Exact solution to the “auxiliary extra-dimension” model of massive gravity

The “auxiliary extra-dimension” model was proposed in order to provide a geometrical interpretation to modifications of general relativity, in particular to non-linear massive gravity. In this context, the theory was shown to be ghost free to third order in perturbations, in the decoupling limit. In this work, we exactly solve the equation of motion in the extra dimension, to obtain a purely 4-dimensional theory. Using this solution, it is shown that the ghost appears at the fourth order and beyond. We explore potential modifications to address the ghost issue and find that their consistent implementation requires going beyond the present framework.     

A cosmological study in massive gravity theory

A detailed study of the various cosmological aspects in massive gravity theory has been presented in the present work. For the homogeneous and isotropic FLRW model, the deceleration parameter has been evaluated, and, it has been examined whether there is any transition from deceleration to acceleration in recent past, or not. With the proper choice of the free parameters, it has been shown that the massive gravity theory is equivalent to Einstein gravity with a modified Newtonian gravitational constant together with a negative cosmological constant. Also, in this context, it has been examined whether the emergent scenario is possible, or not, in massive gravity theory. Finally, we have done a cosmographic analysis in massive gravity theory.     

Nonuniqueness of a massive spin-2 theory

The nonunique nature of massive spin-2 fields is explicitly shown in this paper through the construction of all possible field equations, using Dirac formalism for spin-1/2 fields. Out of these four possible theories, we point out two that do not show up scalar representations.     

Nonlinear massive spin-2 field generated by higher derivative gravity

We present a systematic exposition of the Lagrangian field theory for the massive spin-2 field generated in higher-derivative gravity upon reduction to a second-order theory by means of the appropriate Legendre transformation. It has been noticed by various authors that this nonlinear field overcomes the well-known inconsistency of the theory for a linear massive spin-2 field interacting with Einstein’s gravity. Starting from a Lagrangian quadratically depending on the Ricci tensor of the metric, we explore the two possible second-order pictures usually called “(Helmholtz-)Jordan frame” and “Einstein frame.” In spite of their mathematical equivalence, the two frames have different structural properties: in Einstein frame, the spin-2 field is minimally coupled to gravity, while in the other frame it is necessarily coupled to the curvature, without a separate kinetic term. We prove that the theory admits a unique and linearly stable ground state solution, and that the equations of motion are consistent, showing that these results can be obtained independently in either frame (each frame therefore provides a self-contained theory). The full equations of motion and the (variational) energy-momentum tensor for the spin-2 field in Einstein frame are given, and a simple but non-trivial exact solution to these equations is found. The comparison of the energy-momentum tensors for the spin-2 field in the two frames suggests that the Einstein frame is physically more acceptable. We point out that the energy-momentum tensor generated by the Lagrangian of the linearized theory is unrelated to the corresponding tensor of the full theory. It is then argued that the ghost-like nature of the nonlinear spin-2 field, found long ago in the linear approximation, may not be so harmful to classical stability issues, as has been expected.     

Tree level gravity—scalar matter interactions in analogy with Fermi theory of weak interactions using only a massive vector field

In this paper we work in perturbative quantum gravity coupled to scalar matter at tree level and we introduce a new effective model in analogy with the Fermi theory of weak interaction and in relation with a previous work where we have studied only the gravity and its self-interaction. This is an extension of the I.T.B. model (Intermediate-Tensor-Boson) for gravity also to gravitationally interacting scalar matter. We show that in a particular gauge the infinite series of interactions containing n gravitons and two scalars could be rewritten in terms of only two Lagrangians containing a massive field, the graviton and, obviously, the scalar field. Using the S-matrix we obtain that the low energy limit of the amplitude reproduces the local Lagrangian for the scalar coupled to gravity.     

Geometric phase and entanglement for massive spin-1 particles

The cyclic evolution of a spin-1 system is studied under the spin-spin interaction between the transverse and the longitudinal states. The eigenstates of the systems are obtained by generalized and extended Jordan-Wigner transformation with an angle described the path of particle propagation. According to the wave functions of time evaluation for many-particle systems, the entanglement effects and geometric phase are observed. The systems with more than two particles, in contrast to the two particle system, evolve in time with two parameters.     

Au-analyte adducts resulting from single massive gold cluster impacts

Utilizing Au₄₀₀⁴⁺ primary ions produces large molecular ion yields, some in excess of unity, with minimal surface damage. A surprising observation is the occurrence of Au-analyte adducts as part of the ejecta desorbed by a single Au-cluster impact. We present data that demonstrate that Au and Au-adducts as secondary ions (e.g., AuCN⁻, AuGly⁻ and AuCsI⁻) are the result of the interaction between a single primary ion, Au₄₀₀⁴⁺ and the target atoms.     

Kaluza-Klein reduction and consistency of the massive spin-3/2 theory with external interaction

A gauge-invariant Rarita-Schwinger theory of a massive spin-3/2 particle interacting with external electromagnetic, gravitational and dilaton fields is obtained by Kaluza-Klein reduction of a massless Rarita-Schwinger theory with graviational interaction. Fermionic gauge invariance serves to determine the background equations of motion. The couplings with external fields obtained by the Kaluza-Klein reduction are shown to lead to the absence of the classical Velo-Zwanziger problem and on quantizing using Dirac's procedure, the field anticommutators are found to be positive definite.     

Quantum discontinuity for massive spin-3/2 with a Λ term

We show that the recently demonstrated absence of the van Dam–Veltman–Zakharov discontinuity for massive spin-3/2 with a Λ term is an artifact of the tree approximation, and that the discontinuity reappears at one loop. As a numerical check on the calculation, we rederive the vanishing of the one-loop beta function for D=11 supergravity on AdS₄×S⁷ level-by-level in the Kaluza–Klein tower.     

Tensor formulation of spin-1 and spin-2 fields

Spin projection operators which constitute a resolution of the identity in the space of second rank tensor wave functions are constructed. These projectors are then used to establish Lagrangian quantum field theories for free massive particles with spin-1 (two equivalent formulations) and spin-2.     

Exploring the entanglement of free spin-(1/2), spin-1 and spin-2 fields

In this study, we explore the entanglement of free spin-(1/2), spin-1, and spin-2 fields. We start with an example involving Majorana fields in 1+1 and 2+1 dimensions. Subsequently, we perform the Bogoliubov transformation and express the vacuum state with a particle pair state in the configuration space, which is used to calculate the entropy. This clearly demonstrates that the entanglement entropy originates from the particles across the boundary.Finally, we generalize this method to free spin-1 and spin-2 fields. These higher free massless spin fields have wellknown complications owing to gauge redundancy. We deal with the redundancy by gauge-fixing in the light-cone gauge. We show that this gauge provides a natural tensor product structure in the Hilbert space, while surrendering explicit Lorentz invariance. We also use the Bogoliubov transformation to calculate the entropy. The area law emerges naturally by this method.     

Accelerating cosmology in modified gravity with scalar field

The modified gravity with 1/R term (R being the scalar curvature) and the Einstein-Hilbert term is studied by incorporating the phantom scalar field. A number of cosmological solutions are derived in the presence of the phantom field in the perfect fluid background. It is shown: the current inflation obtained in the modified gravity is affected by the existence of the phantom field.     

Behavior of a spin-1/2 massive charged particle in Schwarzschild immersed in an electromagnetic universe

The Dirac equation is considered in a spacetime that represents a Schwarzschild metric coupled to a uniform external electromagnetic field. Due to the presence of electromagnetic field from the surroundings, the interaction with the spin-1/2 massive charged particle is considered. The equations of the spin-1/2 massive charged particle are separated into radial and angular equations by adopting the Newman–Penrose formalism. The angular equations obtained are similar to the Schwarzschild geometry. For the radial equations we manage to obtain the one dimensional Schrödinger-type wave equations with effective potentials. Finally, we study the behavior of the potentials by plotting them as a function of radial distance and expose the effect of the external parameter, charge and the frequency of the particle on them.     

4D gravity on a BPS brane in 5D AdS-Minkowski space

We calculate small correction terms to gravitational potential near an asymmetric BPS brane embedded in a 5D AdS-Minkowski space in the context of supergravity. The normalizable wave functions of gravity fluctuations around the brane describe only massive modes. We compute such wave functions analytically in the thin wall limit. We estimate the correction to gravitational potential for small and long distances, and show that there is an intermediate range of distances in which we can identify 4D gravity on the brane below a crossover scale. The 4D gravity is metastable and for distances much larger than the crossover scale the 5D gravity is recovered.     

Quark–hadron phase transition in massive gravity

We study the quark–hadron phase transition in the framework of massive gravity. We show that the modification of the FRW cosmological equations leads to the quark–hadron phase transition in the early massive Universe. Using numerical analysis, we consider that a phase transition based on the chiral symmetry breaking after the electroweak transition, occurred at approximately 10 μs after the Big Bang to convert a plasma of free quarks and gluons into hadrons.     

Cartan's contortion as a system of spin-2 and spin-0 fields

In several previous papers the author proposed to consider Cartan's contortion as a gauge field of Lorentz-group mediated by a massless spin-2 fields twin. In this article it is shown that these fields may be accompanied by a further pair of massive or massless spin-0 fields. Unfortunately, the study of the interaction of contortion with a Proca field shows that there is no reasonable macroscopic source generating the contortion. This defect is essential; the contortion mediated by standard fields can hardly exist in nature.     

Simplified parent-child formalism for spin-0 and spin-1/2 parents

We develop further the parent-child relation, that is the calculation of the cross-sections and correlations of observed particles, typically charged leptons, arising from the decay of long-lived primarily produced “parent” particles. In the high-momentum regime, when the momenta of parent and child are closely aligned, we show how, for spinless parents, the relation can be simplified by the introduction of “fragmentation” functions derived from the invariant inclusive decay distributions. We extend the formalism to the case of spin-1/2 parents and advocate its application to charm production and decay at the quark level.     

Effects of massive neutrinos on the structure formation of the universe

Massive neutrinos affect the structure formation of the universe, characteristically the harmonic pattern of the cosmic microwave background (CMB) radiation and the clustering property of galaxies. Precision observations of the CMB and the power spectrum of galaxy clustering thus lead to the limit on the neutrino mass on the 1 eV scale. I address the principles and the typical results that can be derived from cosmological arguments.     

The Casimir interaction of a massive vector field between concentric spherical bodies

The Casimir interaction energy due to the vacuum fluctuations of a massive vector field between two perfectly conducting concentric spherical bodies is computed. The TE contribution to the Casimir interaction energy is a direct generalization of the massless case but the TM contribution is much more complicated. Each TM mode is a linear combination of a transverse mode which is the generalization of a TM mode in the massless case and a longitudinal mode that does not appear in the massless case. In contrast to the case of two parallel perfectly conducting plates, there are no TM discrete modes that vanish identically in the perfectly conducting spherical bodies. Numerical simulations show that the Casimir interaction force between the two bodies is always attractive.