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.     

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.     

Critical gravity in four dimensions

We study four-dimensional gravity theories that are rendered renormalizable by the inclusion of curvature-squared terms to the usual Einstein action with a cosmological constant. By choosing the parameters appropriately, the massive scalar mode can be eliminated and the massive spin-2 mode can become massless. This "critical" theory may be viewed as a four-dimensional analogue of chiral topologically massive gravity, or of critical "new massive gravity" with a cosmological constant, in three dimensions. We find that the on-shell energy for the remaining massless gravitons vanishes. There are also logarithmic spin-2 modes, which have positive energy. The mass and entropy of standard Schwarzschild-type black holes vanish. The critical theory might provide a consistent toy model for quantum gravity in four dimensions.     

Einstein gravity on the codimension 2 brane?

We look at general brane worlds in six-dimensional Einstein-Gauss-Bonnet gravity. We find the general matching conditions for the brane world, which remarkably give precisely the four-dimensional Einstein equations for the brane, even when the extra dimensions are noncompact and have infinite volume. Relaxing regularity of the curvature in the vicinity of the brane, or having a thick brane, gives rise to an additional term containing information on the brane's embedding in the bulk. We comment on the relevance of these results to a possible solution of the cosmological constant problem.     

Randall-Sundrum model for self-tuning the cosmological constant

The vanishing cosmological constant in the four-dimensional space-time is obtained in a 5D Randall-Sundrum model with a brane (B1) located at y = 0. The matter fields can be located at the brane. For settling any vacuum energy generated at the brane to zero, we need a three-index antisymmetric tensor field A(MNP) with a specific form for the Lagrangian. For the self-tuning mechanism, the bulk cosmological constant should be negative.     

Massive gravitons trapped inside a hypermonopole

We propose a regular classical field theory realisation of the Dvali–Gabadadze–Porrati mechanism by considering our universe to be the four-dimensional core of a seven-dimensional 't Hooft–Polyakov hypermonopole. We show the existence of metastable gravitons trapped in the core. Their mass spectrum is discrete, positive definite, and computed for various values of the field coupling constants: the resulting Newton gravity law is seven-dimensional at small and large distances but can be made four-dimensional on intermediate length scales. There is no need of a cosmological constant in the bulk, the spacetime is asymptotically flat and of infinite volume in the extra-dimensions. Confinement is achieved through the local positive curvature of the extra-dimensions induced by the monopole-forming fields and for natural values of the coupling constants of order unity.     

Essay: Deconstructing the Cosmological Constant

Deconstruction provides a novel way of dealing with the notoriously difficult ultraviolet problems of four-dimensional gravity. This approach also naturally leads to a new perspective on the holographic principle, tying it to the fundamental requirements of unitarity and diffeomorphism invariance, as well as to a new viewpoint on the cosmological constant problem. The numerical smallness of the cosmological constant is implied by a unique combination of holography and supersymmetry, opening a new window into the fundamental physics of the vacuum.     

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.     

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.     

Deformations of the constraint algebra of Ashtekar's Hamiltonian formulation of general relativity

We show that the constraint algebra of Ashtekar's Hamiltonian formulation of general relativity can be nontrivially deformed by allowing the cosmological constant to become an arbitrary function of the (Weyl) curvature. Our result implies that there is not one but infinitely many (parametrized by an arbitrary function) four-dimensional generally covariant local gravity theories propagating 2 degrees of freedom.     

On gravity localization under Lorentz violation in warped scenario

Recently Rizzo studied the Lorentz Invariance Violation (LIV) in a brane scenario with one extra dimension where he found a non-zero mass for the four-dimensional graviton. This leads to the conclusion that five-dimensional models with LIV are not phenomenologically viable. In this work we re-examine the issue of Lorentz Invariance Violation in the context of higher-dimensional theories. We show that a six-dimensional geometry describing a string-like defect with a bulk-dependent cosmological constant can yield a massless 4D graviton, if we allow the cosmological constant variation along the bulk, and thus can provides a phenomenologically viable solution for the gauge hierarchy problem.     

Kaluza-Klein solutions with non-compact internal spaces

Einstein's equations with a cosmological constant in arbitrary dimensions admit solutions with unobservable internal space and flat four-dimensional space. Internal space is non-compact, has finite volume and admits a compact group of symmetries. No fine tuning of parameters is needed to obtain a vanishing four-dimensional cosmological constant.     

On the cosmological constant problem and brane-world geometry

The cosmological constant problem is examined within the context of the covariant brane-world gravity, based on Nash’s embedding theorem for Riemannian geometries. We show that the vacuum structure of the brane-world is more complex than General Relativity’s because it involves extrinsic elements, in specific, the extrinsic curvature. In other words, the shape (or local curvature) of an object becomes a relative concept, instead of the “absolute shape” of General Relativity. We point out that the immediate consequence is that the cosmological constant and the energy density of the vacuum quantum fluctuations have different physical meanings: while the vacuum energy density remains confined to the four-dimensional brane-world, the cosmological constant is a property of the bulk’s gravitational field that leads to the conclusion that these quantities cannot be compared, as it is usually done in General Relativity. Instead, the vacuum energy density contributes to the extrinsic curvature, which in turn generates Nash’s perturbation of the gravitational field. On the other hand, the cosmological constant problem ceases to be in the brane-world geometry, reappearing only in the limit where the extrinsic curvature vanishes.     

Dark energy and gravity

I review the problem of dark energy focussing on cosmological constant as the candidate and discuss what it tells us regarding the nature of gravity. Section 1 briefly overviews the currently popular “concordance cosmology” and summarizes the evidence for dark energy. It also provides the observational and theoretical arguments in favour of the cosmological constant as a candidate and emphasizes why no other approach really solves the conceptual problems usually attributed to cosmological constant. Section 2 describes some of the approaches to understand the nature of the cosmological constant and attempts to extract certain key ingredients which must be present in any viable solution. In the conventional approach, the equations of motion for matter fields are invariant under the shift of the matter Lagrangian by a constant while gravity breaks this symmetry. I argue that until the gravity is made to respect this symmetry, one cannot obtain a satisfactory solution to the cosmological constant problem. Hence cosmological constant problem essentially has to do with our understanding of the nature of gravity. Section 3 discusses such an alternative perspective on gravity in which the gravitational interaction—described in terms of a metric on a smooth spacetime—is an emergent, long wavelength phenomenon, and can be described in terms of an effective theory using an action associated with normalized vectors in the spacetime. This action is explicitly invariant under the shift of the matter energy momentum tensor T _ab → T _ab + Λ _gab and any bulk cosmological constant can be gauged away. Extremizing this action leads to an equation determining the background geometry which gives Einstein’s theory at the lowest order with Lanczos–Lovelock type corrections. In this approach, the observed value of the cosmological constant has to arise from the energy fluctuations of degrees of freedom located in the boundary of a spacetime region.     

The solution of the cosmological constant problem from the inhomogeneous equation of state — a hint from modified gravity?

The cosmological constant problem is studied in a two component cosmological model. The universe contains a cosmological constant of an arbitrary size and sign and an additional component with an inhomogeneous equation of state. It is shown that, in a proper parameter regime, the expansion of the universe with a large absolute value of the cosmological constant may asymptotically tend to de Sitter space corresponding to a small effective positive cosmological constant. It is argued that such a behavior can be regarded as a solution of the cosmological constant problem in this model. The mechanism behind the relaxation of the cosmological constant is discussed. A connection with modified gravity theories is discussed and an example of a possible realization of the cosmological constant relaxation in f(R) modified gravity is described.     

Brane universes with Gauss-Bonnet-induced-gravity

The DGP brane world model allows us to get the observed late time acceleration via modified gravity, without the need for a “dark energy” field. This can then be generalised by the inclusion of high energy terms, in the form of a Gauss-Bonnet bulk. This is the basis of the Gauss-Bonnet-Induced-Gravity (GBIG) model explored here with both early and late time modifications to the cosmological evolution. Recently the simplest GBIG models (Minkowski bulk and no brane tension) have been analysed. Two of the three possible branches in these models start with a finite density “Big-Bang” and with late time acceleration. Here we present a comprehensive analysis of more general models where we include a bulk cosmological constant and brane tension. We show that by including these factors it is possible to have late time phantom behaviour.     

Cosmological constant: a lesson from Bose-Einstein condensates

The cosmological constant is one of the most pressing problems in modern physics. We address this issue from an emergent gravity standpoint, by using an analogue gravity model. Indeed, the dynamics of the emergent metric in a Bose-Einstein condensate can be described by a Poisson-like equation with a vacuum source term reminiscent of a cosmological constant. The direct computation of this term shows that in emergent gravity scenarios this constant may be naturally much smaller than the naive ground-state energy of the emergent effective field theory. This suggests that a proper computation of the cosmological constant would require a detailed understanding about how Einstein equations emerge from the full microscopic quantum theory. In this light, the cosmological constant appears as a decisive test bench for any quantum or emergent gravity scenario.     

Warped compactification to de Sitter space

We explore in detail the prospects of obtaining a four-dimensional de Sitter universe in classical supergravity models with warped and time-independent extra dimensions, presenting explicit cosmological solutions of the (4+n)$(4+n)$-dimensional Einstein equations with and without a bulk cosmological constant term. For the first time in the literature we show that there may exist a large class of warped supergravity models with a noncompact extra dimension which lead to a finite 4D Newton constant as well as a massless 4D graviton localized on an inflating four-dimensional FLRW universe. This result helps establish that the ‘no-go’ theorem forbidding acceleration in ‘standard’ compactification of string/M-theory on physically compact spaces should not apply to a general class of warped supergravity models that allows at least one noncompact direction. We present solutions for which the size of the radial dimension takes a constant value in the large volume limit, providing an explicit example of spontaneous compactification.     

Surface tension and the cosmological constant

One of the few predictions from quantum gravity models is Sorkin's observation that the cosmological constant has quantum fluctuations originating in the fundamental discreteness of spacetime at the Planck scale. Here we present a compelling analogy between the cosmological constant of the Universe and the surface tension of fluid membranes. The discreteness of spacetime on the Planck scale translates into the discrete molecular structure of a fluid membrane. We propose an analog quantum gravity experiment which realizes Sorkin's idea in the laboratory. We also notice that the analogy sheds light on the cosmological constant problem, suggesting a mechanism for dynamically generating a vanishingly small cosmological constant. We emphasize the generality of Sorkin's idea and suggest that similar effects occur generically in quantum gravity models.