending on asymptotic boundary conditions, and the amount of supersymmetry. The cosmological constant is one of the fundamental parameters that characterizes different theories. If it is positive, supersymmetry must be broken. A heuristic calculation shows that a cosmological constant of the observed size predicts superpartners in the TeV range. This mechanism for SUSY breaking also puts important constraints on low energy particle physics models.     

Tomographic representation of minisuperspace quantum cosmology and noether symmetries

The probability representation, in which cosmological quantum states are described by a standard positive probability distribution, is constructed for minisuperspace models selected by Noether symmetries. In such a case, the tomographic probability distribution provides the classical evolution for the models and can be considered an approach to select “observable” universes. Some specific examples, derived from Extended Theories of Gravity, are worked out. We discuss also how to connect tomograms, symmetries and cosmological parameters.     

RG flows of Quantum Einstein Gravity in the linear-geometric approximation

We construct a novel Wetterich-type functional renormalization group equation for gravity which encodes the gravitational degrees of freedom in terms of gauge-invariant fluctuation fields. Applying a linear-geometric approximation the structure of the new flow equation is considerably simpler than the standard Quantum Einstein Gravity construction since only transverse-traceless and trace part of the metric fluctuations propagate in loops. The geometric flow reproduces the phase-diagram of the Einstein–Hilbert truncation including the non-Gaussian fixed point essential for Asymptotic Safety. Extending the analysis to the polynomial f(R)$f\left(R\right)$-approximation establishes that this fixed point comes with similar properties as the one found in metric Quantum Einstein Gravity; in particular it possesses three UV-relevant directions and is stable with respect to deformations of the regulator functions by endomorphisms.     

Letter: The Quantum Theory of the Quadratic Gravity Action for Heterotic Strings

The wave function for the quadratic gravity theory derived from the heterotic string effective action is deduced to first order in by solving a perturbed second-order Wheeler-DeWitt equation, assuming that the potential is slowly varying with respect to . Predictions for inflation based on the solutionto the second-order Wheeler-DeWitt equation continue to hold for this higher-order theory. It is shown how formal expressions for the average paths in minisuperspace {a(t), (t)} for this theory can be used to determine the shifts from the classical solutions a _cl (t) and _cl (t), which occur only at third order in the expansion of the functional integrals representing the expectation values.     

A Dodecalogue of Basic Didactics from Applications of Abstract Differential Geometry to Quantum Gravity

We summarize the twelve most important in our view novel concepts that have arisen, based on results that have been obtained, from various applications of Abstract Differential Geometry (ADG) to Quantum Gravity (QG). The present document may be used as a concise, yet informal, discursive and peripatetic conceptual guide-cum-terminological glossary to the voluminous technical research literature on the subject. In a bonus section at the end, we dwell on the significance of introducing new conceptual terminology in future QG research by means of ‘poetic language’.     

Gravity,Quantum Fields and Quantum Information: Problems with Classical Channel and Stochastic Theories

In recent years an increasing number of papers have attempted to mimic or supplant quantum field theory in discussions of issues related to gravity by the tools and through the perspective of quantum information theory, often in the context of alternative quantum theories. In this article, we point out three common problems in such treatments. First, we show that the notion of interactions mediated by an information channel is not, in general, equivalent to the treatment of interactions by quantum field theory. When used to describe gravity, this notion may lead to inconsistencies with general relativity. Second, we point out that in general one cannot replace a quantum field by a classical stochastic field, or mock up the effects of quantum fluctuations by that of classical stochastic sources (noises), because in so doing important quantum features such as coherence and entanglement will be left out. Third, we explain how under specific conditions semi-classical and stochastic theories indeed can be formulated from their quantum origins and play a role at certain regimes of interest.     

Relationships of exponents in multifractal detrended fluctuation analysis and conventional multifractal analysis

Multifractal detrended fluctuation analysis (MF-DFA) is a relatively new method of multifractal analysis. It is extended from detrended fluctuation analysis (DFA), which was developed for detecting the long-range correlation and the fractal properties in stationary and non-stationary time series. Although MF-DFA has become a widely used method, some relationships among the exponents established in the original paper seem to be incorrect under the general situation. In this paper, we theoretically and experimentally demonstrate the invalidity of the expression τ(q)=qh(q)-1 stipulating the relationship between the multifractal exponent τ(q) and the generalized Hurst exponent h(q). As a replacement, a general relationship is established on the basis of the universal multifractal formalism for the stationary series as τ(q)=qh(q)-qH'-1, where H' is the nonconservation parameter in the universal multifractal formalism. The singular spectra, α and f(α), are also derived according to this new relationship.     

Null Fluid Collapse in Rastall Theory of Gravity

A Vaidya spacetime is considered for gravitational collapse of a type II fluid in the context of the Rastall theory of gravity. For a linear equation of state for the fluid profiles, the conditions under which the dynamical evolution of the collapse can give rise to the formation of a naked singularity are examined. It is shown that depending on the model parameters, strong curvature, naked singularities would arise as exact solutions to the Rastall's field equations. The allowed values of these parameters satisfy certain conditions on the physical reliability, nakedness, and the curvature strength of the singularity. It turns out that Rastall gravity, in comparison to general relativity, provides a wider class of physically reasonable spacetimes that admit both locally and globally naked singularities.     

Quantum gravitational contributions to the beta function of quantum electrodynamics

We show in a diagrammatic and regularization independent analysis that the quadratic contribution to the beta function which has been conjectured to render quantum electrodynamics asymptotically free near the Planck scale has its origin in a surface term. Such surface term is intrinsically arbitrarily valued and it is argued to vanish in a consistent treatment of the model.     

Higher-derivative Quantum Cosmology

The quantum cosmology of a higher-derivative gravity theory arising from the heterotic string effective action is reviewed. A new type of Wheeler–DeWitt equation is obtained when the dilaton is coupled to the quadratic curvature terms. Techniques for solving the Wheeler–DeWitt equation with appropriate boundary conditions shall be described, and implications for semiclassical theories of inflationary cosmology will be outlined.     

Quantum Gravity and Phenomenological Philosophy

The central thesis of this paper is that contemporary theoretical physics is grounded in philosophical presuppositions that make it difficult to effectively address the problems of subject-object interaction and discontinuity inherent to quantum gravity. The core objectivist assumption implicit in relativity theory and quantum mechanics is uncovered and we see that, in string theory, this assumption leads into contradiction. To address this challenge, a new philosophical foundation is proposed based on the phenomenology of Maurice Merleau-Ponty and Martin Heidegger. Then, through the application of qualitative topology and hypernumbers, phenomenological ideas about space, time, and dimension are brought into focus so as to provide specific solutions to the problems of force-field generation and unification. The phenomenological string theory that results speaks to the inconclusiveness of conventional string theory and resolves its core contradiction. This article is based on my 2008 book, The Self-Evolving Cosmos, appearing in the Series on Knots and Everything of World Scientific Publishing Company.     

Deterrents to a Theory of Quantum Gravity

As shown previously, quantum mechanics directly violates the weak equivalence principle in general, and thus indirectly violates the strong equivalence principle in all dimensions. The present paper shows that quantum mechanics also directly violates the strong equivalence principle unless it is arbitrarily abetted in hindsight. Vital domains are shown to exist in which quantum gravity would be non-applicable. There are classical subtleties in which the strong equivalence principle appears to be violated, but is not. Neutron free fall interference experiments in a gravitational field are examined, as is Galileo's falling body assertion and the misconception it leads to.     

Deconstruction of Gravity

We review how one can construct a deconstructed gravity by a transverse latticification of 5D General Relativity. The obtained theory is a multigravity theory, with link fields that are explicitly constructed out of the metric. We also discuss the spectrum of the theory at the level of the linearized theory.     

Nonquantum Gravity

One of the great challenges for 21st century physics is to quantize gravity and generate a theory that will unify gravity with the other three fundamental forces of nature. This paper takes the (heretical) point of view that gravity may be an inherently classical, i.e., nonquantum, phenomenon and investigates the experimental consequences of such a conjecture. At present there is no experimental evidence of the quantum nature of gravity and the likelihood of definitive tests in the future is not at all certain. If gravity is, indeed, a nonquantum phenomenon, then it is suggested that evidence will most likely appear at mesoscopic scales.     

Exact classical and quantum solutions for a covariant oscillator near the black hole horizon in Stueckelberg-Horwitz-Piron theory

We found exact solutions for canonical classical and quantum dynamics for general relativity in Horwitz general covariance theory. These solutions can be obtained by solving the generalized geodesic equation and Schrödinger-Stueckelberg-Horwitz-Piron (SHP) wave equation for a simple harmonic oscillator in the background of a two dimensional dilaton black hole spacetime metric. We proved the existence of an orthonormal basis of eigenfunctions for generalized wave equation. This basis functions form an orthogonal and normalized (orthonormal) basis for an appropriate Hilbert space. The energy spectrum has a mixed spectrum with one conserved momentum p according to a quantum number n. To find the ground state energy we used a variational method with appropriate boundary conditions. A set of mode decomposed wave functions and calculated for the Stueckelberg-Schrodinger equation on a general five dimensional blackhole spacetime in Hamilton gauge.     

Testing Gravity on Astrophysical Scales

We summarize a series of observational tests of the law of gravity on large astrophysical scales. These tests account for testing both the Poisson equation (inverse square law) using weak lensing and the Einstein equivalence principle through the test of the constancy of the constants of Nature. We emphasize the need to test general relativity on cosmological scales in light of the cosmological constant problem and of recent observational claims concerning the variation of fine structure constant.