3D black holes on a 2-brane in 4D Minkowski space

We investigate three-dimensional black hole solutions in the realm of pure and new massive gravity in 2+1 dimensions induced on a 2-brane embedded in a flat four-dimensional spacetime. There is no cosmological constant neither on the brane nor on the four-dimensional bulk. Only gravitational fields are turned on and we indeed find vacuum solutions as black holes in 2+1 dimensions even in the absence of any cosmological solution. There is a crossover scale that controls how far the three- or four-dimensional gravity manifests on the 2-brane. Our solutions also indicate that local BTZ and SdS₃ solutions can flow to local four-dimensional Schwarzschild-like black holes, as one probes from small to large distances, which is clearly a higher dimensional manifestation on the 2-brane. This is similar to the DGP scenario where the effects of extra dimensions for large probed distances along the brane manifest.     

All spin-2 cubic vertices with two derivatives

In this paper we provide a complete list of spin-2 cubic interaction vertices with two derivatives. We work in (anti) de Sitter space with dimension d?4$d?4$ and arbitrary value of cosmological constante and use simple metric formalism without any auxiliary or Stueckelberg fields. We separately consider cases with one, two and three different spin-2 fields entering the vertex where each field may be massive, massless or partially massless one. The connection of our results with massive (bi)gravity theories is also briefly discussed.     

Cosmic Acceleration in a Model of Interacting Massive Gravitons Dark Energy

We propose an alternative understanding of gravity, resulting from the extension of N. Wu’s gauge theory of gravity with massive gravitons, which are minimally coupled to massless gravitons. Based on this, we derive the equations of state for massive gravitons. We study the dynamics of these massive gravitons in a flat, homogeneous and isotropic Friedmann-Robertson-Walker (FRW) universe. We calculate the critical points of the massive graviton dark energy interacting with background perfect fluid. These calculations may have crucial implications for the massive gravitons and dark energy theories. They could, therefore, have important repercussions for current cosmological problems.     

Spin-3 topologically massive gravity

In this Letter, we study the spin-3 topologically massive gravity (TMG), paying special attention to its properties at the chiral point. We propose an action describing the higher spin fields coupled to TMG. We discuss the traceless spin-3 fluctuations around the AdS₃ vacuum and find that there is an extra local massive mode, besides the left-moving and right-moving boundary massless modes. At the chiral point, such extra mode becomes massless and degenerates with the left-moving mode. We show that at the chiral point the only degrees of freedom in the theory are the boundary right-moving graviton and spin-3 field. We conjecture that spin-3 chiral gravity with generalized Brown-Henneaux boundary condition is holographically dual to 2D chiral CFT with classical W₃ algebra and central charge cR=3l/G.     

Gauge theories of weak and strong gravity

A review of some recent papers on gauge theories of weak and strong gravity is presented. For weak gravity, SL(2, C) gauge theory along with tetrad formulation is described which yields massless spin-2 gauge fields (quanta gravitons). Next a unified SL(2n,C) model is discussed along with Higgs fields. Its internal symmetry is SU(n). The free field solutions after symmetry breaking yield massless spin-1 (photons) and spin-2 (gravitons) gauge fields and also massive spin-1 and spin-2 bosons. The massive spin-2 gauge fields are responsible for short range superstrong gravity. Higgs-fermion interaction can lead to baryon and lepton number non-conservation. The relationship of strong gravity with other forces is also briefly considered.     

Decoupling and reduction in Chern–Simons modified gravity

We show that for four-dimensional spacetimes with a non-null hypersurface orthogonal Killing vector and for a Chern–Simons (CS) background (non-dynamical) scalar field, which is constant along the Killing vector, the source-free equations of CS modified gravity decouple into their Einstein and Cotton constituents. Thus, the model supports only general relativity solutions. We also show that, when the cosmological constant vanishes and the gradient of the CS scalar field is parallel to the non-null hypersurface orthogonal Killing vector of constant length, CS modified gravity reduces to topologically massive gravity in three dimensions. Meanwhile, with the cosmological constant such a reduction requires an appropriate source term for CS modified gravity.     

Localizing gravity on a stringlike defect in six dimensions

We present a metric solution in six dimensions, where gravity is localized on a four-dimensional singular stringlike defect. The corrections to four-dimensional gravity from the bulk continuum modes are suppressed by O(1/r(3)). No tuning of the bulk cosmological constant to the brane tension is required in order to cancel the four-dimensional cosmological constant.     

Our world as an intersection of walls and a string

A solution of Einstein equations is obtained for our four-dimensional world as an intersection of a wall and a string-like defect in seven-dimensional spacetime with a negative cosmological constant. A matter energy–momentum tensor localized on the wall and on the string is needed. A single massless graviton is found and is localized around the intersection. The leading correction to the gravitational Newton potential from massive spin 2 graviton is found to be almost identical to that of a wall in five dimensions, contrary to the case of a string in six dimensions. The generalization to the intersection of a string and n orthogonally intersecting walls is also obtained and a similar result is found for the gravitational potential.     

Emergence of a 4D world from causal quantum gravity

Causal Dynamical Triangulations in four dimensions provide a background-independent definition of the sum over geometries in nonperturbative quantum gravity, with a positive cosmological constant. We present evidence that a macroscopic four-dimensional world emerges from this theory dynamically.     

Nonlinear properties of vielbein massive gravity

We propose a nonlinear extension of the Fierz–Pauli mass for the graviton through a functional of the vielbein and an external Minkowski background. The functional generalizes the notion of the measure, since it reduces to a cosmological constant if the external background is formally sent to zero. Such a term and the explicit external background emerge dynamically from a bi-gravity theory, having both a massless and a massive graviton in its spectrum, in a specific limit in which the massless mode decouples, while the massive one couples universally to matter. We investigate the massive theory using the Stückelberg method and providing a ’t Hooft–Feynman gauge fixing, in which the tensor, vector and scalar Stückelberg fields decouple. We show that this model has the softest possible ultraviolet behavior that can be expected from any generic (Lorentz-invariant) theory of massive gravity, namely that it becomes strong only at the scale Λ₃=(m_g ²M_P)^1/3.     

Spontaneous Compactification of Extra Dimensions in Eleven-Dimensional Quantum Gravity

The reduction of the eleven-dimensional pure gravity theory to a field theory to a field theory in the four-dimensional Minkowski space-time by means of the spontaneous compactification of the extra dimensions is investigated. The contribution of the quantum fluctuations of the eleven-dimensional second rank symmetric tensor field to the curvatures of the space-time and the compactified space of the extra dimensions are calculated in the one-loop approximations. It is shown that there exist the values of the cosmological constant such that the resulting four-dimensional theory is self-consistent.     

Mass spectrum of the M4×SD solution in Euler invariant type higher derivative gravity

The mass spectrum is computed in Euler invariant type higher derivative gravity theory in the case that the space-time is dimensionally reduced to the four-dimensional Minkowski space × D-dimensional sphere. It is shown at the linearized level that after the compactification there appear massless gravitons, massive spin-two particles, massless vectors and one massive scalar mode. All the vectors are massless and the masses of massive spin-two particles are proportional to the S^D eigenvalues of the laplacian. Classical stability is shown to depend only on three parameters.     

Massive spin 3/2 theories in 3 dimensions

Topologically massive spin 3/2 theory in 3 spacetime dimensions, which is gauge invariant and involves second derivatives, is shown to be equivalent to the normal gauge variant first derivative massive Rarita-Schwinger model. The equivalence persists in arbitrary background geometries. In the particular anti-de Sitter space whose cosmological constant is minus the mass squared, the model effectively behaves like the massless theory in flat space: its degree of freedom disappears.     

Geodesic Motions in 2 + 1-Dimensional Charged Black Holes

We study the geodesic motions of a test particle around 2 + 1-dimensional charged black holes. We obtain a class of exact geodesic motions for the massless test particle when the ratio of its energy and angular momentum is given by the square root of the cosmological constant. The other geodesic motions for both massless and massive test particles are analyzed using the numerical method.     

Gravitational divergences of the electromagnetic interactions of massive vector particles

In a search for the explanation of the finite quantum gravity corrections to anomalous moments we examined a spontaneous broken O(3) model with Yang-Mills particles and Higgs scalars coupled to gravitons. We found several new cancellations which prove that the coupling of all these particles together does not produce new counterterms apart from these which are known to exist in the subsystems and the cosmological term. The finiteness of the anomalous magnetic moment of a massive spin-1 particle is necessary for this to be valid. The finiteness of the anomalous quadrupole moment is a consequence of a known cancellation in the Einstein-Yang-Mills system. We also checked infrared finiteness and showed how to treat logarithmically divergent massless integrals in dimensional regularization.     

Renormalizable 4D Quantum Gravity as a Perturbed Theory from CFT

We study the renormalizable quantum gravity formulated as a perturbed theory from conformal field theory (CFT) on the basis of conformal gravity in four dimensions. The conformal mode in the metric field is managed non-perturbatively without introducing its own coupling constant so that conformal symmetry becomes exact quantum mechanically as a part of diffeomorphism invariance. The traceless tensor mode is handled in the perturbation with a dimensionless coupling constant indicating asymptotic freedom, which measures a degree of deviation from CFT. Higher order renormalization is carried out using dimensional regularization, in which the Wess-Zumino integrability condition is applied to reduce indefiniteness existing in higher-derivative actions. The effective action of quantum gravity improved by renormalization group is obtained. We then make clear that conformal anomalies are indispensable quantities to preserve diffeomorphism invariance. Anomalous scaling dimensions of the cosmological constant and the Planck mass are calculated. The effective cosmological constant is obtained in the large number limit of matter fields.     

Comprehensive solution to the cosmological constant,zero-point energy,and quantum gravity problems

We present a solution to the cosmological constant, the zero-point energy, and the quantum gravity problems within a single comprehensive framework. We show that in quantum theories of gravity in which the zero-point energy density of the gravitational field is well-defined, the cosmological constant and zero-point energy problems solve each other by mutual cancellation between the cosmological constant and the matter and gravitational field zero-point energy densities. Because of this cancellation, regulation of the matter field zero-point energy density is not needed, and thus does not cause any trace anomaly to arise. We exhibit our results in two theories of gravity that are well-defined quantum-mechanically. Both of these theories are locally conformal invariant, quantum Einstein gravity in two dimensions and Weyl-tensor-based quantum conformal gravity in four dimensions (a fourth-order derivative quantum theory of the type that Bender and Mannheim have recently shown to be ghost-free and unitary). Central to our approach is the requirement that any and all departures of the geometry from Minkowski are to be brought about by quantum mechanics alone. Consequently, there have to be no fundamental classical fields, and all mass scales have to be generated by dynamical condensates. In such a situation the trace of the matter field energy-momentum tensor is zero, a constraint that obliges its cosmological constant and zero-point contributions to cancel each other identically, no matter how large they might be. In our approach quantization of the gravitational field is caused by its coupling to quantized matter fields, with the gravitational field not needing any independent quantization of its own. With there being no a priori classical curvature, one does not have to make it compatible with quantization.     

A search for sterile neutrinos with the latest cosmological observations

We report the result of a search for sterile neutrinos with the latest cosmological observations. Both cases of massless and massive sterile neutrinos are considered in the \(\Lambda \)CDM cosmology. The cosmological observations used in this work include the Planck 2015 temperature and polarization data, the baryon acoustic oscillation data, the Hubble constant direct measurement data, the Planck Sunyaev–Zeldovich cluster counts data, the Planck lensing data, and the cosmic shear data. We find that the current observational data give a hint of the existence of massless sterile neutrino (as dark radiation) at the 1.44\(\sigma \) level, and the consideration of an extra massless sterile neutrino can indeed relieve the tension between observations and improve the cosmological fit. For the case of massive sterile neutrino, the observations give a rather tight upper limit on the mass, which implies that actually a massless sterile neutrino is more favored. Our result is consistent with the recent result of neutrino oscillation experiment done by the Daya Bay and MINOS collaborations, as well as the recent result of cosmic ray experiment done by the IceCube collaboration.     

A Modified Gravity Theory: Null Aether

General quantum gravity arguments predict that Lorentz symmetry might not hold exactly in nature. This has motivated much interest in Lorentz breaking gravity theories recently. Among such models are vector-tensor theories with preferred direction established at every point of spacetime by a fixed-norm vector field. The dynamical vector field defined in this way is referred to as the "aether". In this paper, we put forward the idea of a null aether field and introduce, for the first time, the Null Aether Theory(NAT) — a vector-tensor theory. We first study the Newtonian limit of this theory and then construct exact spherically symmetric black hole solutions in the theory in four dimensions, which contain Vaidya-type non-static solutions and static Schwarzschild-(A)dS type solutions, Reissner-Nordstr?m-(A)dS type solutions and solutions of conformal gravity as special cases. Afterwards, we study the cosmological solutions in NAT:We find some exact solutions with perfect fluid distribution for spatially flat FLRW metric and null aether propagating along the x direction. We observe that there are solutions in which the universe has big-bang singularity and null field diminishes asymptotically. We also study exact gravitational wave solutions — AdS-plane waves and pp-waves — in this theory in any dimension D ≥ 3. Assuming the Kerr-Schild-Kundt class of metrics for such solutions, we show that the full field equations of the theory are reduced to two, in general coupled, differential equations when the background metric assumes the maximally symmetric form. The main conclusion of these computations is that the spin-0 aether field acquires a "mass" determined by the cosmological constant of the background spacetime and the Lagrange multiplier given in the theory.     

Dimensional reduction of Weyl,Majorana and Majorana-Weyl spinors

We discuss the dimensional reduction for Weyl, Majorana, or Majorana-Weyl spinors coupled to pure d-dimensional (d ? 4) gravity. The only case where a realistic four-dimensional low-energy spectrum for the fermions may be obtained, is for a Majorana-Weyl spinor in d = 2 mod 8 dimensions. Chiral massless fermions are not excluded in this case. The minimal number of dimensions for the construction of a realistic theory out of pure gravity is d = 18.